Stellated icositetrachoron

Stellated icositetrachoron
Rank	4
Type	Regular
Notation
Bowers style acronym	Stico
Elements
Components	3 hexadecachora
Cells	48 tetrahedra as 24 stella octangulas
Faces	96 triangles
Edges	72
Vertices	24
Vertex figure	Octahedron, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Inradius	${\frac {\sqrt {2}}{4}}\approx 0.35355$
Hypervolume	${\frac {1}{2}}=0.5$
Dichoral angle	$120^{\circ }$
Related polytopes
Army	Ico
Regiment	Stico
Dual	Great icositetrachoron
Conjugate	None
Convex core	Icositetrachoron
Abstract & topological properties
Flag count	1152
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

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:

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

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

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

External links

• Klitzing, Richard. "stico".