Möbius-Kantor configuration
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| Möbius-Kantor configuration | |
|---|---|
 | |
| Rank | 2 |
| Type | Regular |
| Elements | |
| Edges | 8 triads |
| Vertices | 8 |
| Vertex figure | Triad |
| Related polytopes | |
| Dual | Möbius-Kantor configuration |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Configuration symbol | (83) |
The Möbius-Kantor configuration is a exotic polygonoid and 3-configuration. It has 8 triads and 8 vertices, with a triadic vertex figure. The Möbius-Kantor configuration cannot be realized in Euclidean space with straight edges. It can however be realized complex projective space.
Related polytopes[edit | edit source]
The Möbius-Kantor configuration is closely related to the Möbius-Kantor polygon, a complex polygon. The two have the same abstract structure.
Gallery[edit | edit source]
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![A realization of the Möbius-Kantor configuration[1] on the surface of a torus](//static.miraheze.org/polytopewiki/c/c2/%288_4%29_square.svg)
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The Möbius-Kantor graph, the incidence graph of the Möbius-Kantor configuration
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The Möbius-Kantor configuration realized in Euclidean space with 7 straight edges. Since the Möbius-Kantor configuration cannot be realized in Euclidean space with only straight edges, this is the most straight edges possible.
![A realization of the Möbius-Kantor configuration[1] on the surface of a torus](/wiki/File:(8_4)_square.svg)
_nearly_euclidean.svg)
External links[edit | edit source]
- Wikipedia contributors. "Möbius-Kantor configuration".
- Weisstein, Eric W. "Möbius-Kantor Configuration" at MathWorld.
References[edit | edit source]
- ↑ Coxeter (1950:429)
Bibliography[edit | edit source]
- Coxeter, Harold (1950), "Self-dual configurations and regular graphs" (PDF), Bulletin of the American Mathematical Society, 56 (5): 427–431, doi:10.1090/S0002-9904-1950-09407-5, MR 0038078