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polyhedra.m
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polyhedra.m
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function [Polyhedron]=polyhedra(geom)
%LOAD PREDEFINED POLYHEDRA
Polyhedron.node=[];
Polyhedron.edge=[];
Polyhedron.face={[]};
switch geom
case {'tetrahedron'}
Polyhedron.node=[0,0,sqrt(2/3)-1/(2*sqrt(6));-(1/(2*sqrt(3))),-(1/2),-(1/(2*sqrt(6)));-(1/(2*sqrt(3))),1/2,-(1/(2*sqrt(6)));1/sqrt(3),0,-(1/(2*sqrt(6)))];
Polyhedron.edge=[1,2;1,3;1,4;2,3;2,4;3,4];
Polyhedron.face={[2, 3, 4];[3, 2, 1];[4, 1, 2];[1, 4, 3]};
case {'cube'}
%Polyhedron.node=([0 0 0;1 0 0;1*cos(1*pi/180) 1*sin(1*pi/180) 0;(1+1*cos(1*pi/180)) 1*sin(1*pi/180) 0;0 0 1;1 0 1;1*cos(1*pi/180) 1*sin(1*pi/180) 1;(1+1*cos(1*pi/180)) 1*sin(1*pi/180) 1;]);%%%([0 0 0;1 0 0;0 1 0;1 1 0;0 0 1;1 0 1;0 1 1; 1 1 1]);%%([0 0 0;1 0 0;1*cos(1*pi/180) 1*sin(1*pi/180) 0;(1+1*cos(1*pi/180)) 1*sin(1*pi/180) 0;0 0 1;1 0 1;1*cos(1*pi/180) 1*sin(1*pi/180) 1;(1+1*cos(1*pi/180)) 1*sin(1*pi/180) 1;]);
Polyhedron.node=([0 0 0;1 0 0;0 1 0;1 1 0;0 0 1;1 0 1;0 1 1; 1 1 1]);%%([0 0 0;1 0 0;1/2 sqrt(3)/2 0;3/2 sqrt(3)/2 0;0 0 1;1 0 1;1/2 sqrt(3)/2 1; 3/2 sqrt(3)/2 1]);
Polyhedron.edge=[1 2;1 3;3 4;2 4;1 5;2 6;3 7;4 8;5 6;6 8;5 7;7 8];
Polyhedron.face={[3 4 2 1];[1 2 6 5];[2 4 8 6];[5 7 3 1];[7 8 4 3];[5 6 8 7]};
case {'Triagular cube'}
Polyhedron.node=([0 0 0;1 0 0;1*cos(120*pi/180) 1*sin(120*pi/180) 0;(1+1*cos(120*pi/180)) 1*sin(120*pi/180) 0;...
0 0 1;1 0 1;1*cos(120*pi/180) 1*sin(120*pi/180) 1;(1+1*cos(120*pi/180)) 1*sin(120*pi/180) 1;]);
Polyhedron.edge=[1 2;1 3;3 4;2 4;1 5;2 6;3 7;4 8;5 6;6 8;5 7;7 8];
Polyhedron.face={[3 4 2 1];[1 2 6 5];[2 4 8 6];[5 7 3 1];[7 8 4 3];[5 6 8 7]};
case {'octahedron'}
Polyhedron.node=[-(1/sqrt(2)),0,0;0,1/sqrt(2),0;0,0,-(1/sqrt(2));0,0,1/sqrt(2);0,-(1/sqrt(2)),0;1/sqrt(2),0,0];
Polyhedron.edge=[1,2;1,3;1,4;1,5;2,3;2,4;2,6;3,5;3,6;4,5;4,6;5,6];
Polyhedron.face={[4,5,6];[4,6,2];[4,2,1];[4,1,5];[5,1,3];[5,3,6];[3,1,2];[6,3,2]};
case {'dodecahedron'}
Polyhedron.node=[-1.376381920471174,0,0.2628655560595668;1.376381920471174,0,-0.2628655560595668;-0.4253254041760200,-1.309016994374947,0.2628655560595668;-0.4253254041760200,1.309016994374947,0.2628655560595668;1.113516364411607,-0.8090169943749474,0.2628655560595668;1.113516364411607,0.8090169943749474,0.2628655560595668;-0.2628655560595668,-0.8090169943749474,1.113516364411607;-0.2628655560595668,0.8090169943749474,1.113516364411607;-0.6881909602355868,-0.5000000000000000,-1.113516364411607;-0.6881909602355868,0.5000000000000000,-1.113516364411607;0.6881909602355868,-0.5000000000000000,1.113516364411607;0.6881909602355868,0.5000000000000000,1.113516364411607;0.8506508083520399,0,-1.113516364411607;-1.113516364411607,-0.8090169943749474,-0.2628655560595668;-1.113516364411607,0.8090169943749474,-0.2628655560595668;-0.8506508083520399,0,1.113516364411607;0.2628655560595668,-0.8090169943749474,-1.113516364411607;0.2628655560595668,0.8090169943749474,-1.113516364411607;0.4253254041760200,-1.309016994374947,-0.2628655560595668;0.4253254041760200,1.309016994374947,-0.2628655560595668];
Polyhedron.edge=[1,14;1,15;1,16;2,5;2,6;2,13;3,7;3,14;3,19;4,8;4,15;4,20;5,11;5,19;6,12;6,20;7,11;7,16;8,12;8,16;9,10;9,14;9,17;10,15;10,18;11,12;13,17;13,18;17,19;18,20];
Polyhedron.face={[15,10,9,14,1];[2,6,12,11,5];[5,11,7,3,19];[11,12,8,16,7];[12,6,20,4,8];[6,2,13,18,20];[2,5,19,17,13];[4,20,18,10,15];[18,13,17,9,10];[17,19,3,14,9];[3,7,16,1,14];[16,8,4,15,1]};
case {'icosahedron'}
Polyhedron.node=[0,0,-(5/sqrt(50-10*sqrt(5)));0,0,5/sqrt(50-10*sqrt(5));-sqrt((2/(5-sqrt(5)))),0,-(1/sqrt(10-2*sqrt(5)));sqrt(2/(5-sqrt(5))),0,1/sqrt(10-2*sqrt(5));(1+sqrt(5))/(2*sqrt(10-2*sqrt(5))),-(1/2),-(1/sqrt(10-2*sqrt(5)));(1+sqrt(5))/(2*sqrt(10-2*sqrt(5))),1/2,-(1/sqrt(10-2*sqrt(5)));-((1+sqrt(5))/(2*sqrt(10-2*sqrt(5)))),-(1/2),1/sqrt(10-2*sqrt(5));-((1+sqrt(5))/(2*sqrt(10-2*sqrt(5)))),1/2,1/sqrt(10-2*sqrt(5));-((-1+sqrt(5))/(2*sqrt(10-2*sqrt(5)))),-(1/2)*sqrt((5+sqrt(5))/(5-sqrt(5))),-(1/sqrt(10-2*sqrt(5)));-((-1+sqrt(5))/(2*sqrt(10-2*sqrt(5)))),1/2*sqrt((5+sqrt(5))/(5-sqrt(5))),-(1/sqrt(10-2*sqrt(5)));(-1+sqrt(5))/(2*sqrt(10-2*sqrt(5))),-(1/2)*sqrt((5+sqrt(5))/(5-sqrt(5))),1/sqrt(10-2*sqrt(5));(-1+sqrt(5))/(2*sqrt(10-2*sqrt(5))),1/2*sqrt((5+sqrt(5))/(5-sqrt(5))),1/sqrt(10-2*sqrt(5))];
Polyhedron.edge=[1,3;1,5;1,6;1,9;1,10;2,4;2,7;2,8;2,11;2,12;3,7;3,8;3,9;3,10;4,5;4,6;4,11;4,12;5,6;5,9;5,11;6,10;6,12;7,8;7,9;7,11;8,10;8,12;9,11;10,12];
Polyhedron.face={[2,12,8];[2,8,7];[2,7,11];[2,11,4];[2,4,12];[5,9,1];[6,5,1];[10,6,1];[3,10,1];[9,3,1];[12,10,8];[8,3,7];[7,9,11];[11,5,4];[4,6,12];[5,11,9];[6,4,5];[10,12,6];[3,8,10];[9,7,3]};
case {'truncated tetrahedron'}
Polyhedron.node=[0,-1,-(sqrt(3/2)/2);0,1,-(sqrt(3/2)/2);-(1/sqrt(3)),-1,1/(2*sqrt(6));-(1/sqrt(3)),1,1/(2*sqrt(6));-(1/(2*sqrt(3))),-(1/2),5/(2*sqrt(6));-(1/(2*sqrt(3))),1/2,5/(2*sqrt(6));1/sqrt(3),0,5/(2*sqrt(6));2/sqrt(3),0,1/(2*sqrt(6));-(sqrt(3)/2),-(1/2),-(sqrt(3/2)/2);-(sqrt(3)/2),1/2,-(sqrt(3/2)/2);sqrt(3)/2,-(1/2),-(sqrt(3/2)/2);sqrt(3)/2,1/2,-(sqrt(3/2)/2)];
Polyhedron.edge=[1,3;1,9;1,11;2,4;2,10;2,12;3,5;3,9;4,6;4,10;5,6;5,7;6,7;7,8;8,11;8,12;9,10;11,12];
Polyhedron.face={[11,12,8];[3,9,1];[2,10,4];[6,5,7];[11,8,7,5,3,1];[2,4,6,7,8,12];[9,3,5,6,4,10];[2,12,11,1,9,10]};
case {'cuboctahedron'}
Polyhedron.node=[-1, 0, 0;-(1/2), -(1/2), -(1/sqrt(2));-(1/2), -(1/2), 1/sqrt(2);-(1/2), 1/2, -(1/sqrt(2));-(1/2), 1/2, 1/sqrt(2);0, -1, 0;0, 1, 0;1/2, -(1/2), -(1/sqrt(2));1/2, -(1/2), 1/sqrt(2);1/2, 1/2, -(1/sqrt(2));1/2, 1/2, 1/sqrt(2);1, 0, 0];
Polyhedron.edge=[1, 2;1, 3;1, 4;1, 5;2, 4;2, 6;2, 8;3, 5;3, 6;3, 9;4, 7;4, 10;5, 7;5, 11;6, 8;6, 9;7, 10;7, 11;8, 10;8, 12;9, 11;9,12;10, 12;11, 12];
Polyhedron.face={[4, 10, 8, 2];[3, 9, 11, 5];[9, 6, 8, 12];[3, 1, 2, 6];[5, 7, 4,1];[11, 12, 10, 7];[12, 11, 9];[3, 5, 1];[6, 9, 3];[5, 11, 7];[8, 10, 12];[1, 4, 2];[2, 8, 6];[7, 10, 4]};
case {'truncated octahedron'}
