openjscad-aurora-webapp

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include <maths_geodesic.scad>
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// Information about platonic solids 
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// This information is useful in constructing the various solids
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// can be found here: http://en.wikipedia.org/wiki/Platonic_solid
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// V - vertices
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// E - edges
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// F - faces
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// number, V, E, F, schlafli symbol, dihedral angle, element, name
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//tetrahedron = [1, 4, 6, 4, [3,3], 70.5333, "fire", "tetrahedron"];
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//hexahedron = [2, 8, 12, 6, [4,3], 90, "earth", "cube"];
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//octahedron = [3, 6, 12, 8, [3,4], 109.467, "air", "air"];
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//dodecahedron = [4, 20, 30, 12, [5,3], 116.565, "ether", "universe"];
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//icosahedron = [5, 12, 30, 20, [3,5], 138.190, "water", "water"];
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// Schlafli representation for the platonic solids
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// Given this representation, we have enough information
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// to derive a number of other attributes of the solids
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tetra_sch = [3,3];
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hexa_sch = [4,3];
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octa_sch = [3,4];
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dodeca_sch = [5,3];
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icosa_sch = [3,5];
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// Given the schlafli representation, calculate
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// the number of edges, vertices, and faces for the solid
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function plat_edges(pq) = (2*pq[0]*pq[1])/
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	((2*pq[0])-(pq[0]*pq[1])+(2*pq[1]));
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function plat_vertices(pq) = (2*plat_edges(pq))/pq[1];
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function plat_faces(pq) = (2*plat_edges(pq))/pq[0];
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// Calculate angular deficiency of each vertex in a platonic solid 
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// p - sides
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// q - number of edges per vertex
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//function angular_defect(pq) = 360 - (poly_single_interior_angle(pq)*pq[1]);
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function plat_deficiency(pq) = DEGREES(2*Cpi - pq[1]*Cpi*(1-2/pq[0]));
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function plat_dihedral(pq) = 2 * asin( cos(180/pq[1])/sin(180/pq[0]));
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function plat_circumradius(pq, a) = 
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	(a/2)*
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	tan(Cpi/pq[1])*
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	tan(plat_dihedral(pq)/2);
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function plat_midradius(pq, a) = 
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	(a/2)*
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	cot(Cpi/pq[0])*
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	tan(plat_dihedral(pq)/2);
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function plat_inradius(pq,a) = 
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	a/(2*tan(DEGREES(Cpi/pq[0])))*
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	sqrt((1-cos(plat_dihedral(pq)))/(1+cos(plat_dihedral(pq))));
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//================================================
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//	Tetrahedron
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//================================================
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tetra_cart = [
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	[+1, +1, +1],
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	[-1, -1, +1],
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	[-1, +1, -1],
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	[+1, -1, -1]
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];
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function tetra_unit(rad=1) = [
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	sph_to_cart(sphu_from_cart(tetra_cart[0], rad)), 
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	sph_to_cart(sphu_from_cart(tetra_cart[1], rad)),
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	sph_to_cart(sphu_from_cart(tetra_cart[2], rad)),
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	sph_to_cart(sphu_from_cart(tetra_cart[3], rad)),
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	];
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tetrafaces = [
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	[0, 3, 1],
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	[0,1,2],
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	[2,1,3],
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	[0,2,3]
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];
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tetra_edges = [
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	[0,1],
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	[0,2],
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	[0,3], 
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	[1,2], 
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	[1,3], 
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	[2,3],	
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	];
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function tetrahedron(rad=1) = [tetra_unit(rad), tetrafaces, tetra_edges];
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//================================================
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//	Hexahedron - Cube 
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//================================================
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// vertices for a unit cube with sides of length 1
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hexa_cart = [
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	[0.5, 0.5, 0.5], 
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	[-0.5, 0.5, 0.5], 
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	[-0.5, -0.5, 0.5], 
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	[0.5, -0.5, 0.5],
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	[0.5, 0.5, -0.5], 
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	[-0.5, 0.5, -0.5], 
