Pentagonal retroprism

From Polytope Wiki
Jump to navigation Jump to search
Pentagonal retroprism
Rank3
TypeIsogonal
Elements
Faces10 isosceles triangles, 2 pentagons
Edges10+10
Vertices10
Vertex figureCrossed isosceles trapezoid
Related polytopes
ArmyPip
Regiment*
DualPentagonal concave antitegum
ConjugatePentagrammic antiprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH2×A1, order 20
ConvexNo
NatureTame

The pentagonal retroprism, also called the pentagonal crossed antiprism, is a prismatic isogonal polyhedron. It consists of 2 base pentagons and 10 isosceles triangles. Each vertex joins one pentagon and three triangles. It is a crossed antiprism based on a pentagon, seen as a 5/4-gon rather than 5/1. It cannot be made uniform.

It is isomorphic to the pentagonal antiprism.

In vertex figures[edit | edit source]

Pentagonal retroprisms appear as vertex figures of four uniform polychora: the small pentagonal retroprismatoverted dishecatonicosachoron, great pentagonal retroprismatoverted dishecatonicosachoron, pentagonal retroprismatoverted hexacosihecatonicosachoron, and quasiprismatohecatonicosachoron.

External links[edit | edit source]