Editing 24-cell (section)

=== Related complex polygons ===
The [[regular complex polygon]] <sub>4</sub>{3}<sub>4</sub>, {{CDD|4node_1|3|4node}} or {{CDD|node_h|6|4node}} contains the 24 vertices of the 24-cell, and 24 4-edges that correspond to central squares of 24 of 48 octahedral cells. Its symmetry is <sub>4</sub>[3]<sub>4</sub>, order 96.{{Sfn|Coxeter|1991|p=}}

The regular complex polytope <sub>3</sub>{4}<sub>3</sub>, {{CDD|3node_1|4|3node}} or {{CDD|node_h|8|3node}}, in <math>\mathbb{C}^2</math> has a real representation as a 24-cell in 4-dimensional space. <sub>3</sub>{4}<sub>3</sub> has 24 vertices, and 24 3-edges. Its symmetry is <sub>3</sub>[4]<sub>3</sub>, order 72.

{| class=wikitable width=600
|+ Related figures in orthogonal projections
|-
!Name
!{3,4,3}, {{CDD|node_1|3|node|4|node|3|node}}
!<sub>4</sub>{3}<sub>4</sub>, {{CDD|4node_1|3|4node}}
!<sub>3</sub>{4}<sub>3</sub>, {{CDD|3node_1|4|3node}}
|-
!Symmetry
![3,4,3], {{CDD|node|3|node|4|node|3|node}}, order 1152
!<sub>4</sub>[3]<sub>4</sub>, {{CDD|4node|3|4node}}, order 96
!<sub>3</sub>[4]<sub>3</sub>, {{CDD|3node|4|3node}}, order 72
|- align=center
!Vertices
|24||24||24
|- align=center
!Edges
|96 2-edges||24 4-edge||24 3-edges
|- valign=top
!valign=center|Image
|[[File:24-cell t0 F4.svg|200px]]<BR>24-cell in F4 Coxeter plane, with 24 vertices in two rings of 12, and 96 edges.
|[[File:Complex polygon 4-3-4.png|200px]]<BR><sub>4</sub>{3}<sub>4</sub>, {{CDD|4node_1|3|4node}} has 24 vertices and 32 4-edges, shown here with 8 red, green, blue, and yellow square 4-edges.
|[[File:Complex polygon 3-4-3-fill1.png|200px]]<BR><sub>3</sub>{4}<sub>3</sub> or {{CDD|3node_1|4|3node}} has 24 vertices and 24 3-edges, shown here with 8 red, 8 green, and 8 blue square 3-edges, with blue edges filled.
|}