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	[-0.5, -0.5, -0.5], 
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	[0.5, -0.5, -0.5],
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];
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function hexa_unit(rad=1) = [
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	sph_to_cart(sphu_from_cart(hexa_cart[0], rad)), 
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	sph_to_cart(sphu_from_cart(hexa_cart[1], rad)),
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	sph_to_cart(sphu_from_cart(hexa_cart[2], rad)),
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	sph_to_cart(sphu_from_cart(hexa_cart[3], rad)),
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	sph_to_cart(sphu_from_cart(hexa_cart[4], rad)), 
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	sph_to_cart(sphu_from_cart(hexa_cart[5], rad)), 
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	sph_to_cart(sphu_from_cart(hexa_cart[6], rad)),
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	sph_to_cart(sphu_from_cart(hexa_cart[7], rad)),
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	];
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// enumerate the faces of a cube
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// vertex order is clockwise winding
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hexafaces = [
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	[0,3,2,1],	// top
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	[0,1,5,4],
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	[1,2,6,5],
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	[2,3,7,6],
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	[3,0,4,7],
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	[4,5,6,7],	// bottom
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];
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hexa_edges = [
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	[0,1],
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	[0,3], 
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	[0,4], 
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	[1,2],
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	[1,5],
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	[2,3],
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	[2,6], 
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	[3,7], 
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	[4,5], 	
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	[4,7], 
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	[5,4],
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	[5,6], 
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	[6,7], 
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	];
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function hexahedron(rad=1) =[hexa_unit(rad), hexafaces, hexa_edges];
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//================================================
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//	Octahedron 
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//================================================
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octa_cart = [
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	[+1, 0, 0],  // + x axis
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	[-1, 0, 0],	// - x axis
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	[0, +1, 0],	// + y axis
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	[0, -1, 0],	// - y axis
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	[0, 0, +1],	// + z axis
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	[0, 0, -1] 	// - z axis
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];
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function octa_unit(rad=1) = [
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	sph_to_cart(sphu_from_cart(octa_cart[0], rad)), 
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	sph_to_cart(sphu_from_cart(octa_cart[1], rad)),
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	sph_to_cart(sphu_from_cart(octa_cart[2], rad)),
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	sph_to_cart(sphu_from_cart(octa_cart[3], rad)),
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	sph_to_cart(sphu_from_cart(octa_cart[4], rad)), 
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	sph_to_cart(sphu_from_cart(octa_cart[5], rad)), 
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	];
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octafaces = [
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	[4,2,0],
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	[4,0,3],
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	[4,3,1],
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	[4,1,2],
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	[5,0,2],
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	[5,3,0],
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	[5,1,3],
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	[5,2,1]
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	];
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octa_edges = [
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	[0,2], 
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	[0,3],
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	[0,4],
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	[0,5],
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	[1,2],
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	[1,3],
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	[1,4],
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	[1,5],
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	[2,4], 
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	[2,5],
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	[3,4],
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	[3,5],
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	];
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function octahedron(rad=1) = [octa_unit(rad), octafaces, octa_edges];
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//================================================
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//	Dodecahedron
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//================================================
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// (+-1, +-1, +-1)
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// (0, +-1/Cphi, +-Cphi)
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// (+-1/Cphi, +-Cphi, 0)
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// (+-Cphi, 0, +-1/Cphi)
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dodeca_cart = [
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	[+1, +1, +1],			// 0, 0
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	[+1, -1, +1],			// 0, 1
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	[-1, -1, +1],			// 0, 2
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	[-1, +1, +1],			// 0, 3
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	[+1, +1, -1],			// 1, 4
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	[-1, +1, -1],			// 1, 5
