Hexagonal antitegum

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Hexagonal antitegum
Rank3
TypeUniform dual
Notation
Bowers style acronymHate
Coxeter diagramp2p12o ()
Conway notationdA6
Elements
Faces12 kites
Edges12+12
Vertices2+12
Vertex figure2 hexagons, 12 triangles
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Central density1
Number of external pieces12
Level of complexity4
Related polytopes
ArmyHate
RegimentHate
DualHexagonal antiprism
ConjugateHexagonal antitegum
Abstract & topological properties
Flag count96
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(12)×A1)/2, order 24
ConvexYes
NatureTame

The hexagonal antitegum, also known as the hexagonal trapezohedron, is an antitegum based on the hexagon, constructed as the dual of a hexagonal antiprism. It has 12 kites as faces, with 2 order 6 and 12 order 3 vertices.

Each face of this polyhedron is a kite with its longer edges ${\displaystyle 2+{\sqrt {3}}\approx 3.73205}$ times the length of its shorter edges.