# Heptagonal antitegum

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Heptagonal antitegum
Rank3
TypeUniform dual
Notation
Bowers style acronymHeate
Coxeter diagramp2p14o ()
Conway notationdA7
Elements
Faces14 kites
Edges14+14
Vertices2+14
Vertex figure2 heptagons, 14 triangles
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left(1+{\frac {2}{2\cos {\frac {\pi }{7}}-3}}\right)\approx 132.01787^{\circ }}$
Central density1
Number of external pieces14
Level of complexity4
Related polytopes
ArmyHeate
RegimentHeate
DualHeptagonal antiprism
ConjugateGreat heptagrammic antitegum
Abstract & topological properties
Flag count112
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(14)×A1)/2, order 28
ConvexYes
NatureTame

The heptagonal antitegum, also known as the heptagonal trapezohedron, is an antitegum based on the heptagon, constructed as the dual of a heptagonal antiprism. It has 14 kites as faces, with 2 order–7 and 14 order–3 vertices.

Each face of this polyhedron is a kite with its longer edges ${\displaystyle {\frac {2+4\cos {\frac {\pi }{7}}+\csc {\frac {\pi }{14}}}{2}}\approx 5.04892}$ times the length of its shorter edges.