Square antitegum

Square antitegum
Rank	3
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Squate
Coxeter diagram	p2p8o
Elements
Faces	8 kites
Edges	8+8
Vertices	2+8
Vertex figure	8 triangles, 2 squares
Measures (edge length 1)
Dihedral angle	$\arccos\left(\frac{1-2\sqrt2}{7}\right) ≈ 105.14151°$
Central density	1
Related polytopes
Army	Squate
Regiment	Squate
Dual	Square antiprism
Conjugate	Square antitegum
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	(I2(8)×A1)/2, order 16
Convex	Yes
Nature	Tame

The square antitegum or squate, also known as the tetragonal trapezohedron, is an antitegum based on the square, constructed as the dual of a square antiprism. It has 8 kites as faces, with 2 order–4 and 8 order–3 vertices.

Each face of this polyhedron is a kite with its longer edges $\frac{2+\sqrt2}{2} ≈ 1.70711$ times the length of its shorter edges.

External links

• Wikipedia Contributors. "Tetragonal trapezohedron".
• McCooey, David. "Tetragonal Trapezohedron"