Polyhedron.node=([-(3/2),-(1/2),0;-(3/2),1/2,0;-1,-1,-(1/sqrt(2));-1,-1,1/sqrt(2);-1,1,-(1/sqrt(2));-1,1,1/sqrt(2);-(1/2),-(3/2),0;-(1/2),-(1/2),-sqrt(2);-(1/2),-(1/2),sqrt(2);-(1/2),1/2,-sqrt(2);-(1/2),1/2,sqrt(2);-(1/2),3/2,0;1/2,-(3/2),0;1/2,-(1/2),-sqrt(2);1/2,-(1/2),sqrt(2);1/2,1/2,-sqrt(2);1/2,1/2,sqrt(2);1/2,3/2,0;1,-1,-(1/sqrt(2));1,-1,1/sqrt(2);1,1,-(1/sqrt(2));1,1,1/sqrt(2);3/2,-(1/2),0;3/2,1/2,0]);
Polyhedron.edge=[1, 2;1, 3;1, 4;2, 5;2, 6;3, 7;3, 8;4, 7;4,9;5, 10;5, 12;6, 11;6, 12;7, 13;8, 10;8, 14;9, 11;9, 15;10, 16;11, 17;12, 18;13, 19;13, 20;14, 16;14, 19;15, 17;15, 20;16, 21;17, 22;18, 21;18, 22;19, 23;20, 23;21, 24;22, 24;23, 24];
Polyhedron.face={[17, 11, 9, 15];[14, 8, 10, 16];[22, 24, 21, 18];[12, 5, 2, 6];[13, 19, 23, 20];[4, 1, 3, 7];[19, 13, 7, 3, 8, 14];[15, 9, 4, 7, 13, 20];[16, 10, 5, 12, 18, 21];[22, 18, 12, 6, 11, 17];[20, 23, 24, 22, 17, 15];[14, 16, 21, 24, 23, 19];[9, 11, 6, 2, 1, 4 ];[3, 1, 2, 5, 10, 8]};
case {'truncated cube'}
Polyhedron.node=[-(1/2),1/2+1/sqrt(2),1/2+1/sqrt(2);-(1/2),1/2+1/sqrt(2),1/(2-2*sqrt(2));-(1/2),1/(2-2*sqrt(2)),1/2+1/sqrt(2);-(1/2),1/(2-2*sqrt(2)),1/(2-2*sqrt(2));1/2,1/2+1/sqrt(2),1/2+1/sqrt(2);1/2,1/2+1/sqrt(2),1/(2-2*sqrt(2));1/2,1/(2-2*sqrt(2)),1/2+1/sqrt(2);1/2,1/(2-2*sqrt(2)),1/(2-2*sqrt(2));1/2+1/sqrt(2),-(1/2),1/2+1/sqrt(2);1/2+1/sqrt(2),-(1/2),1/(2-2*sqrt(2));1/2+1/sqrt(2),1/2,1/2+1/sqrt(2);1/2+1/sqrt(2),1/2,1/(2-2*sqrt(2));1/2+1/sqrt(2),1/2+1/sqrt(2),-(1/2);1/2+1/sqrt(2),1/2+1/sqrt(2),1/2;1/2+1/sqrt(2),1/(2-2*sqrt(2)),-(1/2);1/2+1/sqrt(2),1/(2-2*sqrt(2)),1/2;1/(2-2*sqrt(2)),-(1/2),1/2+1/sqrt(2);1/(2-2*sqrt(2)),-(1/2),1/(2-2*sqrt(2));1/(2-2*sqrt(2)),1/2,1/2+1/sqrt(2);1/(2-2*sqrt(2)),1/2,1/(2-2*sqrt(2));1/(2-2*sqrt(2)),1/2+1/sqrt(2),-(1/2);1/(2-2*sqrt(2)),1/2+1/sqrt(2),1/2;1/(2-2*sqrt(2)),1/(2-2*sqrt(2)),-(1/2);1/(2-2*sqrt(2)),1/(2-2*sqrt(2)),1/2];
Polyhedron.edge=[1,5;1,19;1,22;2,6;2,20;2,21;3,7;3,17;3,24;4,8;4,18;4,23;5,11;5,14;6,12;6,13;7,9;7,16;8,10;8,15;9,11;9,16;10,12;10,15;11,14;12,13;13,14;15,16;17,19;17,24;18,20;18,23;19,22;20,21;21,22;23,24];
Polyhedron.face={[6,12,10,8,4,18,20,2];[1,19,17,3,7,9,11,5];[3,24,23,4,8,15,16,7];[5,14,13,6,2,21,22,1];[9,16,15,10,12,13,14,11];[19,22,21,20,18,23,24,17];[16,9,7];[5,11,14];[3,17,24];[22,19,1];[8,10,15];[13,12,6];[23,18,4];[2,20,21]};
case {'rhombicuboctahedron'}
Polyhedron.node=[-(1/2), -(1/2), -(1/2) - 1/sqrt(2);-(1/2), -(1/2), 1/2 + 1/sqrt(2);-(1/2), 1/2, -(1/2) - 1/sqrt(2);-(1/2), 1/2, 1/2 + 1/sqrt(2);-(1/2), -(1/2) - 1/sqrt(2), -(1/2);-(1/2), -(1/2) - 1/sqrt(2), 1/2;-(1/2), 1/2 + 1/sqrt(2), -(1/2);-(1/2), 1/2 + 1/sqrt(2), 1/2;1/2, -(1/2), -(1/2) - 1/sqrt(2);1/2, -(1/2), 1/2 + 1/sqrt(2);1/2, 1/2, -(1/2) - 1/sqrt(2);1/2, 1/2, 1/2 + 1/sqrt(2);1/2, -(1/2) - 1/sqrt(2), -(1/2);1/2, -(1/2) - 1/sqrt(2), 1/2;1/2, 1/2 + 1/sqrt(2), -(1/2);1/2, 1/2 + 1/sqrt(2), 1/2;-(1/2) - 1/sqrt(2), -(1/2), -(1/2);-(1/2) - 1/sqrt(2), -(1/2), 1/2;-(1/2) - 1/sqrt(2), 1/2, -(1/2);-(1/2) - 1/sqrt(2), 1/2, 1/2;1/2 + 1/sqrt(2), -(1/2), -(1/2);1/2 + 1/sqrt(2), -(1/2), 1/2;1/2 + 1/sqrt(2), 1/2, -(1/2);1/2 + 1/sqrt(2), 1/2, 1/2];
Polyhedron.edge=[1, 3;1, 5;1, 9;1, 17;2, 4;2, 6;2, 10;2, 18;3,7;3, 11;3, 19;4, 8;4, 12;4, 20;5, 6;5, 13;5,17;6, 14;6, 18;7, 8;7, 15;7, 19;8, 16;8, 20;9, 11;9, 13;9, 21;10, 12;10, 14;10, 22;11, 15;11, 23;12, 16;12, 24;13, 14;13, 21;14, 22;15, 16;15, 23;16, 24;17, 18;17, 19;18, 20;19, 20;21, 22;21, 23;22, 24;23, 24];
Polyhedron.face={[3, 11, 9, 1];[2, 10, 12, 4];[24, 22, 21, 23];[19, 17, 18, 20];[5, 13, 14, 6];[8, 16, 15, 7];[13, 21, 22, 14];[16, 24, 23, 15];[6,18, 17, 5];[7, 19, 20, 8];[6, 14, 10, 2];[4, 12, 16, 8];[22, 24, 12, 10];[2, 4, 20, 18];[1, 9, 13, 5];[7, 15, 11, 3];[9, 11, 23, 21];[17, 19, 3, 1];[22, 10, 14];[16, 12, 24];[6, 2, 18];[20, 4, 8];[13, 9, 21];[23, 11, 15];[17, 1, 5];[7, 3, 19]};
case {'snub cube'}
Polyhedron.node=[-1.142613508925962,-0.3377539738137524,-0.6212264105565853;-1.142613508925962,0.3377539738137524,0.6212264105565853;-1.142613508925962,-0.6212264105565853,0.3377539738137524;-1.142613508925962,0.6212264105565853,-0.3377539738137524;1.142613508925962,-0.3377539738137524,0.6212264105565853;1.142613508925962,0.3377539738137524,-0.6212264105565853;1.142613508925962,-0.6212264105565853,-0.3377539738137524;1.142613508925962,0.6212264105565853,0.3377539738137524;-0.3377539738137524,-1.142613508925962,0.6212264105565853;-0.3377539738137524,1.142613508925962,-0.6212264105565853;-0.3377539738137524,-0.6212264105565853,-1.142613508925962;-0.3377539738137524,0.6212264105565853,1.142613508925962;0.3377539738137524,-1.142613508925962,-0.6212264105565853;0.3377539738137524,1.142613508925962,0.6212264105565853;0.3377539738137524,-0.6212264105565853,1.142613508925962;0.3377539738137524,0.6212264105565853,-1.142613508925962;-0.6212264105565853,-1.142613508925962,-0.3377539738137524;-0.6212264105565853,1.142613508925962,0.3377539738137524;-0.6212264105565853,-0.3377539738137524,1.142613508925962;-0.6212264105565853,0.3377539738137524,-1.142613508925962;0.6212264105565853,-1.142613508925962,0.3377539738137524;0.6212264105565853,1.142613508925962,-0.3377539738137524;0.6212264105565853,-0.3377539738137524,-1.142613508925962;0.6212264105565853,0.3377539738137524,1.142613508925962];
Polyhedron.edge=[1,3;1,4;1,11;1,17;1,20;2,3;2,4;2,12;2,18;2,19;3,9;3,17;3,19;4,10;4,18;4,20;5,7;5,8;5,15;5,21;5,24;6,7;6,8;6,16;6,22;6,23;7,13;7,21;7,23;8,14;8,22;8,24;9,15;9,17;9,19;9,21;10,16;10,18;10,20;10,22;11,13;11,17;11,20;11,23;12,14;12,18;12,19;12,24;13,17;13,21;13,23;14,18;14,22;14,24;15,19;15,21;15,24;16,20;16,22;16,23];
Polyhedron.face={[3,1,17];[3,17,9];[3,19,2];[3,9,19];[1,4,20];[1,20,11];[1,11,17];[2,19,12];[2,18,4];[2,12,18];[4,18,10];[4,10,20];[17,11,13];[19,9,15];[18,12,14];[20,10,16];[9,21,15];[11,23,13];[12,24,14];[10,22,16];[13,23,7];[13,7,21];[15,21,5];[15,5,24];[16,22,6];[16,6,23];[14,24,8];[14,8,22];[21,7,5];[23,6,7];[24,5,8];[22,8,6];[1,3,2,4];[21,9,17,13];[24,12,19,15];[10,18,14,22];[11,20,16,23];[8,5,7,6]};
case {'icododecahedron'}
