Hexagonal tegum

From Polytope Wiki
Jump to navigation Jump to search
Hexagonal tegum
Rank3
TypeUniform dual
Notation
Bowers style acronymHat
Coxeter diagramm2m6o
Elements
Faces12 isosceles triangles
Edges6+12
Vertices2+6
Vertex figure2 hexagons, 6 squares
Measures (edge lengths 1, )
Dihedral angle
Central density1
Number of external pieces12
Level of complexity3
Related polytopes
ArmyHat
RegimentHat
DualHexagonal prism
ConjugateHexagonal tegum
Abstract & topological properties
Flag count72
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryG2×A1, order 24
ConvexYes
NatureTame

The hexagonal tegum, 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. The variant with equilateral triangles is flat, and is not considered to be a Johnson solid.

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 and base angles . If the base hexagon has edge length 1, its height is .

External links[edit | edit source]