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
This uniform polyhedron compound is a composition of 2 small stellated dodecahedra, in the same arrangement as in the compound of 2 icosahedra.
It is one of only five polyhedral compounds (along with the compound of six tetrahedra, the comp ...
, and the
compound of five small stellated dodecahedra
This uniform polyhedron compound is a composition of 5 small stellated 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 compo ...
) which is
vertex-transitive
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of fa ...
and
face-transitive
In geometry, a tessellation of dimension (a plane tiling) or higher, or a polytope of dimension (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same. More specifically, all faces must be not merely congrue ...
but not
edge-transitive
In geometry, a polytope (for example, a polygon or a polyhedron) or a Tessellation, tiling is isotoxal () or edge-transitive if its Symmetry, symmetries act Transitive group action, transitively on its Edge (geometry), edges. Informally, this mea ...
.
References
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Polyhedral compounds
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