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polyhedrons_catalan.jscad
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polyhedrons_catalan.jscad
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// title : Polyhedrons : Catalan solids
// author : Gilbert Duval
// license : MIT License
// revision : 0.001
// tags : polyhedron
// file : polyhedrons_catalan.jscad
// Data from dmccooey.com/polyhedra
// Library to include with : include("polyhedrons_catalan.jscad");
// Instanciate before use : polyh3();
polyh3 = function () {
polyh3.triakis_tetrahedron = function (){
// http://dmccooey.com/polyhedra/TriakisTetrahedron.html
var C0, C1, vertices, faces;
C0 = 9 * sqrt(2) / 20;
C1 = 3 * sqrt(2) / 4;
vertices = [
[ C1, C1, C1],
[ C1, -C1, -C1],
[-C1, -C1, C1],
[-C1, C1, -C1],
[ C0, -C0, C0],
[ C0, C0, -C0],
[-C0, C0, C0],
[-C0, -C0, -C0]
];
faces = [
[4, 0, 2],
[4, 2, 1],
[4, 1, 0],
[5, 0, 1],
[5, 1, 3],
[5, 3, 0],
[6, 0, 3],
[6, 3, 2],
[6, 2, 0],
[7, 1, 2],
[7, 2, 3],
[7, 3, 1]
];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.rhombic_dodecahedron = function (){
// http://dmccooey.com/polyhedra/RhombicDodecahedron.html
var C0, C1, vertices, faces;
C0 = 3 * sqrt(2) / 8;
C1 = 3 * sqrt(2) / 4;
vertices = [
[0.0, 0.0, C1],
[0.0, 0.0, -C1],
[ C1, 0.0, 0.0],
[-C1, 0.0, 0.0],
[0.0, C1, 0.0],
[0.0, -C1, 0.0],
[ C0, C0, C0],
[ C0, C0, -C0],
[ C0, -C0, C0],
[ C0, -C0, -C0],
[-C0, C0, C0],
[-C0, C0, -C0],
[-C0, -C0, C0],
[-C0, -C0, -C0]];
faces = [
[6, 0, 8, 2],
[6, 2, 7, 4],
[6, 4, 10, 0],
[9, 1, 7, 2],
[9, 2, 8, 5],
[9, 5, 13, 1],
[11, 1, 13, 3],
[11, 3, 10, 4],
[11, 4, 7, 1],
[12, 0, 10, 3],
[12, 3, 13, 5],
[12, 5, 8, 0]];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.tetrakis_hexahedron = function (){
// http://dmccooey.com/polyhedra/TetrakisHexahedron.html
var C0, C1, vertices, faces;
C0 = 3 * sqrt(2) / 4;
C1 = 9 * sqrt(2) / 8;
vertices = [
[0.0, 0.0, C1],
[0.0, 0.0, -C1],
[ C1, 0.0, 0.0],
[-C1, 0.0, 0.0],
[0.0, C1, 0.0],
[0.0, -C1, 0.0],
[ C0, C0, C0],
[ C0, C0, -C0],
[ C0, -C0, C0],
[ C0, -C0, -C0],
[-C0, C0, C0],
[-C0, C0, -C0],
[-C0, -C0, C0],
[-C0, -C0, -C0]];
faces = [
[0, 6, 10],
[0, 10, 12],
[0, 12, 8],
[0, 8, 6],
[1, 7, 9],
[1, 9, 13],
[1, 13, 11],
[1, 11, 7],
[2, 6, 8],
