Möbius–Kantor polygon

In geometry, the Möbius–Kantor polygon is a regular complex polygon ₃{3}₃, , in ${\displaystyle \mathbb {C} ^{2}}$. ₃{3}₃ has 8 vertices, and 8 edges. It is self-dual. Every vertex is shared by 3 triangular edges. Coxeter named it a Möbius–Kantor polygon for sharing the complex configuration structure as the Möbius–Kantor configuration, (8₃).

Discovered by G.C. Shephard in 1952, he represented it as 3(24)3, with its symmetry, Coxeter called as ₃[3]₃, isomorphic to the binary tetrahedral group, order 24.

The 8 vertex coordinates of this polygon can be given in ${\displaystyle \mathbb {C} ^{3}}$, as:

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