# m

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m | |
---|---|

Rank | 3 |

Type | Acrohedron |

Space | Spherical |

Notation | |

Stewart notation | m |

Elements | |

Faces | 2 squares, 2+4+4 triangles |

Edges | 1+2+2+2+4+4+4 |

Vertices | 1+2+2+4 |

Abstract & topological properties | |

Flag count | 52 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{2}×I, order 4 |

Convex | No |

**m** is a non-convex polyhedron with regular faces.

## Vertex coordinates[edit | edit source]

Vertex coordinates for m with unit edge length can be given as:

- ,
- ,
- ,
- .

## Related polytopes[edit | edit source]

m has 3 concave triangular faces in the same configuration as three faces of the icosahedron. This allows a blend of the icosahedron with m along these faces. Several notable polyhedra are formed as diminishings of this blend.

m can be augmented by a pentagonal pyramid to form m*,

^{[1]}the smallest 5-4-3 acrohedron by face count.

In addition to m*, m is related to another 5-4-3 acrohedron. Two copies of m can be excavated from A_{5}'' to form the prize substitute, a 5-4-3 acrohedron with 16 faces.^{[1]}

## References[edit | edit source]

- ↑
^{1.0}^{1.1}Stewart (1964:157)

## Bibliography[edit | edit source]

- Stewart, Bonnie (1964).
*Adventures Amoung the Toroids*(2 ed.). ISBN 0686-119 36-3.