[2, 8, 9],
[2, 9, 7],
[2, 7, 6],
[3, 10, 11],
[3, 11, 13],
[3, 13, 12],
[3, 12, 10],
[4, 6, 7],
[4, 7, 11],
[4, 11, 10],
[4, 10, 6],
[5, 8, 12],
[5, 12, 13],
[5, 13, 9],
[5, 9, 8]
];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.triakis_octahedron = function (){
// http://dmccooey.com/polyhedra/TriakisOctahedron.html
var C0, vertices, faces;
C0 = 1 + sqrt(2);
vertices = [
[ 0.0, 0.0, C0],
[ 0.0, 0.0, -C0],
[ C0, 0.0, 0.0],
[ -C0, 0.0, 0.0],
[ 0.0, C0, 0.0],
[ 0.0, -C0, 0.0],
[ 1.0, 1.0, 1.0],
[ 1.0, 1.0, -1.0],
[ 1.0, -1.0, 1.0],
[ 1.0, -1.0, -1.0],
[-1.0, 1.0, 1.0],
[-1.0, 1.0, -1.0],
[-1.0, -1.0, 1.0],
[-1.0, -1.0, -1.0]];
faces =[
[6, 0, 2],
[6, 2, 4],
[6, 4, 0],
[7, 1, 4],
[7, 4, 2],
[7, 2, 1],
[8, 0, 5],
[8, 5, 2],
[8, 2, 0],
[9, 1, 2],
[9, 2, 5],
[9, 5, 1],
[10, 0, 4],
[10, 4, 3],
[10, 3, 0],
[11, 1, 3],
[11, 3, 4],
[11, 4, 1],
[12, 0, 3],
[12, 3, 5],
[12, 5, 0],
[13, 1, 5],
[13, 5, 3],
[13, 3, 1]
];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.deltoidal_icositetrahedron = function (){
// http://dmccooey.com/polyhedra/DeltoidalIcositetrahedron.html
var C0, C1, vertices, faces;
C0 = (4 + sqrt(2)) / 7;
C1 = sqrt(2);
vertices = [
[ 0.0, 0.0, C1],
[ 0.0, 0.0, -C1],
[ C1, 0.0, 0.0],
[ -C1, 0.0, 0.0],
[ 0.0, C1, 0.0],
[ 0.0, -C1, 0.0],
[ 1.0, 0.0, 1.0],
[ 1.0, 0.0, -1.0],
[-1.0, 0.0, 1.0],
[-1.0, 0.0, -1.0],
[ 1.0, 1.0, 0.0],
[ 1.0, -1.0, 0.0],
[-1.0, 1.0, 0.0],
[-1.0, -1.0, 0.0],
[ 0.0, 1.0, 1.0],
[ 0.0, 1.0, -1.0],
[ 0.0, -1.0, 1.0],
[ 0.0, -1.0, -1.0],
[ C0, C0, C0],
[ C0, C0, -C0],
[ C0, -C0, C0],
[ C0, -C0, -C0],
[ -C0, C0, C0],
[ -C0, C0, -C0],
[ -C0, -C0, C0],
[ -C0, -C0, -C0]];
faces= [
[0, 6, 18, 14],
[0, 14, 22, 8],
[0, 8, 24, 16],
[0, 16, 20, 6],
[1, 9, 23, 15],
[1, 15, 19, 7],
[1, 7, 21, 17],
[1, 17, 25, 9],
[2, 7, 19, 10],
[2, 10, 18, 6],
[2, 6, 20, 11],
[2, 11, 21, 7],
[3, 8, 22, 12],
[3, 12, 23, 9],
[3, 9, 25, 13],
[3, 13, 24, 8],
[4, 10, 19, 15],
[4, 15, 23, 12],
[4, 12, 22, 14],
[4, 14, 18, 10],
[5, 11, 20, 16],
[5, 16, 24, 13],
[5, 13, 25, 17],
[5, 17, 21, 11]];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.pentagonal_icositetrahedron_dextro = function (){
// http://dmccooey.com/polyhedra/RpentagonalIcositetrahedron.html
var C0, C1, C2, C3, C4, vertices, faces;
