MöbiusKantor configuration
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MöbiusKantor configuration  

Rank  2 
Type  Regular 
Elements  
Edges  8 triads 
Vertices  8 
Vertex figure  Triad 
Related polytopes  
Dual  MöbiusKantor configuration 
Abstract & topological properties  
Euler characteristic  0 
Configuration symbol  (8_{3}) 
The MöbiusKantor configuration is a exotic polygonoid and 3configuration. It has 8 triads and 8 vertices, with a triadic vertex figure. The MöbiusKantor configuration cannot be realized in Euclidean space with straight edges. It can however be realized complex projective space.
Related polytopes[edit  edit source]
The MöbiusKantor configuration is closely related to the MöbiusKantor polygon, a complex polygon. The two have the same abstract structure.
Gallery[edit  edit source]

A realization of the MöbiusKantor configuration^{[1]} on the surface of a torus

The MöbiusKantor graph, the incidence graph of the MöbiusKantor configuration

The MöbiusKantor configuration realized in Euclidean space with 7 straight edges. Since the MöbiusKantor configuration cannot be realized in Euclidean space with only straight edges, this is the most straight edges possible.
External links[edit  edit source]
 Wikipedia contributors. "MöbiusKantor configuration".
 Weisstein, Eric W. "MöbiusKantor Configuration" at MathWorld.
References[edit  edit source]
 ↑ Coxeter (1950:429)
Bibliography[edit  edit source]
 Coxeter, Harold (1950), "Selfdual configurations and regular graphs" (PDF), Bulletin of the American Mathematical Society, 56 (5): 427–431, doi:10.1090/S000299041950094075, MR 0038078