Polyhedron.node=[0,-1.618033988749895,0;0,1.618033988749895,0;0.2628655560595668,-0.8090169943749474,-1.376381920471174;0.2628655560595668,0.8090169943749474,-1.376381920471174;0.4253254041760200,-1.309016994374947,0.8506508083520399;0.4253254041760200,1.309016994374947,0.8506508083520399;0.6881909602355868,-0.5000000000000000,1.376381920471174;0.6881909602355868,0.5000000000000000,1.376381920471174;1.113516364411607,-0.8090169943749474,-0.8506508083520399;1.113516364411607,0.8090169943749474,-0.8506508083520399;-1.376381920471174,0,-0.8506508083520399;-0.6881909602355868,-0.5000000000000000,-1.376381920471174;-0.6881909602355868,0.5000000000000000,-1.376381920471174;1.376381920471174,0,0.8506508083520399;0.9510565162951536,-1.309016994374947,0;0.9510565162951536,1.309016994374947,0;0.8506508083520399,0,-1.376381920471174;-0.9510565162951536,-1.309016994374947,0;-0.9510565162951536,1.309016994374947,0;-1.538841768587627,-0.5000000000000000,0;-1.538841768587627,0.5000000000000000,0;1.538841768587627,-0.5000000000000000,0;1.538841768587627,0.5000000000000000,0;-0.8506508083520399,0,1.376381920471174;-1.113516364411607,-0.8090169943749474,0.8506508083520399;-1.113516364411607,0.8090169943749474,0.8506508083520399;-0.4253254041760200,-1.309016994374947,-0.8506508083520399;-0.4253254041760200,1.309016994374947,-0.8506508083520399;-0.2628655560595668,-0.8090169943749474,1.376381920471174;-0.2628655560595668,0.8090169943749474,1.376381920471174];
Polyhedron.edge=[1,5;1,15;1,18;1,27;2,6;2,16;2,19;2,28;3,9;3,12;3,17;3,27;4,10;4,13;4,17;4,28;5,7;5,15;5,29;6,8;6,16;6,30;7,8;7,14;7,29;8,14;8,30;9,15;9,17;9,22;10,16;10,17;10,23;11,12;11,13;11,20;11,21;12,13;12,27;13,28;14,22;14,23;15,22;16,23;18,20;18,25;18,27;19,21;19,26;19,28;20,21;20,25;21,26;22,23;24,25;24,26;24,29;24,30;25,29;26,30];
Polyhedron.face={[30,24,29,7,8];[26,24,30];[25,29,24];[5,7,29];[14,8,7];[6,30,8];[16,2,6];[19,21,26];[20,18,25];[1,15,5];[22,23,14];[2,19,26,30,6];[21,20,25,24,26];[18,1,5,29,25];[15,22,14,7,5];[23,16,6,8,14];[12,13,4,17,3];[3,17,9];[17,4,10];[4,13,28];[13,12,11];[12,3,27];[27,1,18];[9,22,15];[10,16,23];[28,19,2];[11,20,21];[27,3,9,15,1];[9,17,10,23,22];[10,4,28,2,16];[28,13,11,21,19];[11,12,27,18,20]};
case {'truncated cuboctahedron'}
Polyhedron.node=[-(1/2), 1/2 + 1/sqrt(2), -(1/2) - sqrt(2);-(1/2), 1/2 + 1/sqrt(2), 1/2 + sqrt(2);-(1/2), 1/(2 - 2*sqrt(2)), -(1/2) - sqrt(2);-(1/2), 1/(2 - 2*sqrt(2)), 1/2 + sqrt(2);-(1/2), -(1/2) - sqrt(2), 1/2 + 1/sqrt(2);-(1/2), -(1/2) - sqrt(2), 1/(2 - 2*sqrt(2));-(1/2), 1/2 + sqrt(2), 1/2 + 1/sqrt(2);-(1/2), 1/2 + sqrt(2), 1/(2 - 2*sqrt(2));1/2, 1/2 + 1/sqrt(2), -(1/2) - sqrt(2);1/2, 1/2 + 1/sqrt(2), 1/2 + sqrt(2);1/2, 1/(2 - 2*sqrt(2)), -(1/2) - sqrt(2);1/2, 1/(2 - 2*sqrt(2)), 1/2 + sqrt(2);1/2, -(1/2) - sqrt(2), 1/2 + 1/sqrt(2);1/2, -(1/2) - sqrt(2), 1/(2 - 2*sqrt(2));1/2, 1/2 + sqrt(2), 1/2 + 1/sqrt(2);1/2, 1/2 + sqrt(2), 1/(2 - 2*sqrt(2));1/2 + 1/sqrt(2), -(1/2), -(1/2) - sqrt(2);1/2 + 1/sqrt(2), -(1/2), 1/2 + sqrt(2);1/2 + 1/sqrt(2), 1/2, -(1/2) - sqrt(2);1/2 + 1/sqrt(2), 1/2, 1/2 + sqrt(2);1/2 + 1/sqrt(2), -(1/2) - sqrt(2), -(1/2);1/2 + 1/sqrt(2), -(1/2) - sqrt(2), 1/2;1/2 + 1/sqrt(2), 1/2 + sqrt(2), -(1/2);1/2 + 1/sqrt(2), 1/2 + sqrt(2), 1/2;1/(2 - 2*sqrt(2)), -(1/2), -(1/2) - sqrt(2);1/(2 - 2*sqrt(2)), -(1/2), 1/2 + sqrt(2);1/(2 - 2*sqrt(2)), 1/2, -(1/2) - sqrt(2);1/(2 - 2*sqrt(2)), 1/2, 1/2 + sqrt(2);1/(2 - 2*sqrt(2)), -(1/2) - sqrt(2), -(1/2);1/(2 - 2*sqrt(2)), -(1/2) - sqrt(2), 1/2;1/(2 - 2*sqrt(2)), 1/2 + sqrt(2), -(1/2);1/(2 - 2*sqrt(2)), 1/2 + sqrt(2), 1/2;-(1/2) - sqrt(2), -(1/2), 1/2 + 1/sqrt(2);-(1/2) - sqrt(2), -(1/2), 1/(2 - 2*sqrt(2));-(1/2) - sqrt(2), 1/2, 1/2 + 1/sqrt(2);-(1/2) - sqrt(2), 1/2, 1/(2 - 2*sqrt(2));-(1/2) - sqrt(2), 1/2 + 1/sqrt(2), -(1/2);-(1/2) - sqrt(2), 1/2 + 1/sqrt(2), 1/2;-(1/2) - sqrt(2), 1/(2 - 2*sqrt(2)), -(1/2);-(1/2) - sqrt(2), 1/(2 - 2*sqrt(2)), 1/2;1/2 + sqrt(2), -(1/2), 1/2 + 1/sqrt(2);1/2 + sqrt(2), -(1/2), 1/(2 - 2*sqrt(2));1/2 + sqrt(2), 1/2, 1/2 + 1/sqrt(2);1/2 + sqrt(2), 1/2, 1/(2 - 2*sqrt(2));1/2 + sqrt(2), 1/2 + 1/sqrt(2), -(1/2);1/2 + sqrt(2), 1/2 + 1/sqrt(2), 1/2;1/2 + sqrt(2), 1/(2 - 2*sqrt(2)), -(1/2);1/2 + sqrt(2), 1/(2 - 2*sqrt(2)), 1/2];
Polyhedron.edge=[1, 8;1, 9;1, 27;2, 7;2, 10;2, 28;3, 6;3, 11;3, 25;4, 5;4, 12;4, 26;5, 13;5, 30;6, 14;6, 29;7, 15;7, 32;8, 16;8, 31;9, 16;9, 19;10, 15;10, 20;11, 14;11, 17;12, 13;12, 18;13, 22;14, 21;15, 24;16, 23;17, 19;17, 42;18, 20;18, 41;19, 44;20, 43;21, 22;21, 47;22, 48;23, 24;23, 45;24, 46;25, 27;25, 34;26, 28;26, 33;27, 36;28, 35;29, 30;29, 39;30, 40;31, 32;31, 37;32, 38;33, 35;33, 40;34, 36;34, 39;35, 38;36, 37;37, 38;39, 40;41, 43;41, 48;42, 44;42, 47;43, 46;44, 45;45, 46;47, 48];
Polyhedron.face={[44, 42, 17, 19];[14, 6, 3, 11];[34, 36, 27, 25];[8, 16, 9, 1];[20, 18, 41, 43];[12, 4, 5, 13];[26, 28, 35, 33];[2, 10, 15, 7];[45, 23, 24, 46];[39, 29, 30, 40];[48, 22, 21, 47];[38, 32, 31, 37];[9, 19, 17, 11, 3, 25, 27, 1];[2, 28, 26, 4, 12, 18, 20, 10];[41, 48, 47, 42, 44, 45, 46, 43];[35, 38, 37, 36, 34, 39, 40, 33];[15, 24, 23, 16, 8, 31, 32, 7];[5, 30, 29, 6, 14, 21, 22, 13];[46, 24, 15, 10, 20, 43];[35, 28, 2, 7, 32, 38];[41, 18, 12, 13, 22, 48];[40, 30, 5, 4, 26, 33];[44, 19, 9, 16, 23, 45];[37, 31, 8, 1, 27, 36];[47, 21, 14, 11, 17, 42];[34, 25, 3, 6, 29, 39]};
case {'truncated icosahedron'}
Polyhedron.node=[-0.1624598481164532,-2.118033988749895,1.275976212528060;-0.1624598481164532,2.118033988749895,1.275976212528060;0.1624598481164532,-2.118033988749895,-1.275976212528060;0.1624598481164532,2.118033988749895,-1.275976212528060;-0.2628655560595668,-0.8090169943749474,-2.327438436766327;-0.2628655560595668,-2.427050983124842,-0.4253254041760200;-0.2628655560595668,0.8090169943749474,-2.327438436766327;-0.2628655560595668,2.427050983124842,-0.4253254041760200;0.2628655560595668,-0.8090169943749474,2.327438436766327;0.2628655560595668,-2.427050983124842,0.4253254041760200;0.2628655560595668,0.8090169943749474,2.327438436766327;0.2628655560595668,2.427050983124842,0.4253254041760200;0.6881909602355868,-0.5000000000000000,-2.327438436766327;0.6881909602355868,0.5000000000000000,-2.327438436766327;1.213922072354720,-2.118033988749895,0.4253254041760200;1.213922072354720,2.118033988749895,0.4253254041760200;-2.064572880706760,-0.5000000000000000,1.275976212528060;-2.064572880706760,0.5000000000000000,1.275976212528060;-1.376381920471174,-1.000000000000000,1.801707324647194;-1.376381920471174,1.000000000000