Octagonal tegum

Octagonal tegum
	(OFF file)
Rank	3
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Ot
Coxeter diagram	m2m8o
Elements
Faces	16 isosceles triangles
Edges	8+16
Vertices	2+8
Vertex figure	2 octagons, 8 squares
Measures (edge length 1)
Dihedral angle
Central density	1
Related polytopes
Army	Ot
Regiment	Ot
Dual	Octagonal prism
Conjugate	Octagrammic tegum
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(8)×A1, order 32
Convex	Yes
Nature	Tame

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 $\sqrt{20+14\sqrt2} \approx 6.30864$ .