# Great icositetrachoron

Great icositetrachoron
Rank4
TypeRegular
SpaceSpherical
Notation
Bowers style acronymGico
Elements
Components3 tesseracts
Cells24 cubes
Faces72 squares
Edges96
Vertices24
Vertex figureStella octangula, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle 1}$
Inradius${\displaystyle \frac 1 2 = 0.5}$
Hypervolume${\displaystyle 3}$
Dichoral angle${\displaystyle 90°}$
Related polytopes
ArmyIco
RegimentIco
DualStellated icositetrachoron
ConjugateNone
Convex coreIcositetrachoron
Topological properties
OrientableYes
Properties
SymmetryF4, order 1152
ConvexNo
NatureTame

The great icositetrachoron or gico is a regular compound polychoron. It is a compound of three tesseracts. It has 24 cubes as cells, with 8 cells joining at a vertex.

This compound has fissary vertices, with each vertex being used in two components and a compound (the stella octangula) for a vertex figure.

Its quotient prismatic equivalent is the tesseractic triorthowedge, which is six-dimensional.

## Vertex coordinates

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

• ${\displaystyle \left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right).}$

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

• ${\displaystyle \left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),}$
• ${\displaystyle \left(±1,\,0,\,0,\,0\right).}$

These are identical to those of a regular icositetrachoron, with which this compound shares its vertices and edges.