# Octagonal antitegum

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Octagonal antitegum
Rank3
TypeUniform dual
Notation
Bowers style acronymOat
Coxeter diagramp2p16o ()
Conway notationdA8
Elements
Faces16 kites
Edges16+16
Vertices2+16
Vertex figure2 octagons, 16 triangles
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left({\frac {5+6{\sqrt {2}}-2{\sqrt {130+79{\sqrt {2}}}}}{47}}\right)\approx 137.37047^{\circ }}$
Central density1
Number of external pieces16
Level of complexity4
Related polytopes
ArmyOat
RegimentOat
DualOctagonal antiprism
ConjugatesOctagrammic antitegum, Octagrammic concave antitegum
Abstract & topological properties
Flag count128
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(16)×A1)/2, order 32
ConvexYes
NatureTame

The octagonal antitegum, also known as the octagonal trapezohedron, is an antitegum based on the octagon, constructed as the dual of an octagonal antiprism. It has 16 kites as faces, with 2 order–8 and 16 order–3 vertices.

Each face of this polyhedron is a kite with its longer edges ${\displaystyle 2+{\sqrt {2}}+{\sqrt {\frac {10+7{\sqrt {2}}}{2}}}\approx 6.56854}$ times the length of its shorter edges.