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The three dodecahedra are all stellations of the regular convex dodecahedron, and the great icosahedron is a stellation of the regular convex icosahedron.
They were originally white, magnetic dodecahedra in three nested sizes, with one reflective side.
Each vertex has 3 truncated dodecahedra and one tetrahedron around it.
There are 4800 edges of two types: 3600 shared by three truncated dodecahedra and 1200 are shared by two truncated dodecahedra and one tetrahedron.
The dodecahedra are regular, but look flattened because of the projection and direction of viewing.
There are 6,384,634 topologically distinct "convex" dodecahedra, excluding mirror images, having at least 8 vertices.
It contains 2640 cells: 120 truncated dodecahedra, 720 decagonal prisms, 1200 triangular prisms, and 600 cuboctahedra.
It is a quotient space of the order-5 dodecahedral honeycomb, a regular tessellation of hyperbolic 3-space by dodecahedra with this dihedral angle.
With twelve faces, it is one of many nonregular dodecahedra.
It has infinitely many dodecahedra 5,3 around each edge.
In this way he constructed the two stellated dodecahedra.
It is a somewhat rare mineral sought after by collectors as it typically forms euhedral isometric crystals exhibiting various cubes, octahedra, and dodecahedra.
The small stellated dodecahedron and the great icosahedron are facettings of the convex dodecahedron, while the two great dodecahedra are facettings of the regular convex icosahedron.
Honeybees use the geometry of rhombic dodecahedra to form honeycomb from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron.
Each of the rhombic dodecahedra corresponds to a maximal cross-section of one of the 24-cells intersecting the hyperplane (the center of each such 24-cell lies in the hyperplane).
