# Hexakis tesseract

The **hexakis tesseract**, also known as the **square-pyramidal tetracontoctachoron**, is a convex isochoric polychoron with 48 square pyramids as cells. It can be obtained as the dual of the truncated hexadecachoron.

Hexakis tesseract | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | o4o3m3m () |

Elements | |

Cells | 48 square pyramids |

Faces | 96 isosceles triangles, 24 squares |

Edges | 32+64 |

Vertices | 8+16 |

Vertex figure | 8 cubes, 16 triakis tetrahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Truncated hexadecachoron |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | Yes |

Nature | Tame |

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anywhere between and times that of the tesseract gives a fully symmetric variant of this polychoron.