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prismatic uniform polyhedron
In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms. All have their vertices in parallel planes and are therefore prismatoids.
== Vertex configuration and symmetry groups ==
Because they are isogonal (vertex-transitive), their vertex arrangement uniquely corresponds to a symmetry group.
The difference between the prismatic and antiprismatic symmetry groups is that D''p''h has the vertices lined up in both planes, which gives it a reflection plane perpendicular to its ''p''-fold axis (parallel to the polygon); while D''p''d has the vertices twisted relative to the other plane, which gives it a rotatory reflection. Each has ''p'' reflection planes which contain the ''p''-fold axis.
The D''p''h symmetry group contains inversion if and only if ''p'' is even, while D''p''d contains inversion symmetry if and only if ''p'' is odd.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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