More fun with Fluxus - I've been learning how to use (build-polygons), where you define the vertices that make up the faces (and the normals to the faces which control lighting). I had a heck of a time getting the tetrahedron working, I found that (recalc-normals) didn't work in a way that was suitable. The function (hint-normal) shows the normals as red lines, so you can check they are pointing in the right directions, very helpful. Once I got used to it, making an octahedron was much easier.
Cube and Octahedron
Five Tetrahedra (left-handed and right-handed variants)
Ten Tetrahedra (some misalignment due to rounding errors or mistakes in my maths)
( Octahedron code )
at Tnow, Mood == geometrical
at Tnow, Music == BBC Radio 4
Text from E M Cundy and A P Rollett - Mathematical Models (Third Edition).
3.10.6. Five cubes in a dodecahedron
[Fig. 167]
The edges of the cubes lie by fives on the faces of the dodecahedron forming star-pentagons; each edge is thus divided by the two other edges in golden section.
The solid common to the cubes as a whole is bounded by thirty rhombi, one on each cube face, and is thus a rhombic triacontahedron.
The edges of these cubes can be grouped to form equilateral triangles, ordinary pentagons, and star pentagons, besides the squares which are the cube faces. By taking different combinations of these figures, several stellated Archimedean polyhedra can be formed. Full details can be found in Coxeter, op. cit., pp. 440-3.
The bibliography seems to indicate (non-definitively) that the referenced work is H S M Coxeter - Regular Polytopes.
Anyway, I had a go at implementing this solid in Fluxus, and after an hour of head-scratching and scribbling to figure out the trigonometry, this was the result:
( Five Cubes code )
at Tnow, Mood == geeky
at Tnow, Music == Karlheinz Stockhausen - Helikopterstreichquartett