# Stellated icositetrachoron

Stellated icositetrachoron
Rank4
TypeRegular
Notation
Bowers style acronymStico
Elements
Cells48 tetrahedra as 24 stella octangulas
Faces96 triangles
Edges72
Vertices24
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${\displaystyle {\frac {1}{2}}=0.5}$
Dichoral angle${\displaystyle 120^{\circ }}$
Related polytopes
ArmyIco
RegimentStico
DualGreat icositetrachoron
ConjugateNone
Convex coreIcositetrachoron
Abstract & topological properties
Flag count1152
OrientableYes
Properties
SymmetryF4, order 1152
ConvexNo
NatureTame

The stellated icositetrachoron or stico is a regular compound polychoron. It is a compound of three hexadecachora. It has 48 tetrahedra as cells which lie in pairs in the same hyperplane, so they combine into 24 stella octangulas. 8 cells join at each vertex.

Its quotient prismatic equivalent is the tridiminished icosiheptaheptacontadipeton, which is six-dimensional.

## Vertex coordinates

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

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

The same stellated icositetrachoron in opposite orientation to this one has vertices given by all permutations of:

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