Compound Of Five Great Dodecahedra
This uniform polyhedron compound is a composition of 5 great dodecahedra, in the same arrangement as in the compound of 5 icosahedra. It is one of only five polyhedral compounds (along with the compound of six tetrahedra, the compound of two great dodecahedra, the compound of two small stellated dodecahedra, and the compound of five small stellated dodecahedra) which is vertex-transitive and face-transitive but not edge-transitive In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal () or edge-transitive if its symmetries act transitively on its edges. Informally, this means that there is only one type of edge to the object: given t .... References *. Polyhedral compounds {{polyhedron-stub ...
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Compound Of Five Icosahedra
The compound of five icosahedra is uniform polyhedron compound. It's composed of 5 icosahedron, icosahedra, rotated around a common axis. It has Icosahedral symmetry, icosahedral symmetry ''Ih''. The triangles in this compound decompose into two Orbit (group theory), orbits under action of the symmetry group: 40 of the triangles lie in coplanar pairs in icosahedral planes, while the other 60 lie in unique planes. Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the cyclic permutations of : (0, ±2, ±2τ) : (±τ−1, ±1, ±(1+τ2)) : (±τ, ±τ2, ±(2τ−1)) where τ = (1+)/2 is the golden ratio (sometimes written φ). References

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