# 26-5 step prism

Jump to navigation
Jump to search

26-5 step prism | |
---|---|

File:26-5 step prism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 26 tetragonal disphenoids, 52+52+52 phyllic disphenoids |

Faces | 104+104 scalene triangles, 52+104 isosceles triangles |

Edges | 52+52+52+52 |

Vertices | 26 |

Vertex figure | 16-vertex polyhedron with 28 triangular faces |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 26-5 gyrochoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(26)-5)×2I, order 104 |

Convex | Yes |

Nature | Tame |

The **26-5 step prism** is a convex isogonal polychoron, member of the step prism family. It has 26 tetragonal disphenoids and 156 phyllic disphenoids of three kinds as cells. 4 tetragonal and 24 phyllic disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1: ≈ 1:1.78000.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 26-5 step prism of circumradius √2 are given by:

- (sin(π
*k*/13), cos(π*k*/13), sin(5π*k*/13), cos(5π*k*/13)),

where *k* is an integer from 0 to 25.