# Octagonal duotegum

Octagonal duotegum
Rank4
TypeNoble
SpaceSpherical
Notation
Bowers style acronymOdit
Coxeter diagramm8o2m8o
Elements
Cells64 tetragonal disphenoids
Faces128 isosceles triangles
Edges16+64
Vertices16
Vertex figureOctagonal tegum
Measures (based on octagons of edge length 1)
Edge lengthsBase (16): 1
Lacing (64): $\sqrt{2+\sqrt2} ≈ 1.84776$ Circumradius$\sqrt{\frac{2+\sqrt2}{2}} ≈ 1.30656$ Inradius$\frac{2+\sqrt2}{4} ≈ 0.85355$ Central density1
Related polytopes
ArmyOdit
RegimentOdit
DualOctagonal duoprism
ConjugateOctagrammic duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2≀S2, order 512
ConvexYes
NatureTame

The octagonal duotegum or odit, also known as the octagonal-octagonal duotegum, the 8 duotegum, or the 8-8 duotegum, is a noble duotegum that consists of 64 tetragonal disphenoids and 16 vertices, with 16 cells joining at each vertex. It is also the digonal double gyroantiprismoid and the 16-7 step prism. It is the first in an infinite family of isogonal octagonal hosohedral swirlchora, the first in an infinite family of isochoric octagonal dihedral swirlchora and also the first in an infinite family of isogonal digonal prismatic swirlchora.

It is one of a number of isogonal polychora that can be obtained as the hull of various arrangements of 2 hexadecachora.

## Vertex coordinates

The vertices of an octagonal duotegum based on 2 octagons of edge length 1, centered at the origin, are given by:

• $\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0,\,0\right),$ • $\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0,\,0\right),$ • $\left(0,\,0,\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$ • $\left(0,\,0,\,±\frac12,\,±\frac{1+\sqrt2}{2}\right).$ 