# Hendecagonal tegum

Hendecagonal tegum
Rank3
TypeUniform dual
SpaceSpherical
Notation
Bowers style acronymHent
Coxeter diagramm2m11o
Elements
Faces22 isosceles triangles
Edges11+22
Vertices2+11
Vertex figure2 hendecagons, 11 squares
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos\left(\frac{\sin^2\frac{\pi}{11}-1}{\sin^2\frac{\pi}{11}+1}\right) ≈ 148.53149^\circ}$
Central density1
Number of external pieces22
Level of complexity3
Related polytopes
ArmyHent
RegimentHent
DualHendecagonal prism
ConjugatesSmall hendecagrammic tegum, Hendecagrammic tegum, Great hendecagrammic tegum, Grand hendecagrammic tegum
Abstract & topological properties
Flag count132
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(11)×A1, order 44
ConvexYes
NatureTame

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 ${\displaystyle \frac{1}{2\sin^2\frac{\pi}{11}} ≈ 6.29935}$ times the length of the edges of the base hendecagon. Each face has apex angle ${\displaystyle \arccos\left(1-2\sin^4\frac{\pi}{11}\right) \approx 9.10508^\circ}$ and base angles ${\displaystyle \arccos\left(\sin^2\frac{\pi}{11}\right) \approx 85.44746^\circ}$. If the base hendecagon has edge length 1, its height is ${\displaystyle \frac{\cos\frac{\pi}{11}}{\sin^2\frac{\pi}{11}} ≈ 12.08837}$.