Hendecagonal tegum

Hendecagonal tegum
Rank	3
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Hent
Coxeter diagram	m2m11o
Elements
Faces	22 isosceles triangles
Edges	11+22
Vertices	2+11
Vertex figure	2 hendecagons, 11 squares
Measures (edge length 1)
Dihedral angle	$\arccos\left(\frac{\sin^2\frac{\pi}{11}-1}{\sin^2\frac{\pi}{11}+1}\right) ≈ 148.53149^\circ$
Central density	1
Number of external pieces	22
Level of complexity	3
Related polytopes
Army	Hent
Regiment	Hent
Dual	Hendecagonal prism
Conjugates	Small hendecagrammic tegum, Hendecagrammic tegum, Great hendecagrammic tegum, Grand hendecagrammic tegum
Abstract & topological properties
Flag count	132
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(11)×A1, order 44
Convex	Yes
Nature	Tame

The hendecagonal tegum or hent, also called a hendecagonal bipyramid, is a tegum with a hendecagon as the midsection, constructed as the dual of a hendecagonal prism. It has 22 isosceles triangles as faces, with 2 order–11 and 11 order–4 vertices. .

In the variant obtained as the dual of a uniform hendecagonal prism, the side edges are $\frac{1}{2\sin^2\frac{\pi}{11}} ≈ 6.29935$ times the length of the edges of the base hendecagon. Each face has apex angle $\arccos\left(1-2\sin^4\frac{\pi}{11}\right) \approx 9.10508^\circ$ and base angles $\arccos\left(\sin^2\frac{\pi}{11}\right) \approx 85.44746^\circ$. If the base hendecagon has edge length 1, its height is $\frac{\cos\frac{\pi}{11}}{\sin^2\frac{\pi}{11}} ≈ 12.08837$.