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	[-1, -1, -1],			// 1, 6
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	[+1, -1, -1],			// 1, 7
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	[0, +1/Cphi, +Cphi],		// 2, 8
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	[0, -1/Cphi, +Cphi],		// 2, 9
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	[0, -1/Cphi, -Cphi],		// 2, 10
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	[0, +1/Cphi, -Cphi],		// 2, 11
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	[-1/Cphi, +Cphi, 0],		// 3, 12
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	[+1/Cphi, +Cphi, 0],		// 3, 13
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	[+1/Cphi, -Cphi, 0],		// 3, 14
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	[-1/Cphi, -Cphi, 0],		// 3, 15
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	[-Cphi, 0, +1/Cphi],		// 4, 16
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	[+Cphi, 0, +1/Cphi],		// 4, 17
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	[+Cphi, 0, -1/Cphi],		// 4, 18
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	[-Cphi, 0, -1/Cphi],		// 4, 19
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];
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function dodeca_unit(rad=1) = [
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	sph_to_cart(sphu_from_cart(dodeca_cart[0], rad)), 
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	sph_to_cart(sphu_from_cart(dodeca_cart[1], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[2], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[3], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[4], rad)), 
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	sph_to_cart(sphu_from_cart(dodeca_cart[5], rad)), 
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	sph_to_cart(sphu_from_cart(dodeca_cart[6], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[7], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[8], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[9], rad)), 
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	sph_to_cart(sphu_from_cart(dodeca_cart[10], rad)), 
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	sph_to_cart(sphu_from_cart(dodeca_cart[11], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[12], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[13], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[14], rad)), 
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	sph_to_cart(sphu_from_cart(dodeca_cart[15], rad)), 
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	sph_to_cart(sphu_from_cart(dodeca_cart[16], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[17], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[18], rad)),
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	sph_to_cart(sphu_from_cart(dodeca_cart[19], rad)), 
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	];
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// These are the pentagon faces
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// but CGAL has a problem rendering if things are 
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// not EXACTLY coplanar
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// so use the triangle faces instead
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//dodeca_faces=[ 
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//	[1,9,8,0,17],
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//	[9,1,14,15,2],
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//	[9,2,16,3,8],
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//	[8,3,12,13,0],
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//	[0,13,4,18,17],
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//	[1,17,18,7,14],
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//	[15,14,7,10,6],
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//	[2,15,6,19,16],
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//	[16,19,5,12,3],
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//	[12,5,11,4,13],
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//	[18,4,11,10,7],
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//	[19,6,10,11,5]
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//	];
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dodeca_faces = [
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	[1,9,8], 
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	[1,8,0],
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	[1,0,17],
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	[9,1,14],
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	[9,14,15],
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	[9,15,2],
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	[9,2,16],
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	[9,16,3],
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	[9,3,8],
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	[8,3,12],
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	[8,12,13],
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	[8,13,0],
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	[0,13,4],
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	[0,4,18],
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	[0,18,17],
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	[1,17,18],
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	[1,18,7],
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	[1,7,14],
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	[15,14,7],
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	[15,7,10],
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	[15,10,6],
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	[2,15,6],
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	[2,6,19],
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	[2,19,16],
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	[16,19,5],
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	[16,5,12],
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	[16,12,3],
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	[12,5,11],
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	[12,11,4],
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	[12,4,13],
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	[18,4,11],
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	[18,11,10],
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	[18,10,7],
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	[19,6,10],
325
	[19,10,11],
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	[19,11,5]
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	];
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dodeca_edges=[
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	[0,8],
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	[0,13],
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	[0,17],
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	[1,9],
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	[1,14],
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	[1,17],
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338
	[2,9],
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	[2,15],
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	[2,16],
341

