# Exact Coordinates of Golden Rhombic Solids

Exact Coordinates of Golden Rhombic Solids

This Demonstration gives exact coordinates of various golden rhombic solids. Using three golden rectangles, the coordinates of the vertices of the regular icosahedron are , , or , where is the golden ratio. The coordinates of all of the golden rhombic solids are constructed by adding vectors, so their coordinates are of the form , where and are integers.

0

±1

±τ

τ=

1+

5

2

a+bτ

a

b

The prolate rhombohedron is constructed using the origin and the vertices on one face of the icosahedron as its first four vertices. Twenty rhombohedra constructed in this way form the hexecontahedron, and the other solids are built up from there.