Stellated tetracontoctachoron

Stellated tetracontoctachoron
Rank	4
Type	Regular
Notation
Bowers style acronym	Stoc
Elements
Components	2 icositetrachora
Cells	48 octahedra
Faces	192 triangles
Edges	192
Vertices	48
Vertex figure	Cube, edge length 1
Measures (edge length 1)
Circumradius	$1$
Inradius	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Hypervolume	$4$
Dichoral angle	$120^{\circ }$
Related polytopes
Army	Bicont
Regiment	Stoc
Dual	Stellated tetracontoctachoron
Conjugate	Stellated tetracontoctachoron
Convex core	Tetracontoctachoron
Abstract & topological properties
Flag count	2304
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The stellated tetracontoctachoron or stoc is a regular compound polychoron. It is a compound of two icositetrachora in dual orientations. it has 48 octahedra as cells, with 6 cells joining at each vertex.

Its quotient prismatic equivalent is the icositetrachoric antiprism, which is five-dimensional.

Vertex coordinates

The vertices of a stellated tetracontoctachoron of edge length 1, centered at the origin, are given by all permutations of:

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

External links

• Klitzing, Richard. "stoc".