C0 = sqrt(6 * (Math.cbrt(6*(9 + sqrt(33))) + Math.cbrt(6*(9 - sqrt(33))) - 6)) / 12;
C1 = sqrt(6 * (6 + Math.cbrt(6*(9 + sqrt(33))) + Math.cbrt(6*(9 - sqrt(33))))) / 12;
C2 = sqrt(6 * (18 + Math.cbrt(6*(9 + sqrt(33))) + Math.cbrt(6*(9 - sqrt(33))))) / 12;
C3 = sqrt(6 * (14+Math.cbrt(2*(1777+33*sqrt(33)))+Math.cbrt(2*(1777-33*sqrt(33))))) / 12;
vertices = [
[0.0, 0.0, C3],
[0.0, 0.0, -C3],
[ C3, 0.0, 0.0],
[-C3, 0.0, 0.0],
[0.0, C3, 0.0],
[0.0, -C3, 0.0],
[ C1, -C0, C2],
[ C1, C0, -C2],
[-C1, C0, C2],
[-C1, -C0, -C2],
[ C2, -C1, C0],
[ C2, C1, -C0],
[-C2, C1, C0],
[-C2, -C1, -C0],
[ C0, -C2, C1],
[ C0, C2, -C1],
[-C0, C2, C1],
[-C0, -C2, -C1],
[ C0, C1, C2],
[ C0, -C1, -C2],
[-C0, -C1, C2],
[-C0, C1, -C2],
[ C2, C0, C1],
[ C2, -C0, -C1],
[-C2, -C0, C1],
[-C2, C0, -C1],
[ C1, C2, C0],
[ C1, -C2, -C0],
[-C1, -C2, C0],
[-C1, C2, -C0],
[ C1, C1, C1],
[ C1, C1, -C1],
[ C1, -C1, C1],
[ C1, -C1, -C1],
[-C1, C1, C1],
[-C1, C1, -C1],
[-C1, -C1, C1],
[-C1, -C1, -C1]];
faces = [
[0, 6, 22, 30, 18],
[0, 18, 16, 34, 8],
[0, 8, 24, 36, 20],
[0, 20, 14, 32, 6],
[1, 7, 23, 33, 19],
[1, 19, 17, 37, 9],
[1, 9, 25, 35, 21],
[1, 21, 15, 31, 7],
[2, 10, 27, 33, 23],
[2, 23, 7, 31, 11],
[2, 11, 26, 30, 22],
[2, 22, 6, 32, 10],
[3, 12, 29, 35, 25],
[3, 25, 9, 37, 13],
[3, 13, 28, 36, 24],
[3, 24, 8, 34, 12],
[4, 15, 21, 35, 29],
[4, 29, 12, 34, 16],
[4, 16, 18, 30, 26],
[4, 26, 11, 31, 15],
[5, 14, 20, 36, 28],
[5, 28, 13, 37, 17],
[5, 17, 19, 33, 27],
[5, 27, 10, 32, 14]
];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.pentagonal_icositetrahedron_laevo = function (){
// http://dmccooey.com/polyhedra/LpentagonalIcositetrahedron.html
var C0, C1, C2, C3, vertices, faces;
C0 = sqrt(6 * (Math.cbrt(6*(9 + sqrt(33))) + Math.cbrt(6*(9 - sqrt(33))) - 6)) / 12;
C1 = sqrt(6 * (6 + Math.cbrt(6*(9 + sqrt(33))) + Math.cbrt(6*(9 - sqrt(33))))) / 12;
C2 = sqrt(6 * (18 + Math.cbrt(6*(9 + sqrt(33))) + Math.cbrt(6*(9 - sqrt(33))))) / 12;
C3 = sqrt(6 * (14+Math.cbrt(2*(1777+33*sqrt(33)))+Math.cbrt(2*(1777-33*sqrt(33))))) / 12;
vertices = [
[0.0, 0.0, -C3],
[0.0, 0.0, C3],
[-C3, 0.0, 0.0],
[ C3, 0.0, 0.0],
[0.0, -C3, 0.0],
[0.0, C3, 0.0],
[-C1, C0, -C2],
[-C1, -C0, C2],
[ C1, -C0, -C2],
[ C1, C0, C2],
[-C2, C1, -C0],
[-C2, -C1, C0],
