Antifrustary distetracontoctachoron

Antifrustary distetracontoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Afdec
Coxeter diagram	x3o4x3o4*a4/3*c ()
Elements
Cells	48 cuboctahedra, 48 great cubicuboctahedra
Faces	384 triangles, 288 squares, 144 octagrams
Edges	1152
Vertices	288
Vertex figure	Rectangular trapezoprism, edge lengths 1 and √2 (base) and √2–√2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Hypervolume	$4(5+6{\sqrt {2}})\approx 53.94113$
Dichoral angles	Gocco–8/3–gocco: 135°
	Co–4–gocco: 135°
	Co–3–gocco: 120°
Central density	5
Related polytopes
Army	Cont, edge length ${\sqrt {2}}-1$
Regiment	Afdec
Conjugate	Great retrofrustary distetracontoctachoron
Abstract & topological properties
Flag count	13824
Euler characteristic	–144
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The antifrustary distetracontoctachoron, or afdec, is a nonconvex uniform polychoron that consists of 48 cuboctahedra and 48 great cubicuboctahedra. 2 cuboctahedra and 4 great cubicuboctahedra join at each vertex.

The antifrustary distetracontoctachoron contains the vertices of a hexagonal duoprism, small skewverted prismatohexadecadisoctachoron, octagonal-octagrammic duoprism, and cuboctatruncated cuboctahedral prism.

Vertex coordinates

Coordinates for the vertices of an antifrustary distetracontoctachoron of edge length 1 are all permutations of:

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

The second set of vertices are identical to those of an inscribed small skewverted prismatohexadecadisoctachoron.

Related polychora

The antifrustary distetracontoctaachoron is the colonel of a regiment that contains 53 uniform members, along with one fissary and one compound. 7 uniform members, plus the fissary and compound have full symmetry, while the other facetings have a single F4 symmetry only.

External links

• Bowers, Jonathan. "Category 15: Afdec Regiment" (#612).

• Klitzing, Richard. "afdec".