000,1.801707324647194;-1.376381920471174,-1.618033988749895,-1.275976212528060;-1.376381920471174,1.618033988749895,-1.275976212528060;-0.6881909602355868,-0.5000000000000000,2.327438436766327;-0.6881909602355868,0.5000000000000000,2.327438436766327;1.376381920471174,-1.000000000000000,-1.801707324647194;1.376381920471174,1.000000000000000,-1.801707324647194;1.376381920471174,-1.618033988749895,1.275976212528060;1.376381920471174,1.618033988749895,1.275976212528060;-1.701301616704080,0,-1.801707324647194;1.701301616704080,0,1.801707324647194;-1.213922072354720,-2.118033988749895,-0.4253254041760200;-1.213922072354720,2.118033988749895,-0.4253254041760200;-1.964167172763647,-0.8090169943749474,-1.275976212528060;-1.964167172763647,0.8090169943749474,-1.275976212528060;2.064572880706760,-0.5000000000000000,-1.275976212528060;2.064572880706760,0.5000000000000000,-1.275976212528060;2.227032728823213,-1.000000000000000,-0.4253254041760200;2.227032728823213,1.000000000000000,-0.4253254041760200;2.389492576939667,-0.5000000000000000,0.4253254041760200;2.389492576939667,0.5000000000000000,0.4253254041760200;-1.113516364411607,-1.809016994374947,1.275976212528060;-1.113516364411607,1.809016994374947,1.275976212528060;1.113516364411607,-1.809016994374947,-1.275976212528060;1.113516364411607,1.809016994374947,-1.275976212528060;-2.389492576939667,-0.5000000000000000,-0.4253254041760200;-2.389492576939667,0.5000000000000000,-0.4253254041760200;-1.639247476530740,-1.809016994374947,0.4253254041760200;-1.639247476530740,1.809016994374947,0.4253254041760200;1.639247476530740,-1.809016994374947,-0.4253254041760200;1.639247476530740,1.809016994374947,-0.4253254041760200;1.964167172763647,-0.8090169943749474,1.275976212528060;1.964167172763647,0.8090169943749474,1.275976212528060;0.8506508083520399,0,2.327438436766327;-2.227032728823213,-1.000000000000000,0.4253254041760200;-2.227032728823213,1.000000000000000,0.4253254041760200;-0.8506508083520399,0,-2.327438436766327;-0.5257311121191336,-1.618033988749895,-1.801707324647194;-0.5257311121191336,1.618033988749895,-1.801707324647194;0.5257311121191336,-1.618033988749895,1.801707324647194;0.5257311121191336,1.618033988749895,1.801707324647194];
Polyhedron.edge=[1,10;1,41;1,59;2,12;2,42;2,60;3,6;3,43;3,57;4,8;4,44;4,58;5,13;5,56;5,57;6,10;6,31;7,14;7,56;7,58;8,12;8,32;9,23;9,53;9,59;10,15;11,24;11,53;11,60;12,16;13,14;13,25;14,26;15,27;15,49;16,28;16,50;17,18;17,19;17,54;18,20;18,55;19,23;19,41;20,24;20,42;21,31;21,33;21,57;22,32;22,34;22,58;23,24;25,35;25,43;26,36;26,44;27,51;27,59;28,52;28,60;29,33;29,34;29,56;30,51;30,52;30,53;31,47;32,48;33,45;34,46;35,36;35,37;36,38;37,39;37,49;38,40;38,50;39,40;39,51;40,52;41,47;42,48;43,49;44,50;45,46;45,54;46,55;47,54;48,55];
Polyhedron.face={[53,11,24,23,9];[51,39,40,52,30];[60,28,16,12,2];[20,42,48,55,18];[19,17,54,47,41];[1,10,15,27,59];[36,26,44,50,38];[4,58,22,32,8];[34,29,33,45,46];[21,57,3,6,31];[37,49,43,25,35];[13,5,56,7,14];[9,59,27,51,30,53];[53,30,52,28,60,11];[11,60,2,42,20,24];[24,20,18,17,19,23];[23,19,41,1,59,9];[13,25,43,3,57,5];[5,57,21,33,29,56];[56,29,34,22,58,7];[7,58,4,44,26,14];[14,26,36,35,25,13];[40,38,50,16,28,52];[16,50,44,4,8,12];[12,8,32,48,42,2];[48,32,22,34,46,55];[55,46,45,54,17,18];[54,45,33,21,31,47];[47,31,6,10,1,41];[10,6,3,43,49,15];[15,49,37,39,51,27];[39,37,35,36,38,40]};
case {'truncated dodecahedron'}
Polyhedron.node=[0,-1.618033988749895,2.489898284882780;0,-1.618033988749895,-2.489898284882780;0,1.618033988749895,2.489898284882780;0,1.618033988749895,-2.489898284882780;0.4253254041760200,-2.927050983124842,0.2628655560595668;0.4253254041760200,2.927050983124842,0.2628655560595668;0.6881909602355868,-2.118033988749895,1.964167172763647;0.6881909602355868,2.118033988749895,1.964167172763647;-2.752763840942347,0,-1.113516364411607;-2.064572880706760,-2.118033988749895,0.2628655560595668;-2.064572880706760,2.118033988749895,0.2628655560595668;-1.376381920471174,-2.618033988749895,-0.2628655560595668;-1.376381920471174,2.618033988749895,-0.2628655560595668;-0.6881909602355868,-2.118033988749895,-1.964167172763647;-0.6881909602355868,2.118033988749895,-1.964167172763647;1.376381920471174,-2.618033988749895,0.2628655560595668;1.376381920471174,2.618033988749895,0.2628655560595668;2.752763840942347,0,1.113516364411607;1.801707324647194,-1.309016994374947,-1.964167172763647;1.801707324647194,1.309016994374947,-1.964167172763647;2.064572880706760,-2.118033988749895,-0.2628655560595668;2.064572880706760,2.118033988749895,-0.2628655560595668;2.227032728823213,0,1.964167172763647;2.227032728823213,-1.618033988749895,-1.113516364411607;2.227032728823213,1.618033988749895,-1.113516364411607;-2.652358132999233,-1.309016994374947,0.2628655560595668;-2.652358132999233,1.309016994374947,0.2628655560595668;2.652358132999233,-1.309016994374947,-0.2628655560595668;2.652358132999233,1.309016994374947,-0.2628655560595668;2.915223689058800,-0.5000000000000000,0.2628655560595668;2.915223689058800,0.5000000000000000,0.2628655560595668;-2.915223689058800,-0.5000000000000000,-0.2628655560595668;-2.915223689058800,0.5000000000000000,-0.2628655560595668;0.9510565162951536,-1.309016994374947,2.489898284882780;0.9510565162951536,-1.309016994374947,-2.489898284882780;0.9510565162951536,1.309016994374947,2.489898284882780;0.9510565162951536,1.309016994374947,-2.489898284882780;0.8506508083520399,-2.618033988749895,1.113516364411607;0.8506508083520399,2.618033988749895,1.113516364411607;-0.9510565162951536,-1.309016994374947,2.489898284882780;-0.9510565162951536,-1.309016994374947,-2.489898284882780;-0.9510565162951536,1.309016994374947,2.489898284882780;-0.9510565162951536,1.309016994374947,-2.489898284882780;-1.538841768587627,-0.5000000000000000,2.489898284882780;-1.538841768587627,-0.5000000000000000,-2.489898284882780;-1.538841768587627,0.5000000000000000,2.489898284882780;-1.538841768587627,0.5000000000000000,-2.489898284882780;1.538841768587627,-0.5000000000000000,2.489898284882780;1.538841768587627,-0.5000000000000000,-2.489898284882780;1.538841768587627,0.5000000000000000,2.489898284882780;1.538841768587627,0.5000000000000000,-2.489898284882780;-2.227032728823213,0,-1.964167172763647;-2.227032728823213,-1.618033988749895,1.113516364411607;-2.227032728823213,1.618033988749895,1.113516364411607;-0.8506508083520399,-2.618033988749895,-1.113516364411607;-0.8506508083520399,2.618033988749895,-1.113516364411607;-1.801707324647194,-1.309016994374947,1.964167172763647;-1.801707324647194,1.309016994374947,1.964167172763647;-0.4253254041760200,-2.927050983124842,-0.2628655560595668;-0.4253254041760200,2.927050983124842,-0.2628655560595668];
