Platonic Solids

dodecahedron.es

#define fip0  1.618
#define fim0 -1.618
#define fip1  0.618
#define fim1 -0.618

#define sqrtp1  0.7071
#define sqrtm1 -0.7071

rule tetrahedron {
	{ x +1 y  0 z sqrtm1 } box
	{ x -1 y  0 z sqrtm1 } box

	{ x  0 y +1 z sqrtp1 } box
	{ x  0 y -1 z sqrtp1 } box
}

rule cube {
	{ x +1 y +1 z +1 } box
	{ x +1 y +1 z -1 } box
	{ x +1 y -1 z +1 } box
	{ x +1 y -1 z -1 } box
	{ x -1 y +1 z +1 } box
	{ x -1 y +1 z -1 } box
	{ x -1 y -1 z +1 } box
	{ x -1 y -1 z -1 } box
}

rule octahedron {
	{ x +1 y  0 z  0 } box
	{ x -1 y  0 z  0 } box

	{ x  0 y +1 z  0 } box
	{ x  0 y -1 z  0 } box

	{ x  0 y  0 z +1 } box
	{ x  0 y  0 z -1 } box
}

rule dodecahedron {
	{ x +1 y +1 z +1 } box
	{ x +1 y +1 z -1 } box
	{ x +1 y -1 z +1 } box
	{ x +1 y -1 z -1 } box
	{ x -1 y +1 z +1 } box
	{ x -1 y +1 z -1 } box
	{ x -1 y -1 z +1 } box
	{ x -1 y -1 z -1 } box

	{ x 0    y fip0 z fip1 } box
	{ x 0    y fip0 z fim1 } box
	{ x 0    y fim0 z fip1 } box
	{ x 0    y fim0 z fim1 } box

	{ x fip1 y    0 z fip0 } box
	{ x fim1 y    0 z fip0 } box
	{ x fip1 y    0 z fim0 } box
	{ x fim1 y    0 z fim0 } box

	{ x fip0 y fip1 z    0 } box
	{ x fip0 y fim1 z    0 } box
	{ x fim0 y fip1 z    0 } box
	{ x fim0 y fim1 z    0 } box
}

rule icosahedron {
	{ x    0 y   +1 z fip0 } box
	{ x    0 y   +1 z fim0 } box
	{ x    0 y   -1 z fip0 } box
	{ x    0 y   -1 z fim0 } box

	{ x   +1 y fip0 z    0 } box
	{ x   +1 y fim0 z    0 } box
	{ x   -1 y fip0 z    0 } box
	{ x   -1 y fim0 z    0 } box

	{ x fip0 y    0 z   +1 } box
	{ x fim0 y    0 z   +1 } box
	{ x fip0 y    0 z   -1 } box
	{ x fim0 y    0 z   -1 } box
}

{ x  0 } tetrahedron
{ x  5 } cube
{ x 10 } octahedron
{ x 15 } dodecahedron
{ x 20 } icosahedron