# Small stellated tetracontoctachoron

Small stellated tetracontoctachoron
Rank4
TypeRegular
Notation
Bowers style acronymSistic
Elements
Cells96 tetrahedra as 48 stella octangulas
Faces192 triangles
Edges144
Vertices48
Vertex figureOctahedron, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Inradius${\displaystyle {\frac {\sqrt {2}}{4}}\approx 0.35355}$
Hypervolume${\displaystyle 1}$
Dichoral angle${\displaystyle 120^{\circ }}$
Related polytopes
ArmyBicont
RegimentSistic
DualGreat stellated tetracontoctachoron
ConjugateSmall stellated tetracontoctachoron
Convex coreTetracontoctachoron
Abstract & topological properties
Flag count2304
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

The small stellated tetracontoctachoron or sistic is a regular compound polychoron. It is a compound of six hexadecachora. It has 96 tetrahedra as cells, which lie in pairs in the same hyperplane so they combine into 48 stella octangulas. 8 cells join at each vertex. It can also be thought of as a compound of two stellated icositetrachora in opposite orientations, with each stellated icositetrachoron replacing an icositetrachoron in the stellated tetracontoctachoron.

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right).}$
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {\sqrt {2}}{4}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,0\right).}$