# Octagonal tegum

Octagonal tegum
Rank3
TypeUniform dual
Notation
Bowers style acronymOt
Coxeter diagramm2m8o
Elements
Faces16 isosceles triangles
Edges8+16
Vertices2+8
Vertex figure2 octagons, 8 squares
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left(-{\frac {7+4{\sqrt {2}}}{17}}\right)\approx 138.11796^{\circ }}$
Central density1
Number of external pieces16
Level of complexity3
Related polytopes
ArmyOt
RegimentOt
DualOctagonal prism
ConjugateOctagrammic tegum
Abstract & topological properties
Flag count96
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(8)×A1, order 32
ConvexYes
NatureTame

The octagonal tegum, also called an octagonal bipyramid, is a tegum with an octagon as the midsection, constructed as the dual of an octagonal prism. It has 16 isosceles triangles as faces, with 2 order–8 and 8 order–4 vertices.

In the variant obtained as the dual of a uniform octagonal prism, the side edges are ${\displaystyle 2+{\sqrt {2}}\approx 3.41421}$ times the length of the edges of the base octagon. Each face has apex angle ${\displaystyle \arccos \left({\frac {1+2{\sqrt {2}}}{4}}\right)\approx 16.84212^{\circ }}$ and base angles ${\displaystyle \arccos \left({\frac {2-{\sqrt {2}}}{4}}\right)\approx 81.57894^{\circ }}$. If the base octagon has edge length 1, its height is ${\displaystyle {\sqrt {20+14{\sqrt {2}}}}\approx 6.30864}$.