Platonic Solids Set

All but dodecahedron.

 

An icosahedron (yellow) and a tetrahedron (green) have intersecting edges. I have already shown this compound here. Each vertex of the icosahedron divides an edge of an octahedron (red) into golden ratio.Each vertex of a cube (blue) coincides with a vertex of the tetrahedron and of the (invisible) dodecahedron. Whole structure has a tetrahedral symmetry.

 

 

Diagram of tetrahedron+icosahedron compound

Octahedron and cube units: 21x5.25 cm, dodecahedron: 13.2x5.25 cm.

Done