Octagrammic duoprism

Octagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Stodip
Coxeter diagram	x8/3o x8/3o ()
Elements
Cells	16 octagrammic prisms
Faces	64 squares, 16 octagrams
Edges	128
Vertices	64
Vertex figure	Tetragonal disphenoid, edge lengths √2–√2 (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{2-\sqrt2} ≈ 0.76537$
Inradius	$\frac{\sqrt2-1}{2} ≈ 0.20711$
Hypervolume	$4(3-2\sqrt2) ≈ 0.68629$
Dichoral angles	Stop–4–stop: 90°
	Stop–8/3–stop: 45°
Central density	9
Number of external pieces	32
Level of complexity	12
Related polytopes
Army	Odip
Regiment	Stodip
Dual	Octagrammic duotegum
Conjugate	Octagonal duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)≀S2, order 512
Convex	No
Nature	Tame

The octagrammic duoprism or stodip, also known as the octagrammic-octagrammic duoprism, the 8/3 duoprism or the 8/3-8/3 duoprism, is a noble uniform duoprism that consists of 16 octagrammic prisms, with 4 meeting at each vertex.

The octagrammic duoprism can be vertex-inscribed into a sphenoverted tesseractitesseractihexadecachoron or great distetracontoctachoron.

Vertex coordinates

The vertices of an octagrammic duoprism, centered at the origin and with unit edge length, are given by:

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

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "stodip".