# 24-7 step prism

The **24-7 step prism**, also known as the **digonal double triswirlprism**, is a convex isogonal polychoron and a member of the step prism family. It has 24 rhombic disphenoids and 96 phyllic disphenoids of two kinds as cells, with 20 (4 rhombic and 16 phyllic disphenoids) joining at each vertex. It is the second in an infinite family of isogonal digonal prismatic swirlchora.

24-7 step prism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 48+48 phyllic disphenoids, 24 rhombic disphenoids |

Faces | 96+96 scalene triangles, 48 isosceles triangles |

Edges | 24+24+48+48 |

Vertices | 24 |

Vertex figure | Paratetraaugmented hexagonal tegum |

Measures (circumradius , based on a uniform duoprism) | |

Edge lengths | 8-valence (24): |

4-valence (24): | |

6-valence (48): | |

3-valence (48): 2 | |

Central density | 1 |

Related polytopes | |

Dual | 24-7 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(24)-7)×2R, order 96 |

Convex | Yes |

Nature | Tame |

The ratio between the longest and shortest edges is 1: ≈ 1:1.84776.

## Vertex coordinates edit

Coordinates for the vertices of a 24-7 step prism of circumradius √2 are given by:

where *k* is an integer from 0 to 23.