Hexagonal tegum

Hexagonal tegum
Rank	3
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Hat
Coxeter diagram	m2m6o
Elements
Faces	12 isosceles triangles
Edges	6+12
Vertices	2+6
Vertex figure	2 hexagons, 6 squares
Measures (edge lengths 1, $\sqrt3$)
Dihedral angle	$\arccos\left(-\frac35\right) ≈ 126.86990°$
Central density	1
Related polytopes
Army	Hat
Regiment	Hat
Dual	Hexagonal prism
Conjugate	Hexagonal tegum
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	G2×A1, order 24
Convex	Yes
Nature	Tame

The hexagonal tegum or hat, also called a hexagonal bipyramid, is a tegum with a hexagon as the midsection, constructed as the dual of a hexagonal prism. It has 12 isosceles triangles as faces, with 2 order–6 and 6 order–4 vertices. .

In the variant obtained as the dual of a uniform hexagonal prism, the side edges are exactly 2 times the length of the edges of the base hexagon. Each face has apex angle $\arccos\left(\frac78\right) \approx 28.95502°$ and base angles $\arccos\left(\frac14\right) \approx 75.52249°$. If the base hexagon has edge length 1, its height is $2\sqrt3 ≈ 3.46410$.

External links

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

• Hi.gher.Space Wiki Contributors. "Hexagonal bipyramid".