Square retroprism

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Square retroprism
Rank3
TypeIsogonal
Elements
Faces8 isosceles triangles, 2 squares
Edges8+8
Vertices8
Vertex figureCrossed isosceles trapezoid
Related polytopes
ArmySquap
Regiment*
DualSquare concave antitegum
ConjugateSquare antiprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Genus0
Properties
Symmetry(I2(8)×A1)/2, order 16
ConvexNo
NatureTame

The square retroprism, also called the square crossed antiprism, is a prismatic isogonal polyhedron. It consists of 2 base squares and 8 isosceles triangles. Each vertex joins one square and three triangles. It is a crossed antiprism based on a square, seen as a 4/3-gon rather than 4/1. It cannot be made uniform.

It is isomorphic to the square antiprism.

In vertex figures[edit | edit source]

A square retroprism with base edges of length 1 and side edges of length occurs as the vertex figure of the small distetracontoctachoron. One using side edges of length occurs as vertex figure of the quasiprismatotetracontoctachoron.

Related polyhedra[edit | edit source]

There are an infinite amount of prismatic isogonal compounds that are the crossed antiprisms of compounds of squares.

External links[edit | edit source]