Polyhedron.edge=[1,7;1,34;1,40;2,14;2,35;2,41;3,8;3,36;3,42;4,15;4,37;4,43;5,16;5,38;5,59;6,17;6,39;6,60;7,34;7,38;8,36;8,39;9,32;9,33;9,52;10,12;10,26;10,53;11,13;11,27;11,54;12,55;12,59;13,56;13,60;14,41;14,55;15,43;15,56;16,21;16,38;17,22;17,39;18,23;18,30;18,31;19,24;19,35;19,49;20,25;20,37;20,51;21,24;21,28;22,25;22,29;23,48;23,50;24,28;25,29;26,32;26,53;27,33;27,54;28,30;29,31;30,31;32,33;34,48;35,49;36,50;37,51;40,44;40,57;41,45;42,46;42,58;43,47;44,46;44,57;45,47;45,52;46,58;47,52;48,50;49,51;53,57;54,58;55,59;56,60];
Polyhedron.face={[3,42,46,44,40,1,34,48,50,36];[47,43,4,37,51,49,35,2,41,45];[2,35,19,24,21,16,5,59,55,14];[49,51,20,25,29,31,30,28,24,19];[37,4,15,56,60,6,17,22,25,20];[43,47,52,9,33,27,11,13,56,15];[45,41,14,55,12,10,26,32,9,52];[6,60,13,11,54,58,42,3,8,39];[27,33,32,26,53,57,44,46,58,54];[10,12,59,5,38,7,1,40,57,53];[16,21,28,30,18,23,48,34,7,38];[31,29,22,17,39,8,36,50,23,18];[9,32,33];[18,30,31];[47,45,52];[50,48,23];[10,53,26];[27,54,11];[21,24,28];[29,25,22];[40,44,57];[58,46,42];[35,49,19];[20,51,37];[12,55,59];[60,56,13];[41,2,14];[15,4,43];[34,1,7];[8,3,36];[38,5,16];[17,6,39]};
case {'rhombicosidodecahedron'}
Polyhedron.node=[-0.5000000000000000,-0.5000000000000000,-2.118033988749895;-0.5000000000000000,-0.5000000000000000,2.118033988749895;-0.5000000000000000,0.5000000000000000,-2.118033988749895;-0.5000000000000000,0.5000000000000000,2.118033988749895;-0.5000000000000000,-2.118033988749895,-0.5000000000000000;-0.5000000000000000,-2.118033988749895,0.5000000000000000;-0.5000000000000000,2.118033988749895,-0.5000000000000000;-0.5000000000000000,2.118033988749895,0.5000000000000000;0,-1.309016994374947,-1.809016994374947;0,-1.309016994374947,1.809016994374947;0,1.309016994374947,-1.809016994374947;0,1.309016994374947,1.809016994374947;0.5000000000000000,-0.5000000000000000,-2.118033988749895;0.5000000000000000,-0.5000000000000000,2.118033988749895;0.5000000000000000,0.5000000000000000,-2.118033988749895;0.5000000000000000,0.5000000000000000,2.118033988749895;0.5000000000000000,-2.118033988749895,-0.5000000000000000;0.5000000000000000,-2.118033988749895,0.5000000000000000;0.5000000000000000,2.118033988749895,-0.5000000000000000;0.5000000000000000,2.118033988749895,0.5000000000000000;-1.809016994374947,0,-1.309016994374947;-1.809016994374947,0,1.309016994374947;-0.8090169943749474,-1.618033988749895,-1.309016994374947;-0.8090169943749474,-1.618033988749895,1.309016994374947;-0.8090169943749474,1.618033988749895,-1.309016994374947;-0.8090169943749474,1.618033988749895,1.309016994374947;-1.618033988749895,-1.309016994374947,-0.8090169943749474;-1.618033988749895,-1.309016994374947,0.8090169943749474;-1.618033988749895,1.309016994374947,-0.8090169943749474;-1.618033988749895,1.309016994374947,0.8090169943749474;-2.118033988749895,-0.5000000000000000,-0.5000000000000000;-2.118033988749895,-0.5000000000000000,0.5000000000000000;-2.118033988749895,0.5000000000000000,-0.5000000000000000;-2.118033988749895,0.5000000000000000,0.5000000000000000;-1.309016994374947,-1.809016994374947,0;-1.309016994374947,-0.8090169943749474,-1.618033988749895;-1.309016994374947,-0.8090169943749474,1.618033988749895;-1.309016994374947,0.8090169943749474,-1.618033988749895;-1.309016994374947,0.8090169943749474,1.618033988749895;-1.309016994374947,1.809016994374947,0;0.8090169943749474,-1.618033988749895,-1.309016994374947;0.8090169943749474,-1.618033988749895,1.309016994374947;0.8090169943749474,1.618033988749895,-1.309016994374947;0.8090169943749474,1.618033988749895,1.309016994374947;1.618033988749895,-1.309016994374947,-0.8090169943749474;1.618033988749895,-1.309016994374947,0.8090169943749474;1.618033988749895,1.309016994374947,-0.8090169943749474;1.618033988749895,1.309016994374947,0.8090169943749474;2.118033988749895,-0.5000000000000000,-0.5000000000000000;2.118033988749895,-0.5000000000000000,0.5000000000000000;2.118033988749895,0.5000000000000000,-0.5000000000000000;2.118033988749895,0.5000000000000000,0.5000000000000000;1.309016994374947,-1.809016994374947,0;1.309016994374947,-0.8090169943749474,-1.618033988749895;1.309016994374947,-0.8090169943749474,1.618033988749895;1.309016994374947,0.8090169943749474,-1.618033988749895;1.309016994374947,0.8090169943749474,1.618033988749895;1.309016994374947,1.809016994374947,0;1.809016994374947,0,-1.309016994374947;1.809016994374947,0,1.309016994374947];
Polyhedron.edge=[1,3;1,9;1,13;1,36;2,4;2,10;2,14;2,37;3,11;3,15;3,38;4,12;4,16;4,39;5,6;5,17;5,23;5,35;6,18;6,24;6,35;7,8;7,19;7,25;7,40;8,20;8,26;8,40;9,13;9,23;9,41;10,14;10,24;10,42;11,15;11,25;11,43;12,16;12,26;12,44;13,15;13,54;14,16;14,55;15,56;16,57;17,18;17,41;17,53;18,42;18,53;19,20;19,43;19,58;20,44;20,58;21,31;21,33;21,36;21,38;22,32;22,34;22,37;22,39;23,27;23,36;24,28;24,37;25,29;25,38;26,30;26,39;27,31;27,35;27,36;28,32;28,35;28,37;29,33;29,38;29,40;30,34;30,39;30,40;31,32;31,33;32,34;33,34;41,45;41,54;42,46;42,55;43,47;43,56;44,48;44,57;45,49;45,53;45,54;46,50;46,53;46,55;47,51;47,56;47,58;48,52;48,57;48,58;49,50;49,51;49,59;50,52;50,60;51,52;51,59;52,60;54,59;55,60;56,59;57,60];
Polyhedron.face={[36,23,27];[37,28,24];[40,8,7];[35,5,6];[38,29,25];[39,26,30];[10,14,2];[9,1,13];[12,4,16];[11,15,3];[54,45,41];[55,42,46];[58,19,20];[53,18,17];[56,43,47];[57,48,44];[34,32,22];[33,21,31];[59,51,49];[60,50,52];[27,31,21,36];[23,36,1,9];[10,2,37,24];[37,22,32,28];[8,40,30,26];[25,29,40,7];[35,27,23,5];[6,24,28,35];[3,38,25,11];[21,33,29,38];[39,30,34,22];[12,26,39,4];[55,14,10,42];[41,9,13,54];[57,44,12,16];[15,11,43,56];[45,54,59,49];[50,60,55,46];[48,58,20,44];[43,19,58,47];[53,17,41,45];[46,42,18,53];[59,56,47,51];[52,48,57,60];[31,32,34,33];[17,18,6,5];[1,3,15,13];[14,16,4,2];[7,8,20,19];[51,52,50,49];[3,1,36,21,38];[22,37,2,4,39];[29,33,34,30,40];[27,35,28,32,31];[42,10,24,6,18];[41,17,5,23,9];[20,8,26,12,44];[11,25,7,19,43];[56,59,54,13,15];[57,16,14,55,60];[58,48,52,51,47];[49,50,46,53,45]};
