# Square antitegum

Square antitegum
Rank3
TypeUniform dual
Notation
Bowers style acronymSquate
Coxeter diagramp2p8o ()
Conway notationdA4
Elements
Faces8 kites
Edges8+8
Vertices2+8
Vertex figure8 triangles, 2 squares
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left({\frac {1-2{\sqrt {2}}}{7}}\right)\approx 105.14151^{\circ }}$
Central density1
Number of external pieces8
Level of complexity4
Related polytopes
ArmySquate
RegimentSquate
DualSquare antiprism
ConjugateSquare antitegum
Abstract & topological properties
Flag count64
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(8)×A1)/2, order 16
ConvexYes
NatureTame

The square antitegum, 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 ${\displaystyle {\frac {2+{\sqrt {2}}}{2}}\approx 1.70711}$ times the length of its shorter edges.