Rhombic Triacontahedron

Written by Paul Bourke
August 2002

PovRay files:
1_0_0.inc, 0_1_0.inc, 0_0_1.inc
scene.pov, scene.ini

Colour codes
Red: edges of dodecahedron
Green: edges of icosahedron
Blue: edges of rhombic triacontahedron

Miscellaneous facts

  • 32 vertices, 60 edges (all the same length), 30 rhombic faces.

  • The center of each rhombic face is the intersection point of the edges of a dodecahedron and icosahedron. (See red and green line intersections). Alternatively, the edges of the dodecahedron and icosahedron form the diagonals of the rhombic faces.

  • The ratio of the long diagonal of the rhombic faces to the short diagonal is the golden ratio, (1 + sqrt(5)) / 2. (Ratio of the length of the green lines to red lines)

  • The vertices are at two distances from the center, the vertices with three connected edges are at one distance and the vertices with 5 connecting edges are at a greater distance.