Stellating the Icosahedron and Facetting the Dodecahedron

Updated 10 May 2022

The regular icosahedron and dodecahedron are two of the five Platonic solids. The stellated icosahedra and facetted dodecahedra are related by polar reciprocation - for every stellated icosahedron there is a twin facetted dodecahedron. The stellated icosahedra were thought to have been understood over sixty years ago, but I have been taking a fresh look. The facetted dodecahedra appear not to have been studied systematically until Bridge in the early 1970's.

For more about stellation and facetting in general, see my stellation and facetting pages.


Main pages

A series of papers tackling the subject, broadly in logical order.

Stellation lists

Images of some lost icosahedra

Here are some assorted images that don't fit the more organised format of the main list of lost stellations.

RISC OS (Acorn) PolyData files

To view and manipulate these 3D data files you will need !PolyDraw from Fortran Friends running on either an Acorn compatible PC with RISC OS 3.1 or above, or on a standard Windows PC with VirtualAcorn.

Other stellation and facetting resources