case {'snub dodecahedron'}
Polyhedron.node=[-2.050215876504471,-0.6430296059140726,0.1753926269615850;2.050215876504471,-0.6430296059140726,-0.1753926269615850;-1.645069107445494,0.6430296059140726,1.236080638790192;1.645069107445494,0.6430296059140726,-1.236080638790192;-2.092754375489906,0.3309210247298442,0.3981270993101259;2.092754375489906,0.3309210247298442,-0.3981270993101259;-1.332963201807377,1.646917940690374,-0.3981270993101259;1.332963201807377,1.646917940690374,0.3981270993101259;-1.825265080808600,-0.3309210247298442,1.098423164412520;1.825265080808600,-0.3309210247298442,-1.098423164412520;-0.6260465263418767,1.746186440985826,-1.098423164412520;0.6260465263418767,1.746186440985826,1.098423164412520;-1.062215752565082,1.454024229338015,1.185388553785668;1.062215752565082,1.454024229338015,-1.185388553785668;-1.932135944910516,0.8475500467890608,-0.4428819216428905;1.932135944910516,0.8475500467890608,0.4428819216428905;-1.144874490434974,-0.8475500467890608,1.618195324206757;1.144874490434974,-0.8475500467890608,-1.618195324206757;-1.581987912359319,-1.454024229338015,-0.1753926269615850;1.581987912359319,-1.454024229338015,0.1753926269615850;-1.057412406163561,0.3748216581145623,-1.840929796555298;1.057412406163561,0.3748216581145623,1.840929796555298;-0.4391378575590853,-0.3748216581145623,-2.077089659743209;0.4391378575590853,-0.3748216581145623,2.077089659743209;-1.562410369575602,-1.249503788463027,0.8032738683691033;1.562410369575602,-1.249503788463027,-0.8032738683691033;-1.863307207721680,-0.7283351769571915,-0.8032738683691033;1.863307207721680,-0.7283351769571915,0.8032738683691033;-1.700067843953274,1.249503788463027,0.4428819216428905;1.700067843953274,1.249503788463027,-0.4428819216428905;-0.7281140440422709,-1.646917940690374,1.185388553785668;0.7281140440422709,-1.646917940690374,-1.185388553785668;-0.2656545796156639,-1.746186440985826,-1.236080638790192;0.2656545796156639,-1.746186440985826,1.236080638790192;-0.7597911736825294,-1.977838965420219,-0.3981270993101259;0.7597911736825294,-1.977838965420219,0.3981270993101259;-1.199218554466724,-1.415265416255982,-1.098423164412520;1.199218554466724,-1.415265416255982,1.098423164412520;-1.790329796607353,0.1928937113523590,-1.185388553785668;1.790329796607353,0.1928937113523590,1.185388553785668;-1.306437116715503,-0.5677153694669213,-1.618195324206757;1.306437116715503,-0.5677153694669213,1.618195324206757;-0.8533112808975971,0.7283351769571915,1.840929796555298;0.8533112808975971,0.7283351769571915,-1.840929796555298;-1.379414527829830,1.103156835071754,-1.236080638790192;1.379414527829830,1.103156835071754,1.236080638790192;-0.1050361490362740,0.5677153694669213,-2.077089659743209;0.1050361490362740,0.5677153694669213,2.077089659743209;-0.4682279641451526,2.097053835252088,-0.1753926269615850;0.4682279641451526,2.097053835252088,0.1753926269615850;-0.3008968381460777,1.977838965420219,0.8032738683691033;0.3008968381460777,1.977838965420219,-0.8032738683691033;-0.1615626262805293,1.415265416255982,1.618195324206757;0.1615626262805293,1.415265416255982,-1.618195324206757;-0.5441740065953593,-0.1928937113523590,2.077089659743209;0.5441740065953593,-0.1928937113523590,-2.077089659743209;-0.2320681009572418,-2.097053835252088,0.4428819216428905;0.2320681009572418,-2.097053835252088,-0.4428819216428905;-0.2041011252659638,-1.103156835071754,1.840929796555298;0.2041011252659638,-1.103156835071754,-1.840929796555298];
Polyhedron.edge=[1,5;1,9;1,19;1,25;1,27;2,6;2,10;2,20;2,26;2,28;3,5;3,9;3,13;3,29;3,43;4,6;4,10;4,14;4,30;4,44;5,9;5,15;5,29;6,10;6,16;6,30;7,11;7,15;7,29;7,45;7,49;8,12;8,16;8,30;8,46;8,50;9,17;9,25;10,18;10,26;11,45;11,49;11,52;11,54;12,46;12,50;12,51;12,53;13,29;13,43;13,51;13,53;14,30;14,44;14,52;14,54;15,29;15,39;15,45;16,30;16,40;16,46;17,25;17,31;17,55;17,59;18,26;18,32;18,56;18,60;19,25;19,27;19,35;19,37;20,26;20,28;20,36;20,38;21,23;21,39;21,41;21,45;21,47;22,24;22,40;22,42;22,46;22,48;23,41;23,47;23,56;23,60;24,42;24,48;24,55;24,59;25,31;26,32;27,37;27,39;27,41;28,38;28,40;28,42;31,34;31,57;31,59;32,33;32,58;32,60;33,35;33,37;33,58;33,60;34,36;34,38;34,57;34,59;35,37;35,57;35,58;36,38;36,57;36,58;37,41;38,42;39,41;39,45;40,42;40,46;43,48;43,53;43,55;44,47;44,54;44,56;47,54;47,56;48,53;48,55;49,50;49,51;49,52;50,51;50,52;51,53;52,54;55,59;56,60;57,58];
Polyhedron.face={[5,1,9];[5,9,3];[5,29,15];[5,3,29];[1,27,19];[1,19,25];[1,25,9];[15,29,7];[15,45,39];[15,7,45];[27,39,41];[27,41,37];[27,37,19];[9,25,17];[39,45,21];[39,21,41];[29,3,13];[3,43,13];[19,37,35];[25,31,17];[45,7,11];[7,49,11];[41,21,23];[37,33,35];[17,31,59];[17,59,55];[13,43,53];[13,53,51];[21,47,23];[43,55,48];[43,48,53];[35,33,58];[35,58,57];[31,57,34];[31,34,59];[11,49,52];[11,52,54];[55,59,24];[55,24,48];[49,51,50];[49,50,52];[23,47,56];[23,56,60];[51,53,12];[51,12,50];[33,60,32];[33,32,58];[57,58,36];[57,36,34];[47,54,44];[47,44,56];[48,24,22];[54,52,14];[54,14,44];[60,56,18];[60,18,32];[34,36,38];[24,42,22];[50,12,8];[12,46,8];[32,18,26];[36,20,38];[44,14,4];[22,42,40];[22,40,46];[14,30,4];[18,10,26];[38,20,28];[38,28,42];[42,28,40];[8,46,16];[8,16,30];[46,40,16];[26,10,2];[26,2,20];[20,2,28];[4,30,6];[4,6,10];[30,16,6];[10,6,2];[39,27,1,5,15];[3,9,17,55,43];[51,49,7,29,13];[57,31,25,19,35];[47,21,45,11,54];[33,37,41,23,60];[42,24,59,34,38];[46,12,53,48,22];[36,58,32,26,20];[14,52,50,8,30];[44,4,10,18,56];[16,40,28,2,6]};
case {'great rhombicosidodecahedron'}