[ C2, -C1, -C0],
[ C2, C1, C0],
[-C0, C2, -C1],
[-C0, -C2, C1],
[ C0, -C2, -C1],
[ C0, C2, C1],
[-C0, -C1, -C2],
[-C0, C1, C2],
[ C0, C1, -C2],
[ C0, -C1, C2],
[-C2, -C0, -C1],
[-C2, C0, C1],
[ C2, C0, -C1],
[ C2, -C0, C1],
[-C1, -C2, -C0],
[-C1, C2, C0],
[ C1, C2, -C0],
[ C1, -C2, C0],
[-C1, -C1, -C1],
[-C1, -C1, C1],
[-C1, C1, -C1],
[-C1, C1, C1],
[ C1, -C1, -C1],
[ C1, -C1, C1],
[ C1, C1, -C1],
[ C1, C1, C1]];
faces = [
[0, 18, 30, 22, 6],
[0, 8, 34, 16, 18],
[0, 20, 36, 24, 8],
[0, 6, 32, 14, 20],
[1, 19, 33, 23, 7],
[1, 9, 37, 17, 19],
[1, 21, 35, 25, 9],
[1, 7, 31, 15, 21],
[2, 23, 33, 27, 10],
[2, 11, 31, 7, 23],
[2, 22, 30, 26, 11],
[2, 10, 32, 6, 22],
[3, 25, 35, 29, 12],
[3, 13, 37, 9, 25],
[3, 24, 36, 28, 13],
[3, 12, 34, 8, 24],
[4, 29, 35, 21, 15],
[4, 16, 34, 12, 29],
[4, 26, 30, 18, 16],
[4, 15, 31, 11, 26],
[5, 28, 36, 20, 14],
[5, 17, 37, 13, 28],
[5, 27, 33, 19, 17],
[5, 14, 32, 10, 27]
];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.rhombic_triacontahedron = function (){
// http://dmccooey.com/polyhedra/RhombicTriacontahedron.html
var C0, C1, C2, vertices, faces;
C0 = sqrt(5) / 4;
C1 = (5 + sqrt(5)) / 8;
C2 = (5 + 3 * sqrt(5)) / 8;
vertices = [
[ C1, 0.0, C2],
[ C1, 0.0, -C2],
[-C1, 0.0, C2],
[-C1, 0.0, -C2],
[ C2, C1, 0.0],
[ C2, -C1, 0.0],
[-C2, C1, 0.0],
[-C2, -C1, 0.0],
[0.0, C2, C1],
[0.0, C2, -C1],
[0.0, -C2, C1],
[0.0, -C2, -C1],
[0.0, C0, C2],
[0.0, C0, -C2],
[0.0, -C0, C2],
[0.0, -C0, -C2],
[ C2, 0.0, C0],
[ C2, 0.0, -C0],
[-C2, 0.0, C0],
[-C2, 0.0, -C0],
[ C0, C2, 0.0],
[ C0, -C2, 0.0],
[-C0, C2, 0.0],
[-C0, -C2, 0.0],
[ C1, C1, C1],
[ C1, C1, -C1],
[ C1, -C1, C1],
[ C1, -C1, -C1],
[-C1, C1, C1],
[-C1, C1, -C1],
[-C1, -C1, C1],
[-C1, -C1, -C1]];
faces = [
[0, 12, 2, 14],
[0, 14, 10, 26],
[0, 26, 5, 16],
[1, 13, 9, 25],
[1, 25, 4, 17],
[1, 17, 5, 27],
[2, 28, 6, 18],
[2, 18, 7, 30],
[2, 30, 10, 14],
[3, 19, 6, 29],
[3, 29, 9, 13],
[3, 13, 1, 15],
[4, 20, 8, 24],
[4, 24, 0, 16],
[4, 16, 5, 17],
[7, 18, 6, 19],
[7, 19, 3, 31],
[7, 31, 11, 23],
[8, 22, 6, 28],
[8, 28, 2, 12],
[8, 12, 0, 24],
[9, 29, 6, 22],
[9, 22, 8, 20],
[9, 20, 4, 25],
[10, 30, 7, 23],
[10, 23, 11, 21],
[10, 21, 5, 26],
[11, 31, 3, 15],
[11, 15, 1, 27],
[11, 27, 5, 21]
