# Möbius-Kantor polygon

Möbius-Kantor polygon
Rank2
TypeRegular
SpaceComplex
Notation
Coxeter diagram
Schläfli symbol${\displaystyle _{3}\{3\}_{3}}$
Elements
Edges8 3-edges
Vertices8
Vertex figure3-edge
Related polytopes
DualMöbius-Kantor polygon
Abstract & topological properties
Flag count24
Euler characteristic0
Configuration symbol(83)
Properties
Symmetry3[3]3, order 24

The Möbius-Kantor polygon is a regular complex polygon. It has 8 3-edges and 8 vertices.

## Related polytopes

The Möbius-Kantor polygon is closely related to the Möbius-Kantor configuration, with the two having the same abstract structure.

If the vertices of the Möbius-Kantor polygon are treated as vertices in ${\displaystyle \mathbb {R} ^{4}}$ rather than ${\displaystyle \mathbb {C} ^{2}}$, they are identical to those of the hexadecachoron. Additionally if the 3-edges of the Möbius-Kantor polygon are replaced with triangles in Euclidean space they form a symmetric subset of the faces of the hexadecachoron.

The Hessian polyhedron, has the Möbius-Kantor polygon as its faces and vertex figure.