# Dodecahedron Measures

Dodecahedron Measures

These facts are enough to reconstruct many of the measures and features of a dodecahedron with edge length one:

(1) The vertices of a cube with edge length coincide with those of the dodecahedron.

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(2) Eight edges of a dodecahedron coincide with the faces of a cube with edge length .

2

ϕ

(3) The same eight edges are also the edges of three mutually perpendicular rectangles with side ratio .

2

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(4) The dodecahedron fits into a golden rhombus. In other words, the angle between two adjacent faces and the angle between two nonadjacent faces of a dodecahedron correspond to the angles of a golden rhombus.

(5) The distance between two opposite faces (i.e., the diameter of the inscribed sphere) equals the spacing of two parallel sides of a golden rhombus.

(6) Eight unit cubes connected vertex to vertex to the inscribed cube fill the space together with dodecahedra and bilunabirotundas.