];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.disdyakis_dodecahedron = function (){
// http://dmccooey.com/polyhedra/DisdyakisDodecahedron.html
var C0, C1, C2, vertices, faces;
C0 = sqrt(2);
C1 = (3 + 6 * sqrt(2)) / 7;
C2 = (6 + 9 * sqrt(2)) / 7;
vertices = [
[0.0, 0.0, C2],
[0.0, 0.0, -C2],
[ C2, 0.0, 0.0],
[-C2, 0.0, 0.0],
[0.0, C2, 0.0],
[0.0, -C2, 0.0],
[ C1, 0.0, C1],
[ C1, 0.0, -C1],
[-C1, 0.0, C1],
[-C1, 0.0, -C1],
[ C1, C1, 0.0],
[ C1, -C1, 0.0],
[-C1, C1, 0.0],
[-C1, -C1, 0.0],
[0.0, C1, C1],
[0.0, C1, -C1],
[0.0, -C1, C1],
[0.0, -C1, -C1],
[ C0, C0, C0],
[ C0, C0, -C0],
[ C0, -C0, C0],
[ C0, -C0, -C0],
[-C0, C0, C0],
[-C0, C0, -C0],
[-C0, -C0, C0],
[-C0, -C0, -C0]];
faces = [
[0, 6, 18],
[0, 18, 14],
[0, 14, 22],
[0, 22, 8],
[0, 8, 24],
[0, 24, 16],
[0, 16, 20],
[0, 20, 6],
[1, 7, 21],
[1, 21, 17],
[1, 17, 25],
[1, 25, 9],
[1, 9, 23],
[1, 23, 15],
[1, 15, 19],
[1, 19, 7],
[2, 6, 20],
[2, 20, 11],
[2, 11, 21],
[2, 21, 7],
[2, 7, 19],
[2, 19, 10],
[2, 10, 18],
[2, 18, 6],
[3, 8, 22],
[3, 22, 12],
[3, 12, 23],
[3, 23, 9],
[3, 9, 25],
[3, 25, 13],
[3, 13, 24],
[3, 24, 8],
[4, 10, 19],
[4, 19, 15],
[4, 15, 23],
[4, 23, 12],
[4, 12, 22],
[4, 22, 14],
[4, 14, 18],
[4, 18, 10],
[5, 11, 20],
[5, 20, 16],
[5, 16, 24],
[5, 24, 13],
[5, 13, 25],
[5, 25, 17],
[5, 17, 21],
[5, 21, 11]
];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.pentakis_dodecahedron = function (){
// http://dmccooey.com/polyhedra/PentakisDodecahedron.html
var C0, C1, C2, C3, vertices, faces;
C0 = 3 * (sqrt(5) - 1) / 4;
C1 = 9 * (9 + sqrt(5)) / 76;
C2 = 9 * (7 + 5 * sqrt(5)) / 76;
C3 = 3 * (1 + sqrt(5)) / 4;
vertices = [
[ 0.0, C0, C3],
[ 0.0, C0, -C3],
[ 0.0, -C0, C3],
[ 0.0, -C0, -C3],
[ C3, 0.0, C0],
[ C3, 0.0, -C0],
[ -C3, 0.0, C0],
[ -C3, 0.0, -C0],
[ C0, C3, 0.0],
[ C0, -C3, 0.0],
[ -C0, C3, 0.0],
[ -C0, -C3, 0.0],
[ C1, 0.0, C2],
[ C1, 0.0, -C2],
[ -C1, 0.0, C2],
[ -C1, 0.0, -C2],
[ C2, C1, 0.0],
[ C2, -C1, 0.0],
[ -C2, C1, 0.0],
[ -C2, -C1, 0.0],
[ 0.0, C2, C1],
[ 0.0, C2, -C1],
[ 0.0, -C2, C1],
[ 0.0, -C2, -C1],
[ 1.5, 1.5, 1.5],
[ 1.5, 1.5, -1.5],
[ 1.5, -1.5, 1.5],
[ 1.5, -1.5, -1.5],
[-1.5, 1.5, 1.5],
[-1.5, 1.5, -1.5],
[-1.5, -1.5, 1.5],
[-1.5, -1.5, -1.5]];
faces = [
[12, 0, 2],
[12, 2, 26],
[12, 26, 4],
[12, 4, 24],
[12, 24, 0],
