# Great distetracontoctachoron

Great distetracontoctachoron
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGiddic
Coxeter diagramx3o4o3x4/3*a ()
Elements
Cells48 octahedra, 48 quasitruncated hexahedra
Faces384 triangles, 144 octagrams
Edges576
Vertices144
Vertex figureSquare antiprism, edge lengths 1 (base) and 2–2 (sides)
Edge figureoct 3 quith 8/3 quith 8/3 quith 3
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{2-\sqrt2} ≈ 0.76537}$
Hypervolume${\displaystyle 2(19-12\sqrt2) ≈ 4.05887}$
Dichoral anglesQuith–8/3–quith: 135°
Oct–3–quith: 120°
Number of external pieces720
Level of complexity23
Related polytopes
ArmySpic
RegimentGiddic
ConjugateSmall distetracontoctachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

The great distetracontoctachoron, or giddic, is a nonconvex uniform polychoron that consists of 48 regular octahedra and 48 quasitruncated hexahedra. 2 octahedra and 8 quasitruncated hexahedra join at each vertex.

The great distetracontoctachoron contains the vertices and edges of an octagrammic duoprism, sphenoverted tesseractitesseractihexadecachoron, and quasitruncated hexahedral prism.

## Vertex coordinates

The vertices of a great distetracontoctachoron of edge length 1 are all permutations of:

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

The second set of vertices are identical to the vertices of an inscribed sphenoverted tesseractitesseractihexadecachoron.

## Related polychora

The great distetracontoctachoron is the colonel of a regiment that includes 20 members, 2 fissaries, and a compound. Among the members, 8 in total have doubled F4 symmetry, including the great distetracontoctachoron itself, the quasiprismatotetracontoctachoron, and the noble great retrotetracontoctachoron, while the 12 remaining members, and the fissaries and compound, have single F4 symmetry only.