# Heptagonal tegum

Heptagonal tegum Rank3
TypeUniform dual
SpaceSpherical
Notation
Bowers style acronymHet
Coxeter diagramm2m7o (     )
Elements
Faces14 isosceles triangles
Edges7+14
Vertices2+7
Vertex figure2 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 density1
Related polytopes
ArmyHet
RegimentHet
DualHeptagonal prism
ConjugatesHeptagrammic tegum, Great heptagrammic tegum
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(7)×A1, order 28
ConvexYes
NatureTame

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 $\frac{\cos\frac\pi7}{\sin^2\frac\pi7} \approx 4.78589$ .