Great distetracontoctachoron

Great distetracontoctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Giddic
Coxeter diagram	x3o4o3x4/3*a ()
Elements
Cells	48 octahedra, 48 quasitruncated hexahedra
Faces	384 triangles, 144 octagrams
Edges	576
Vertices	144
Vertex figure	Square antiprism, edge lengths 1 (base) and √2–√2 (sides)
Edge figure	oct 3 quith 8/3 quith 8/3 quith 3
Measures (edge length 1)
Circumradius	$\sqrt{2-\sqrt2} ≈ 0.76537$
Hypervolume	$2(19-12\sqrt2) ≈ 4.05887$
Dichoral angles	Quith–8/3–quith: 135°
	Oct–3–quith: 120°
Number of external pieces	720
Level of complexity	23
Related polytopes
Army	Spic, edge length $\sqrt2-1$
Regiment	Giddic
Conjugate	Small distetracontoctachoron
Abstract & topological properties
Flag count	9216
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

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.

Gallery

Vertex coordinates

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

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

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.

External links

• Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#532).

• Klitzing, Richard. "giddic".