# Hexagonal tegum

Hexagonal tegum Rank3
TypeUniform dual
SpaceSpherical
Notation
Bowers style acronymHat
Coxeter diagramm2m6o
Elements
Faces12 isosceles triangles
Edges6+12
Vertices2+6
Vertex figure2 hexagons, 6 squares
Measures (edge lengths 1, $\sqrt3$ )
Dihedral angle$\arccos\left(-\frac35\right) ≈ 126.86990°$ Central density1
Related polytopes
ArmyHat
RegimentHat
DualHexagonal prism
ConjugateHexagonal tegum
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryG2×A1, order 24
ConvexYes
NatureTame

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 $2\sqrt3 ≈ 3.46410$ .