Octagonal duotegum

Octagonal duotegum
(OFF file)
Rank	4
Type	Noble
Notation
Bowers style acronym	Odit
Coxeter diagram	m8o2m8o ()
Elements
Cells	64 tetragonal disphenoids
Faces	128 isosceles triangles
Edges	16+64
Vertices	16
Vertex figure	Octagonal tegum
Measures (based on octagons of edge length 1)
Edge lengths	Base (16): 1
	Lacing (64): ${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Circumradius	${\sqrt {\frac {2+{\sqrt {2}}}{2}}}\approx 1.30656$
Inradius	${\frac {2+{\sqrt {2}}}{4}}\approx 0.85355$
Central density	1
Related polytopes
Army	Odit
Regiment	Odit
Dual	Octagonal duoprism
Conjugate	Octagrammic duotegum
Abstract & topological properties
Flag count	1536
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2≀S2, order 512
Convex	Yes
Nature	Tame

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:

• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,0,\,0\right)$,
• $\left(0,\,0,\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right)$.

Related polytopes

Related complex polygon

Orthographic projection

The regular complex polygon ${}_{2}\{4\}_{8}$ has 16 vertices in $\mathbb {C} ^{2}$ with a real representation in $\mathbb {R} ^{4}$ matching the vertex coordinates of the octagonal duotegum. It has 64 2-edges corresponding to the connecting edges of the octagonal duotegum, while the 16 edges connecting the two octagons are not included.

The skeleton of ${}_{2}\{4\}_{8}$ is a biclique, $K_{8,8}$.