# Stellated tetracontoctachoron

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Stellated tetracontoctachoron
Rank4
TypeRegular
Notation
Bowers style acronymStoc
Elements
Components2 icositetrachora
Cells48 octahedra
Faces192 triangles
Edges192
Vertices48
Vertex figureCube, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle 1}$
Inradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Hypervolume${\displaystyle 4}$
Dichoral angle${\displaystyle 120^{\circ }}$
Related polytopes
ArmyBicont
RegimentStoc
DualStellated tetracontoctachoron
ConjugateStellated tetracontoctachoron
Convex coreTetracontoctachoron
Abstract & topological properties
Flag count2304
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

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:

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