γ 2,3

γ 3 2
Rank	2
Dimension	2
Type	Regular
Space	Complex
Notation
Coxeter diagram
Schläfli symbol	3{4}2
Elements
Edges	6 3-edges
Vertices	9
Vertex figure	Dyad
Related polytopes
Real analog	Triangular duoprism
Dual	β 3 2
Abstract & topological properties
Flag count	18
Properties
Symmetry	3[4]2, order 18

γ 3
2  is a regular complex polygon. It is the simplest generalized square other than the real square.

Vertex coordinates

Vertex coordinates for the generalized square γ 3
2  can be given as:

• $\left({\frac {\sqrt {3}}{3}},\,{\frac {\sqrt {3}}{3}}\right)$,
• $\left(-{\frac {\sqrt {3}}{6}}\pm {\frac {i}{2}},\,-{\frac {\sqrt {3}}{6}}\pm {\frac {i}{2}}\right)$,

and both permuations of:

• $\left({\frac {\sqrt {3}}{3}},\,-{\frac {\sqrt {3}}{6}}\pm {\frac {i}{2}}\right)$,

Gallery

• 
  A stereographic projection of γ 3
  2 

Coxeter diagrams

A generalized square γ 3
2  can be represented by the following Coxeter diagrams:

• (full symmetry)
• (₃[2]₃ symmetry. Prism product of two 3-edges.)