[13, 3, 1],
[13, 1, 25],
[13, 25, 5],
[13, 5, 27],
[13, 27, 3],
[14, 2, 0],
[14, 0, 28],
[14, 28, 6],
[14, 6, 30],
[14, 30, 2],
[15, 1, 3],
[15, 3, 31],
[15, 31, 7],
[15, 7, 29],
[15, 29, 1],
[16, 4, 5],
[16, 5, 25],
[16, 25, 8],
[16, 8, 24],
[16, 24, 4],
[17, 5, 4],
[17, 4, 26],
[17, 26, 9],
[17, 9, 27],
[17, 27, 5],
[18, 7, 6],
[18, 6, 28],
[18, 28, 10],
[18, 10, 29],
[18, 29, 7],
[19, 6, 7],
[19, 7, 31],
[19, 31, 11],
[19, 11, 30],
[19, 30, 6],
[20, 8, 10],
[20, 10, 28],
[20, 28, 0],
[20, 0, 24],
[20, 24, 8],
[21, 10, 8],
[21, 8, 25],
[21, 25, 1],
[21, 1, 29],
[21, 29, 10],
[22, 11, 9],
[22, 9, 26],
[22, 26, 2],
[22, 2, 30],
[22, 30, 11],
[23, 9, 11],
[23, 11, 31],
[23, 31, 3],
[23, 3, 27],
[23, 27, 9]];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.triakis_icosahedron = function (){
// http://dmccooey.com/polyhedra/TriakisIcosahedron.html
var C0, C1, C2, C3, C4, vertices, faces;
C0 = 5 * (7 + sqrt(5)) / 44;
C1 = 5 * (3 + 2 * sqrt(5)) / 22;
C2 = (5 + sqrt(5)) / 4;
C3 = 5 * (13 + 5 * sqrt(5)) / 44;
C4 = (5 + 3 * sqrt(5)) / 4;
vertices = [
[ C2, 0.0, C4],
[ C2, 0.0, -C4],
[-C2, 0.0, C4],
[-C2, 0.0, -C4],
[ C4, C2, 0.0],
[ C4, -C2, 0.0],
[-C4, C2, 0.0],
[-C4, -C2, 0.0],
[0.0, C4, C2],
[0.0, C4, -C2],
[0.0, -C4, C2],
[0.0, -C4, -C2],
[0.0, C0, C3],
[0.0, C0, -C3],
[0.0, -C0, C3],
[0.0, -C0, -C3],
[ C3, 0.0, C0],
[ C3, 0.0, -C0],
[-C3, 0.0, C0],
[-C3, 0.0, -C0],
[ C0, C3, 0.0],
[ C0, -C3, 0.0],
[-C0, C3, 0.0],
[-C0, -C3, 0.0],
[ C1, C1, C1],
[ C1, C1, -C1],
[ C1, -C1, C1],
[ C1, -C1, -C1],
[-C1, C1, C1],
[-C1, C1, -C1],
[-C1, -C1, C1],
[-C1, -C1, -C1]];
faces = [
[12, 0, 8],
[12, 8, 2],
[12, 2, 0],
[13, 1, 3],
[13, 3, 9],
[13, 9, 1],
[14, 0, 2],
[14, 2, 10],
[14, 10, 0],
[15, 1, 11],
[15, 11, 3],
[15, 3, 1],
[16, 0, 5],
[16, 5, 4],
[16, 4, 0],
[17, 1, 4],
[17, 4, 5],
[17, 5, 1],
[18, 2, 6],
[18, 6, 7],
[18, 7, 2],
[19, 3, 7],
[19, 7, 6],
[19, 6, 3],
[20, 4, 9],
[20, 9, 8],
[20, 8, 4],
[21, 5, 10],
[21, 10, 11],
[21, 11, 5],
[22, 6, 8],
[22, 8, 9],
[22, 9, 6],
[23, 7, 11],
[23, 11, 10],
[23, 10, 7],
[24, 0, 4],
[24, 4, 8],
[24, 8, 0],
[25, 1, 9],
[25, 9, 4],
[25, 4, 1],
[26, 0, 10],
[26, 10, 5],
[26, 5, 0],
[27, 1, 5],
[27, 5, 11],
[27, 11, 1],
[28, 2, 8],
[28, 8, 6],
[28, 6, 2],
[29, 3, 6],
