Dodecahedron Measures

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.

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

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

(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.


Contributed by: Sándor Kabai (January 2008)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.