This
uniform polyhedron compound
In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e. the symmetry group of the compound acts tran ...
is a symmetric arrangement of 12
pentagrammic prism
In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.
It is a special case of a right prism with a pentagram as base, which in ge ...
s, aligned in pairs with the axes of fivefold rotational symmetry of a
dodecahedron.
It results from composing the two
enantiomorphs
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be ...
of the
compound of six pentagrammic prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagrammic prism
In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this cas ...
. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two pentagrammic prisms incident on each of its vertices.
Related polyhedra
This compound shares its
vertex arrangement with four
uniform polyhedra as follows:
References
*.
Polyhedral compounds
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