Antifrustary distetracontoctachoron

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Antifrustary distetracontoctachoron
Rank4
TypeUniform
Notation
Bowers style acronymAfdec
Coxeter diagramx3o4x3o4*a4/3*c ()
Elements
Cells48 cuboctahedra, 48 great cubicuboctahedra
Faces384 triangles, 288 squares, 144 octagrams
Edges1152
Vertices288
Vertex figureRectangular trapezoprism, edge lengths 1 and 2 (base) and 2–2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGocco–8/3–gocco: 135°
 Co–4–gocco: 135°
 Co–3–gocco: 120°
Central density5
Related polytopes
ArmyCont, edge length
RegimentAfdec
ConjugateGreat retrofrustary distetracontoctachoron
Abstract & topological properties
Flag count13824
Euler characteristic–144
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

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[edit | edit source]

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

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

Related polychora[edit | edit source]

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[edit | edit source]