[29, 6, 9],
[29, 9, 3],
[30, 2, 7],
[30, 7, 10],
[30, 10, 2],
[31, 3, 11],
[31, 11, 7],
[31, 7, 3]];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.deltoidal_hexecontahedron = function (){
// http://dmccooey.com/polyhedra/DeltoidalHexecontahedron.html
var C0, C1, C2, C3, C4, C5, C6, C7, C8, vertices, faces;
C0 = (5 - sqrt(5)) / 4;
C1 = (15 + sqrt(5)) / 22;
C2 = sqrt(5) / 2;
C3 = (5 + sqrt(5)) / 6;
C4 = (5 + 4 * sqrt(5)) / 11;
C5 = (5 + sqrt(5)) / 4;
C6 = (5 + 3 * sqrt(5)) / 6;
C7 = (25 + 9 * sqrt(5)) / 22;
C8 = sqrt(5);
vertices = [
[0.0, 0.0, C8],
[0.0, 0.0, -C8],
[ C8, 0.0, 0.0],
[-C8, 0.0, 0.0],
[0.0, C8, 0.0],
[0.0, -C8, 0.0],
[0.0, C1, C7],
[0.0, C1, -C7],
[0.0, -C1, C7],
[0.0, -C1, -C7],
[ C7, 0.0, C1],
[ C7, 0.0, -C1],
[-C7, 0.0, C1],
[-C7, 0.0, -C1],
[ C1, C7, 0.0],
[ C1, -C7, 0.0],
[-C1, C7, 0.0],
[-C1, -C7, 0.0],
[ C3, 0.0, C6],
[ C3, 0.0, -C6],
[-C3, 0.0, C6],
[-C3, 0.0, -C6],
[ C6, C3, 0.0],
[ C6, -C3, 0.0],
[-C6, C3, 0.0],
[-C6, -C3, 0.0],
[0.0, C6, C3],
[0.0, C6, -C3],
[0.0, -C6, C3],
[0.0, -C6, -C3],
[ C0, C2, C5],
[ C0, C2, -C5],
[ C0, -C2, C5],
[ C0, -C2, -C5],
[-C0, C2, C5],
[-C0, C2, -C5],
[-C0, -C2, C5],
[-C0, -C2, -C5],
[ C5, C0, C2],
[ C5, C0, -C2],
[ C5, -C0, C2],
[ C5, -C0, -C2],
[-C5, C0, C2],
[-C5, C0, -C2],
[-C5, -C0, C2],
[-C5, -C0, -C2],
[ C2, C5, C0],
[ C2, C5, -C0],
[ C2, -C5, C0],
[ C2, -C5, -C0],
[-C2, C5, C0],
[-C2, C5, -C0],
[-C2, -C5, C0],
[-C2, -C5, -C0],
[ C4, C4, C4],
[ C4, C4, -C4],
[ C4, -C4, C4],
[ C4, -C4, -C4],
[-C4, C4, C4],
[-C4, C4, -C4],
[-C4, -C4, C4],
[-C4, -C4, -C4]];
faces = [
[18, 0, 8, 32],
[18, 32, 56, 40],
[18, 40, 10, 38],
[18, 38, 54, 30],
[18, 30, 6, 0],
[19, 1, 7, 31],
[19, 31, 55, 39],
[19, 39, 11, 41],
[19, 41, 57, 33],
[19, 33, 9, 1],
[20, 0, 6, 34],
[20, 34, 58, 42],
[20, 42, 12, 44],
[20, 44, 60, 36],
[20, 36, 8, 0],
[21, 1, 9, 37],
[21, 37, 61, 45],
[21, 45, 13, 43],
[21, 43, 59, 35],
[21, 35, 7, 1],
[22, 2, 11, 39],
[22, 39, 55, 47],
[22, 47, 14, 46],
[22, 46, 54, 38],
[22, 38, 10, 2],
[23, 2, 10, 40],
[23, 40, 56, 48],
[23, 48, 15, 49],
[23, 49, 57, 41],
[23, 41, 11, 2],
[24, 3, 12, 42],
[24, 42, 58, 50],
[24, 50, 16, 51],
[24, 51, 59, 43],
[24, 43, 13, 3],
[25, 3, 13, 45],
[25, 45, 61, 53],
[25, 53, 17, 52],
[25, 52, 60, 44],