Polyhedron.node=[-1,1/4*(-3-sqrt(5)),1/4*(-7-3*sqrt(5));-1,1/4*(-3-sqrt(5)),1/4*(7+3*sqrt(5));-1,1/4*(3+sqrt(5)),1/4*(-7-3*sqrt(5));-1,1/4*(3+sqrt(5)),1/4*(7+3*sqrt(5));-(1/2),-(1/2),-(3/2)-sqrt(5);-(1/2),-(1/2),3/2+sqrt(5);-(1/2),1/2,-(3/2)-sqrt(5);-(1/2),1/2,3/2+sqrt(5);-(1/2),-(3/2)-sqrt(5),-(1/2);-(1/2),-(3/2)-sqrt(5),1/2;-(1/2),-1-sqrt(5)/2,-2-sqrt(5)/2;-(1/2),-1-sqrt(5)/2,1/2*(4+sqrt(5));-(1/2),3/2+sqrt(5),-(1/2);-(1/2),3/2+sqrt(5),1/2;-(1/2),1/2*(2+sqrt(5)),-2-sqrt(5)/2;-(1/2),1/2*(2+sqrt(5)),1/2*(4+sqrt(5));1/2,-(1/2),-(3/2)-sqrt(5);1/2,-(1/2),3/2+sqrt(5);1/2,1/2,-(3/2)-sqrt(5);1/2,1/2,3/2+sqrt(5);1/2,-(3/2)-sqrt(5),-(1/2);1/2,-(3/2)-sqrt(5),1/2;1/2,-1-sqrt(5)/2,-2-sqrt(5)/2;1/2,-1-sqrt(5)/2,1/2*(4+sqrt(5));1/2,3/2+sqrt(5),-(1/2);1/2,3/2+sqrt(5),1/2;1/2,1/2*(2+sqrt(5)),-2-sqrt(5)/2;1/2,1/2*(2+sqrt(5)),1/2*(4+sqrt(5));1,1/4*(-3-sqrt(5)),1/4*(-7-3*sqrt(5));1,1/4*(-3-sqrt(5)),1/4*(7+3*sqrt(5));1,1/4*(3+sqrt(5)),1/4*(-7-3*sqrt(5));1,1/4*(3+sqrt(5)),1/4*(7+3*sqrt(5));1/4*(-7-3*sqrt(5)),-1,1/4*(-3-sqrt(5));1/4*(-7-3*sqrt(5)),-1,1/4*(3+sqrt(5));1/4*(-7-3*sqrt(5)),1,1/4*(-3-sqrt(5));1/4*(-7-3*sqrt(5)),1,1/4*(3+sqrt(5));1/4*(-5-3*sqrt(5)),1/4*(-5-sqrt(5)),1/2*(-1-sqrt(5));1/4*(-5-3*sqrt(5)),1/4*(-5-sqrt(5)),1/2*(1+sqrt(5));1/4*(-5-3*sqrt(5)),1/4*(5+sqrt(5)),1/2*(-1-sqrt(5));1/4*(-5-3*sqrt(5)),1/4*(5+sqrt(5)),1/2*(1+sqrt(5));1/4*(-5-sqrt(5)),1/2*(-1-sqrt(5)),1/4*(-5-3*sqrt(5));1/4*(-5-sqrt(5)),1/2*(-1-sqrt(5)),1/4*(5+3*sqrt(5));1/4*(-5-sqrt(5)),1/2*(1+sqrt(5)),1/4*(-5-3*sqrt(5));1/4*(-5-sqrt(5)),1/2*(1+sqrt(5)),1/4*(5+3*sqrt(5));1/4*(-3-sqrt(5)),1/4*(-7-3*sqrt(5)),-1;1/4*(-3-sqrt(5)),1/4*(-7-3*sqrt(5)),1;1/4*(-3-sqrt(5)),-(3/4)*(1+sqrt(5)),1/2*(-3-sqrt(5));1/4*(-3-sqrt(5)),-(3/4)*(1+sqrt(5)),1/2*(3+sqrt(5));1/4*(-3-sqrt(5)),3/4*(1+sqrt(5)),1/2*(-3-sqrt(5));1/4*(-3-sqrt(5)),3/4*(1+sqrt(5)),1/2*(3+sqrt(5));1/4*(-3-sqrt(5)),1/4*(7+3*sqrt(5)),-1;1/4*(-3-sqrt(5)),1/4*(7+3*sqrt(5)),1;1/2*(-3-sqrt(5)),1/4*(-3-sqrt(5)),-(3/4)*(1+sqrt(5));1/2*(-3-sqrt(5)),1/4*(-3-sqrt(5)),3/4*(1+sqrt(5));1/2*(-3-sqrt(5)),1/4*(3+sqrt(5)),-(3/4)*(1+sqrt(5));1/2*(-3-sqrt(5)),1/4*(3+sqrt(5)),3/4*(1+sqrt(5));-(3/2)-sqrt(5),-(1/2),-(1/2);-(3/2)-sqrt(5),-(1/2),1/2;-(3/2)-sqrt(5),1/2,-(1/2);-(3/2)-sqrt(5),1/2,1/2;1/2*(-1-sqrt(5)),1/4*(-5-3*sqrt(5)),1/4*(-5-sqrt(5));1/2*(-1-sqrt(5)),1/4*(-5-3*sqrt(5)),1/4*(5+sqrt(5));1/2*(-1-sqrt(5)),1/4*(5+3*sqrt(5)),1/4*(-5-sqrt(5));1/2*(-1-sqrt(5)),1/4*(5+3*sqrt(5)),1/4*(5+sqrt(5));-2-sqrt(5)/2,-(1/2),-1-sqrt(5)/2;-2-sqrt(5)/2,-(1/2),1/2*(2+sqrt(5));-2-sqrt(5)/2,1/2,-1-sqrt(5)/2;-2-sqrt(5)/2,1/2,1/2*(2+sqrt(5));-1-sqrt(5)/2,-2-sqrt(5)/2,-(1/2);-1-sqrt(5)/2,-2-sqrt(5)/2,1/2;-1-sqrt(5)/2,1/2*(4+sqrt(5)),-(1/2);-1-sqrt(5)/2,1/2*(4+sqrt(5)),1/2;-(3/4)*(1+sqrt(5)),1/2*(-3-sqrt(5)),1/4*(-3-sqrt(5));-(3/4)*(1+sqrt(5)),1/2*(-3-sqrt(5)),1/4*(3+sqrt(5));-(3/4)*(1+sqrt(5)),1/2*(3+sqrt(5)),1/4*(-3-sqrt(5));-(3/4)*(1+sqrt(5)),1/2*(3+sqrt(5)),1/4*(3+sqrt(5));1/2*(1+sqrt(5)),1/4*(-5-3*sqrt(5)),1/4*(-5-sqrt(5));1/2*(1+sqrt(5)),1/4*(-5-3*sqrt(5)),1/4*(5+sqrt(5));1/2*(1+sqrt(5)),1/4*(5+3*sqrt(5)),1/4*(-5-sqrt(5));1/2*(1+sqrt(5)),1/4*(5+3*sqrt(5)),1/4*(5+sqrt(5));3/4*(1+sqrt(5)),1/2*(-3-sqrt(5)),1/4*(-3-sqrt(5));3/4*(1+sqrt(5)),1/2*(-3-sqrt(5)),1/4*(3+sqrt(5));3/4*(1+sqrt(5)),1/2*(3+sqrt(5)),1/4*(-3-sqrt(5));3/4*(1+sqrt(5)),1/2*(3+sqrt(5)),1/4*(3+sqrt(5));3/2+sqrt(5),-(1/2),-(1/2);3/2+sqrt(5),-(1/2),1/2;3/2+sqrt(5),1/2,-(1/2);3/2+sqrt(5),1/2,1/2;1/2*(2+sqrt(5)),-2-sqrt(5)/2,-(1/2);1/2*(2+sqrt(5)),-2-sqrt(5)/2,1/2;1/2*(2+sqrt(5)),1/2*(4+sqrt(5)),-(1/2);1/2*(2+sqrt(5)),1/2*(4+sqrt(5)),1/2;1/4*(3+sqrt(5)),1/4*(-7-3*sqrt(5)),-1;1/4*(3+sqrt(5)),1/4*(-7-3*sqrt(5)),1;1/4*(3+sqrt(5)),-(3/4)*(1+sqrt(5)),1/2*(-3-sqrt(5));1/4*(3+sqrt(5)),-(3/4)*(1+sqrt(5)),1/2*(3+sqrt(5));1/4*(3+sqrt(5)),3/4*(1+sqrt(5)),1/2*(-3-sqrt(5));1/4*(3+sqrt(5)),3/4*(1+sqrt(5)),1/2*(3+sqrt(5));1/4*(3+sqrt(5)),1/4*(7+3*sqrt(5)),-1;1/4*(3+sqrt(5)),1/4*(7+3*sqrt(5)),1;1/2*(3+sqrt(5)),1/4*(-3-sqrt(5)),-(3/4)*(1+sqrt(5));1/2*(3+sqrt(5)),1/4*(-3-sqrt(5)),3/4*(1+sqrt(5));1/2*(3+sqrt(5)),1/4*(3+sqrt(5)),-(3/4)*(1+sqrt(5));1/2*(3+sqrt(5)),1/4*(3+sqrt(5)),3/4*(1+sqrt(5));1/2*(4+sqrt(5)),-(1/2),-1-sqrt(5)/2;1/2*(4+sqrt(5)),-(1/2),1/2*(2+sqrt(5));1/2*(4+sqrt(5)),1/2,-1-sqrt(5)/2;1/2*(4+sqrt(5)),1/2,1/2*(2+sqrt(5));1/4*(5+sqrt(5)),1/2*(-1-sqrt(5)),1/4*(-5-3*sqrt(5));1/4*(5+sqrt(5)),1/2*(-1-sqrt(5)),1/4*(5+3*sqrt(5));1/4*(5+sqrt(5)),1/2*(1+sqrt(5)),1/4*(-5-3*sqrt(5));1/4*(5+sqrt(5)),1/2*(1+sqrt(5)),1/4*(5+3*sqrt(5));1/4*(5+3*sqrt(5)),1/4*(-5-sqrt(5)),1/2*(-1-sqrt(5));1/4*(5+3*sqrt(5)),1/4*(-5-sqrt(5)),1/2*(1+sqrt(5));1/4*(5+3*sqrt(5)),1/4*(5+sqrt(5)),1/2*(-1-sqrt(5));1/4*(5+3*sqrt(5)),1/4*(5+sqrt(5)),1/2*(1+sqrt(5));1/4*(7+3*sqrt(5)),-1,1/4*(-3-sqrt(5));1/4*(7+3*sqrt(5)),-1,1/4*(3+sqrt(5));1/4*(7+3*sqrt(5)),1,1/4*(-3-sqrt(5));1/4*(7+3*sqrt(5)),1,1/4*(3+sqrt(5))];
Polyhedron.edge=[1,5;1,11;1,41;2,6;2,12;2,42;3,7;3,15;3,43;4,8;4,16;4,44;5,7;5,17;6,8;6,18;7,19;8,20;9,10;9,21;9,45;10,22;10,46;11,23;11,47;12,24;12,48;13,14;13,25;13,51;14,26;14,52;15,27;15,49;16,28;16,50;17,19;17,29;18,20;18,30;19,31;20,32;21,22;21,93;22,94;23,29;23,95;24,30;24,96;25,26;25,99;26,100;27,31;27,97;28,32;28,98;29,109;30,110;31,111;32,112;33,37;33,57;33,65;34,38;34,58;34,66;35,39;35,59;35,67;36,40;36,60;36,68;37,53;37,73;38,54;38,74;39,55;39,75;40,56;40,76;41,47;41,53;42,48;42,54;43,49;43,55;44,50;44,56;45,61;45,69;46,62;46,70;47,61;48,62;49,63;50,64;51,63;51,71;52,64;52,72;53,65;54,66;55,67;56,68;57,58;57,59;58,60;59,60;61,73;62,74;63,75;64,76;65,67;66,68;69,70;69,73;70,74;71,72;71,75;72,76;77,81;77,93;77,95;78,82;78,94;78,96;79,83;79,97;79,99;80,84;80,98;80,100;81,89;81,113;82,90;82,114;83,91;83,115;84,92;84,116;85,86;85,87;85,117;86,88;86,118;87,88;87,119;88,120;89,90;89,93;90,94;91,92;91,99;92,100;95,109;96,110;97,111;98,112;101,105;101,109;101,113;102,106;102,110;102,114;103,107;103,111;103,115;104,108;104,112;104,116;105,107;105,117;106,108;106,118;107,119;108,120;113,117;114,118;115,119;116,120];
