Great icositetrachoron

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Great icositetrachoron
Schlegel wireframe 24-cell.png
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
Inradius
Hypervolume
Dichoral angle
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.

Cross-sections[edit | edit source]

Gico-slices.gif

Vertex coordinates[edit | edit source]

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

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

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

External links[edit | edit source]