Square retroprism

Square retroprism
Rank	3
Type	Isogonal
Space	Spherical
Elements
Faces	8 isosceles triangles, 2 squares
Edges	8+8
Vertices	8
Vertex figure	Crossed isosceles trapezoid
Related polytopes
Army	Squap
Regiment	*
Dual	Square concave antitegum
Conjugate	Square antiprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	(I2(8)×A1)/2, order 16
Convex	No
Nature	Tame

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

A square retroprism with base edges of length 1 and side edges of length $\sqrt{2+\sqrt2}$ occurs as the vertex figure of the small distetracontoctachoron. One using side edges of length $\sqrt2$ occurs as vertex figure of the quasiprismatotetracontoctachoron.

Related polyhedra

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

External links

• Klitzing, Richard. "n/d-ap".