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Welcome to the Polytope Wiki

A free-to-edit wiki about polytopes.

### About the Polytope Wiki

The Polytope Wiki is a wiki dedicated to the classification, description, and discovery of polytopes.

Polytopes are a wide class of geometric shapes that generalize the intuitive notions of "flat" shapes like polygons and polyhedra into higher (and lower) dimensions. Some of their main categories are:

- Regular polytopes
- Uniform polytopes
- Semi-uniform polytopes
- Scaliform polytopes
- Convex regular-faced polytopes

If you want to get started, you might be interested in the following:

### Recent changes

**List of abbreviations:**

- N
- This edit created a new page (also see list of new pages)
- m
- This is a minor edit
- b
- This edit was performed by a bot
- (
*±123*) - The page size changed by this number of bytes

#### 4 October 2024

N 16:37 | Dodecahedral pyramid diffhist +93 2405:4802:1C9A:4820:2967:966E:AA13:5F7B talk (Done) |

16:33 | Triangular tegum diffhist −62 2405:4802:1C9A:4820:2967:966E:AA13:5F7B talk (Done) |

N 16:32 | Affinely isomorphic diffhist +623 Vel talk contribs (Created page with "Two convex polytopes <math>P \subseteq \mathbb{R}^d</math> and <math>Q \subseteq \mathbb{R}^e</math> are '''affinely isomorphic''' if they are related to each other by a affine map <math>f : \mathbb{R}^d \rightarrow \mathbb{R}^e</math> that is a bijection over the points of {{mvar|P}} and {{mvar|Q}}.<ref>{{Cite Ziegler}}</ref> The map itself does not need to be surjective or injective on the spaces, only on the polytopes themselves. Affine isomorphism is a condition...") |

16:17 | Sesquitruncated octahedron diffhist +96 Vel talk contribs (revise to discuss 2 variants) |

15:59 | Pentellated 6-cube diffhist +12 Username5243 talk contribs |

### Wiki statistics

- Age of wiki: 4 years, 5 months and 1 day
- Number of articles: 7,497
- Number of files: 7,342
- Number of edits: 109,641
- Number of users: 694

### News

**29 Jan 2024**- Mecejide discovers a new uniform 5-polytope.**27 Oct 2023**- Plasmath completes the enumeration of the non-prismatic noble polyhedra (there are 146 in total!).**15 June 2023**– Jonathan Bowers' website is updated, with new uniform polychora (bringing the count to 2191), polytera, and polypeta, among other things.

### Polytope of the Day

The**mucube**, short for multiple cube, is a regular skew apeirohedron consisting of an infinite number of squares. Discovered by John Flinders Petrie in 1926, it has a skew hexagon vertex figure and the Schläfli symbol {4,6∣4}.