[25, 44, 12, 3],
[26, 4, 16, 50],
[26, 50, 58, 34],
[26, 34, 6, 30],
[26, 30, 54, 46],
[26, 46, 14, 4],
[27, 4, 14, 47],
[27, 47, 55, 31],
[27, 31, 7, 35],
[27, 35, 59, 51],
[27, 51, 16, 4],
[28, 5, 15, 48],
[28, 48, 56, 32],
[28, 32, 8, 36],
[28, 36, 60, 52],
[28, 52, 17, 5],
[29, 5, 17, 53],
[29, 53, 61, 37],
[29, 37, 9, 33],
[29, 33, 57, 49],
[29, 49, 15, 5]];
return polyhedron({points:vertices, polygons:faces});
}
polyh3.pentagonal_hexecontahedron_dextro = function (){
// http://dmccooey.com/polyhedra/RpentagonalHexecontahedron.html
var phi, x, C0, C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15
, C16, C17, C18, C19 , vertices, faces;
phi = (1 + sqrt(5)) / 2;
x = Math.cbrt((phi + sqrt(phi-5/27))/2) + Math.cbrt((phi - sqrt(phi-5/27))/2);
C0 = phi * sqrt(3 - (x*x)) / 2;
C1 = phi * sqrt((x - 1 - (1/x)) * phi) / (2 * x);
C2 = phi * sqrt((x - 1 - (1/x)) * phi) / 2;
C3 = (x*x) * phi * sqrt(3 - (x*x)) / 2;
C4 = phi * sqrt(1 - x + (1 + phi) / x) / 2;
C5 = sqrt(x * (x + phi) + 1) / (2 * x);
C6 = sqrt((x + 2) * phi + 2) / (2 * x);
C7 = sqrt(-(x*x) * (2 + phi) + x * (1 + 3 * phi) + 4) / 2;
C8 = (1 + phi) * sqrt(1 + (1/x)) / (2 * x);
C9 = sqrt(2 + 3 * phi - 2 * x + (3/x)) / 2;
C10 = sqrt((x*x)*(392 + 225*phi) + x*(249 + 670*phi) + (470 + 157*phi))/62;
C11 = phi * sqrt(x * (x + phi) + 1) / (2 * x);
C12 = phi * sqrt((x*x) + x + 1 + phi) / (2 * x);
C13 = phi * sqrt((x*x) + 2 * x * phi + 2) / (2 * x);
C14 = sqrt((x*x) * (1 + 2 * phi) - phi) / 2;
C15 = phi * sqrt((x*x) + x) / 2;
C16 = (phi*phi*phi) * sqrt(x * (x + phi) + 1) / (2 * (x*x));
C17 = sqrt((x*x)*(617 + 842*phi) + x*(919 + 1589*phi) + (627 + 784*phi))/62;
C18 = (phi*phi) * sqrt(x * (x + phi) + 1) / (2 * x);
C19 = phi * sqrt(x * (x + phi) + 1) / 2;
vertices = [
[ C0, C1, C19],
[ C0, -C1, -C19],
[ -C0, -C1, C19],
[ -C0, C1, -C19],
[ C19, C0, C1],
[ C19, -C0, -C1],
[-C19, -C0, C1],
[-C19, C0, -C1],
[ C1, C19, C0],
[ C1, -C19, -C0],
[ -C1, -C19, C0],
[ -C1, C19, -C0],
[ 0.0, C5, C18],
[ 0.0, C5, -C18],
[ 0.0, -C5, C18],
[ 0.0, -C5, -C18],
[ C18, 0.0, C5],
[ C18, 0.0, -C5],
[-C18, 0.0, C5],
[-C18, 0.0, -C5],
[ C5, C18, 0.0],
[ C5, -C18, 0.0],
[ -C5, C18, 0.0],
[ -C5, -C18, 0.0],
[ C10, 0.0, C17],
[ C10, 0.0, -C17],
[-C10, 0.0, C17],
[-C10, 0.0, -C17],