# Octagonal tegum

Octagonal tegum Rank3
TypeUniform dual
SpaceSpherical
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$\arccos\left(-\frac{7+4\sqrt2}{17}\right) \approx 138.11796^\circ$ Central density1
Related polytopes
ArmyOt
RegimentOt
DualOctagonal prism
ConjugateOctagrammic tegum
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(8)×A1, order 32
ConvexYes
NatureTame

The octagonal tegum or ot, 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 $2+\sqrt2 \approx 3.41421$ times the length of the edges of the base octagon. Each face has apex angle $\arccos\left(\frac{1+2\sqrt2}{4}\right) \approx 16.84212^\circ$ and base angles $\arccos\left(\frac{2-\sqrt2}{4}\right) \approx 81.57894^\circ$ . If the base octagon has edge length 1, its height is $\sqrt{20+14\sqrt2} \approx 6.30864$ .