Heptagonal tegum

Heptagonal tegum
Rank	3
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Het
Coxeter diagram	m2m7o ()
Elements
Faces	14 isosceles triangles
Edges	7+14
Vertices	2+7
Vertex figure	2 heptagons, 7 squares
Measures (edge length 1)
Dihedral angle	$\arccos\left(\frac{\sin^2\frac\pi7-1}{\sin^2\frac\pi7+1}\right) \approx 133.08952^\circ$
Central density	1
Related polytopes
Army	Het
Regiment	Het
Dual	Heptagonal prism
Conjugates	Heptagrammic tegum, Great heptagrammic tegum
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(7)×A1, order 28
Convex	Yes
Nature	Tame

The heptagonal tegum or het, also called a heptagonal bipyramid, is a tegum with a heptagon as the midsection, constructed as the dual of a heptagonal prism. It has 14 isosceles triangles as faces, with 2 order–7 and 7 order–4 vertices.

In the variant obtained as the dual of a uniform heptagonal prism, the side edges are $\frac{1}{2\sin^2\frac\pi7} \approx 2.65597$ times the length of the edges of the base heptagon. Each face has apex angle $\arccos\left(1-2\sin^4\frac\pi7\right) \approx 21.70194^\circ$ and base angles $\arccos\left(\sin^2\frac\pi7\right) \approx 79.14903^\circ$. If the base heptagon has edge length 1, its height is $\frac{\cos\frac\pi7}{\sin^2\frac\pi7} \approx 4.78589$.

External links

• Wikipedia Contributors. "Heptagonal bipyramid".
• McCooey, David. "Heptagonal Dipyramid"