Polyhedron.face={[2,6,8,4,44,56,68,66,54,42];[109,29,17,19,31,111,103,107,105,101];[24,30,18,6,2,12];[7,3,15,27,31,19];[58,57,33,37,73,69,70,74,38,34];[84,116,120,88,87,119,115,83,91,92];[90,89,81,113,117,85,86,118,114,82];[36,40,76,72,71,75,39,35,59,60];[5,17,29,23,11,1];[4,8,20,32,28,16];[67,55,43,3,7,5,1,41,53,65];[18,30,110,102,106,108,104,112,32,20];[79,83,115,103,111,97];[38,74,62,48,42,54];[4,16,50,44];[23,29,109,95];[96,110,30,24];[43,49,15,3];[53,41,47,61,73,37];[98,112,104,116,84,80];[69,45,9,10,46,70];[26,100,92,91,99,25];[82,114,102,110,96,78];[55,39,75,63,49,43];[1,11,47,41];[28,32,112,98];[61,47,11,23,95,77,93,21,9,45];[50,16,28,98,80,100,26,14,52,64];[97,111,31,27];[42,48,12,2];[44,50,64,76,40,56];[77,95,109,101,113,81];[63,51,13,25,99,79,97,27,15,49];[46,10,22,94,78,96,24,12,48,62];[52,14,13,51,71,72];[22,21,93,89,90,94];[115,119,107,103];[34,38,54,66];[71,51,63,75];[94,90,82,78];[114,118,106,102];[35,39,55,67];[70,46,62,74];[99,91,83,79];[65,53,37,33];[104,108,120,116];[77,81,89,93];[76,64,52,72];[59,35,67,65,33,57];[106,118,86,88,120,108];[68,56,40,36];[101,105,117,113];[80,84,92,100];[73,61,45,69];[34,66,68,36,60,58];[105,107,119,87,85,117];[7,19,17,5];[6,18,20,8];[14,26,25,13];[9,21,22,10];[58,60,59,57];[85,87,88,86]};
case {'triangular prism'}
Polyhedron.node=([0 0 0;1 0 0;1/2 sqrt(3)/2 0;0 0 1;1 0 1;1/2 sqrt(3)/2 1]);
Polyhedron.edge=[1 2;2 3;3 1;4 5;5 6;6 4;1 4;2 5;3 6];
Polyhedron.face={[1 2 5 4];[2 3 6 5];[3 1 4 6];[3 2 1];[4 5 6]};
case {'hexagonal prism'}
Polyhedron.node=([0 0 0;1 0 0; 1.5 sqrt(3)/2 0;1 sqrt(3) 0;0 sqrt(3) 0;-0.5 sqrt(3)/2 0;0 0 1;1 0 1;1.5 sqrt(3)/2 1;1 sqrt(3) 1;0 sqrt(3) 1;-0.5 sqrt(3)/2 1]);
Polyhedron.edge=[1 2;2 3;3 4;4 5;5 6;6 1;7 8;8 9;9 10;10 11;11 12;12 7;1 7;2 8;3 9;4 10;5 11;6 12];
Polyhedron.face={[6 5 4 3 2 1];[7 8 9 10 11 12];[1 2 8 7];[2 3 9 8];[3 4 10 9];[4 5 11 10];[5 6 12 11];[6 1 7 12]};
case {'octagonal prism'}
Polyhedron.node=[0,-(1/2)*csc(pi/8),-(1/2);0,-(1/2)*csc(pi/8),1/2;0,1/2*csc(pi/8),-(1/2);0,1/2*csc(pi/8),1/2;-(1/2)*csc(pi/8),0,-(1/2);-(1/2)*csc(pi/8),0,1/2;1/2*csc(pi/8),0,-(1/2);1/2*csc(pi/8),0,1/2;-(csc(pi/8)/(2*sqrt(2))),-(csc(pi/8)/(2*sqrt(2))),-(1/2);-(csc(pi/8)/(2*sqrt(2))),-(csc(pi/8)/(2*sqrt(2))),1/2;-(csc(pi/8)/(2*sqrt(2))),csc(pi/8)/(2*sqrt(2)),-(1/2);-(csc(pi/8)/(2*sqrt(2))),csc(pi/8)/(2*sqrt(2)),1/2;csc(pi/8)/(2*sqrt(2)),-(csc(pi/8)/(2*sqrt(2))),-(1/2);csc(pi/8)/(2*sqrt(2)),-(csc(pi/8)/(2*sqrt(2))),1/2;csc(pi/8)/(2*sqrt(2)),csc(pi/8)/(2*sqrt(2)),-(1/2);csc(pi/8)/(2*sqrt(2)),csc(pi/8)/(2*sqrt(2)),1/2];
Polyhedron.edge=[1,2;1,9;1,13;2,10;2,14;3,4;3,11;3,15;4,12;4,16;5,6;5,9;5,11;6,10;6,12;7,8;7,13;7,15;8,14;8,16;9,10;11,12;13,14;15,16];
Polyhedron.face={[13,1,9,5,11,3,15,7];[8,16,4,12,6,10,2,14];[7,15,16,8];[15,3,4,16];[3,11,12,4];[11,5,6,12];[5,9,10,6];[9,1,2,10];[1,13,14,2];[13,7,8,14]};
n=length(Polyhedron.face);
case {'decagonal prism'}
theta=(0:2*pi/12:2*pi);r=1/(2*acos(2*pi/12));x=r^2*cos(theta);y=r^2*sin(theta);
Polyhedron.node=[[x(1:12)';x(1:12)'],[y(1:12)';y(1:12)'],[zeros(12,1);ones(12,1)]];
Polyhedron.edge=[1 2; 2 3; 3 4; 4 5; 5 6; 6 7; 7 8; 8 9; 9 10; 10 11; 11 12; 12 1; 13 14; 14 15; 15 16; 16 17; 17 18; 18 19; 19 20; 20 21; 21 22; 22 23; 23 24; 24 13; 1 13; 2 14; 3 15; 4 16; 5 17; 6 18; 7 19; 8 20; 9 21; 10 22; 11 23; 12 24];
Polyhedron.face={[12:-1:1];[13:24];[1 2 14 13];[2 3 15 14];[3 4 16 15];[4 5 17 16];[5 6 18 17];[6 7 19 18];[7 8 20 19];[8 9 21 20];[9 10 22 21];[10 11 23 22];[11 12 24 23];[12 1 13 24]};
Polyhedron.node(:,1:2)=Polyhedron.node(:,1:2)/norm(Polyhedron.node(1,:)-Polyhedron.node(2,:));
case {'rhombic triacontahedron'}
aa=2;bb=sqrt(5)-1;cc=sqrt(aa^2/4+bb^2/4);dd=aa*bb/(2*cc);
z1=sqrt((aa/2)^2-(bb/(2*tan(36*pi/180)))^2); z2=2*z1; z3=3*z1; z4=cc+z2; z5=z3+cc; z6=z5+z1;z7=z5+z2;
r1=bb/(2*cos(54*pi/180)); r2=aa/(2*cos(54*pi/180)); r3=dd/(2*sin(18*pi/180));
Polyhedron.node=[0,r1,z1;r1*cos(18*pi/180),r1*sin(18*pi/180),z1;r1*cos(54*pi/180),-r1*sin(54*pi/180),z1;-r1*cos(54*pi/180),-r1*sin(54*pi/180),z1;-r1*cos(18*pi/180),r1*sin(18*pi/180),z1;...
r2*cos(54*pi/180),r2*sin(54*pi/180),z2; r2*cos(18*pi/180),-r2*sin(18*pi/180),z2; 0,-r2,z2; -r2*cos(18*pi/180),-r2*sin(18*pi/180),z2; -r2*cos(54*pi/180),r2*sin(54*pi/180),z2;...
0,r3,z3;r3*cos(18*pi/180),r3*sin(18*pi/180),z3;r3*cos(54*pi/180),-r3*sin(54*pi/180),z3;-r3*cos(54*pi/180),-r3*sin(54*pi/180),z3;-r3*cos(18*pi/180),r3*sin(18*pi/180),z3;...
r2*cos(54*pi/180),r2*sin(54*pi/180),z4; r2*cos(18*pi/180),-r2*sin(18*pi/180),z4; 0,-r2,z4; -r2*cos(18*pi/180),-r2*sin(18*pi/180),z4; -r2*cos(54*pi/180),r2*sin(54*pi/180),z4;...
0,r3,z5;r3*cos(18*pi/180),r3*sin(18*pi/180),z5;r3*cos(54*pi/180),-r3*sin(54*pi/180),z5;-r3*cos(54*pi/180),-r3*sin(54*pi/180),z5;-r3*cos(18*pi/180),r3*sin(18*pi/180),z5;...
r1*cos(54*pi/180),r1*sin(54*pi/180),z6; r1*cos(18*pi/180),-r1*sin(18*pi/180),z6; 0,-r1,z6; -r1*cos(18*pi/180),-r1*sin(18*pi/180),z6; -r1*cos(54*pi/180),r1*sin(54*pi/180),z6;...
0,0,0;0,0,z7];
Polyhedron.edge=[1 31;2 31;3 31;4 31;5 31;...
1 6; 2 6;2 7;3 7;3 8;4 8;4 9;5 9;5 10;1 10;...
6 11;6 12;7 12;7 13;8 13;8 14;9 14;9 15;10 15;10 11;...
11 21;6 16;12 22;7 17;13 23;8 18;14 24;9 19;15 25;10 20;...
16 21;16 22;17 22;17 23;18 23;18 24;19 24;19 25;20 25;20 21;...
21 26;22 26;22 27;23 27;23 28;24 28;24 29;25 29;25 30;21 30;...
26 32;27 32;28 32; 29 32;30 32;] ;
Polyhedron.face={[31 1 6 2] ; [31 2 7 3]; [31 3 8 4];[31 4 9 5];[31 5 10 1];...
[1 10 11 6]; [2 6 12 7]; [3 7 13 8 ];[4 8 14 9];[5 9 15 10];...
[6 11 21 16]; [6 16 22 12];[7 12 22 17];[7 17 23 13];[8 13 23 18];...
[8 18 24 14]; [9 14 24 19];[9 19 25 15];[10 15 25 20];[10 20 21 11];...
[16 21 26 22];[17 22 27 23];[18 23 28 24];[19 24 29 25];[20 25 30 21];...
[21 30 32 26];[22 26 32 27];[23 27 32 28];[24 28 32 29];[25 29 32 30]};
case {'rhombic dodecahedron'}
node1=[-sqrt(2)/2,0,0]; node2=[0,-1/2,0]; node3=[sqrt(2)/2,0,0];node4=[0,1/2,0]; vector37=[0,-1/2,sqrt(2)/2]; vector38=[0,1/2,sqrt(2)/2];
node5=node1+vector37;node6=node2+vector37;node7=node3+vector37; node8=node3+vector38; node9=node4+vector38; node10=node1+vector38;
node11=node5+vector38; node12=node6+vector38; node13=node7+vector38; node14=node9+vector37;
Polyhedron.node=1.5*[node1;node2;node3;node4;node5;node6;node7;node8;node9;node10;node11;node12;node13;node14];
Polyhedron.edge=[1,2; 2,3; 3,4; 4,1; 1,5; 2,6; 3,7; 3,8; 4,9; 1,10; 5,11; 6,12; 7,13; 8,13; 9,14; 10,11; 11,12; 12,13; 13,14; 14,11];
Polyhedron.face={[1 ,4, 3, 2];[1,2, 6,5]; [3,7,6,2];[3,8,13,7];[3,4,9,8];[4,1,10,9];[1,5,11,10];[5,6,12,11];[6,7,13,12];[8,9,14,13];[9,10,11,14];[11,12,13,14]};
otherwise
error('Geometry does not excist\n')
end
Polyhedron.nFace=length(Polyhedron.face);
Polyhedron.nEdge=size(Polyhedron.edge,1);
end