Heptagonal tegum

Heptagonal tegum
Rank	3
Type	Uniform dual
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	$\arccos \left({\frac {\sin ^{2}{\frac {\pi }{7}}-1}{\sin ^{2}{\frac {\pi }{7}}+1}}\right)\approx 133.08952^{\circ }$
Central density	1
Number of external pieces	14
Level of complexity	3
Related polytopes
Army	Het
Regiment	Het
Dual	Heptagonal prism
Conjugates	Heptagrammic tegum, Great heptagrammic tegum
Abstract & topological properties
Flag count	84
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(7)×A1, order 28
Convex	Yes
Nature	Tame

The heptagonal tegum, 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 ${\frac {1}{2\sin ^{2}{\frac {\pi }{7}}}}\approx 2.65597$ times the length of the edges of the base heptagon. Each face has apex angle $\arccos \left(1-2\sin ^{4}{\frac {\pi }{7}}\right)\approx 21.70194^{\circ }$ and base angles $\arccos \left(\sin ^{2}{\frac {\pi }{7}}\right)\approx 79.14903^{\circ }$. If the base heptagon has edge length 1, its height is ${\frac {\cos {\frac {\pi }{7}}}{\sin ^{2}{\frac {\pi }{7}}}}\approx 4.78589$.

External links

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