# Great icositetrachoron

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Great icositetrachoron | |
---|---|

Rank | 4 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Gico |

Elements | |

Components | 3 tesseracts |

Cells | 24 cubes |

Faces | 72 squares |

Edges | 96 |

Vertices | 24 |

Vertex figure | Stella octangula, edge length √2 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angle | |

Related polytopes | |

Army | Ico |

Regiment | Ico |

Dual | Stellated icositetrachoron |

Conjugate | None |

Convex core | Icositetrachoron |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

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]

## 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]

- Klitzing, Richard. "gico".