342
	[3,8],
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	[3,12],
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	[3,16],
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	[4,11],
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	[4,13],
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	[4,18],
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	[5,11],
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	[5,12],
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	[5,19],
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	[6,10],
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	[6,15],
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	[6,19],
357

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	[7,10],
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	[7,14],
360
	[7,18],
361

362
	[8,9],
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	[10,11],
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	[12,13],
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	[14,15],
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	[16,19],
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	[17,18],
368
	];
369

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function dodecahedron(rad=1) = [dodeca_unit(rad), dodeca_faces, dodeca_edges];
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372
//================================================
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//	Icosahedron
374
//================================================
375
//
376
// (0, +-1, +-Cphi)
377
// (+-Cphi, 0, +-1)
378
// (+-1, +-Cphi, 0)
379

380
icosa_cart = [
381
	[0, +1, +Cphi],	// 0
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	[0, +1, -Cphi],	// 1
383
	[0, -1, -Cphi],	// 2
384
	[0, -1, +Cphi],	// 3
385

386
	[+Cphi, 0, +1],	// 4
387
	[+Cphi, 0, -1],	// 5
388
	[-Cphi, 0, -1],	// 6
389
	[-Cphi, 0, +1],	// 7
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391
	[+1, +Cphi, 0],	// 8
392
	[+1, -Cphi, 0],	// 9
393
	[-1, -Cphi, 0],	// 10
394
	[-1, +Cphi, 0]	// 11
395
	];
396

397
function icosa_sph(rad=1) = [
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	sphu_from_cart(icosa_cart[0], rad), 
399
	sphu_from_cart(icosa_cart[1], rad),
400
	sphu_from_cart(icosa_cart[2], rad),
401
	sphu_from_cart(icosa_cart[3], rad),
402
	sphu_from_cart(icosa_cart[4], rad), 
403
	sphu_from_cart(icosa_cart[5], rad), 
404
	sphu_from_cart(icosa_cart[6], rad),
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	sphu_from_cart(icosa_cart[7], rad),
406
	sphu_from_cart(icosa_cart[8], rad),
407
	sphu_from_cart(icosa_cart[9], rad), 
408
	sphu_from_cart(icosa_cart[10], rad), 
409
	sphu_from_cart(icosa_cart[11], rad),
410
	];
411

412
function icosa_unit(rad=1) = [
413
	sph_to_cart(sphu_from_cart(icosa_cart[0], rad)), 
414
	sph_to_cart(sphu_from_cart(icosa_cart[1], rad)),
415
	sph_to_cart(sphu_from_cart(icosa_cart[2], rad)),
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	sph_to_cart(sphu_from_cart(icosa_cart[3], rad)),
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	sph_to_cart(sphu_from_cart(icosa_cart[4], rad)), 
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	sph_to_cart(sphu_from_cart(icosa_cart[5], rad)), 
419
	sph_to_cart(sphu_from_cart(icosa_cart[6], rad)),
420
	sph_to_cart(sphu_from_cart(icosa_cart[7], rad)),
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	sph_to_cart(sphu_from_cart(icosa_cart[8], rad)),
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	sph_to_cart(sphu_from_cart(icosa_cart[9], rad)), 
423
	sph_to_cart(sphu_from_cart(icosa_cart[10], rad)), 
424
	sph_to_cart(sphu_from_cart(icosa_cart[11], rad)),
425
	];
426

427
icosa_faces = [ 
428
	[3,0,4],
429
	[3,4,9],
430
	[3,9,10],
431
	[3,10,7],
432
	[3,7,0],
433
	[0,8,4],
434
	[0,7,11],
435
	[0,11,8],
436
	[4,8,5],
437
	[4,5,9],
438
	[7,10,6],
439
	[7,6,11],
440
	[9,5,2],
441
	[9,2,10],
442
	[2,6,10],
443
	[1,5,8],
444
	[1,8,11],
445
	[1,11,6],
446
	[5,1,2],
447
	[2,1,6]
448
	];
449

450
icosa_edges = [
451
	[0,3],
452
	[0,4],
453
	[0,7],
454
	[0,8],
455
	[0,11],
456
	[1,5],
457
	[1,8],
458
	[1,11],
459
	[1,6],
460
	[1,2],
461
	[2,5],
462
	[2,6],
463
	[2,9],
464
	[2,10],
465
	[3,4],
466
	[3,9],
467
	[3,10],
468
	[3,7],
469
	[4,5],
470
	[4,8],
471
	[4,9],
472
	[5,8],
473
	[5,9],
474
	[6,7],		
475
	[6,10],
476
	[6,11],
477
	[7,10],
478
	[7,11],
479
	[8,11],
480
	[9,10],
481
	];
482

483
function icosahedron(rad=1) = [icosa_unit(rad), icosa_faces, icosa_edges];
484