Heptagonal antitegum

Heptagonal antitegum
Rank	3
Type	Uniform dual
Notation
Bowers style acronym	Heate
Coxeter diagram	p2p14o ()
Conway notation	dA7
Elements
Faces	14 kites
Edges	14+14
Vertices	2+14
Vertex figure	2 heptagons, 14 triangles
Measures (edge length 1)
Dihedral angle	$\arccos \left(1+{\frac {2}{2\cos {\frac {\pi }{7}}-3}}\right)\approx 132.01787^{\circ }$
Central density	1
Number of external pieces	14
Level of complexity	4
Related polytopes
Army	Heate
Regiment	Heate
Dual	Heptagonal antiprism
Conjugate	Great heptagrammic antitegum
Abstract & topological properties
Flag count	112
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	(I2(14)×A1)/2, order 28
Convex	Yes
Nature	Tame

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 ${\frac {2+4\cos {\frac {\pi }{7}}+\csc {\frac {\pi }{14}}}{2}}\approx 5.04892$ times the length of its shorter edges.

External links

• Wikipedia contributors. "Heptagonal trapezohedron".
• McCooey, David. "Heptagonal Trapezohedron"