Editing 5-cell (section)

=== As a configuration ===
This [[Regular 4-polytope#As configurations|configuration matrix]] represents the 5-cell. The rows and columns correspond to vertices, edges, faces, and cells. The diagonal numbers say how many of each element occur in the whole 5-cell. The nondiagonal numbers say how many of the column's element occur in or at the row's element. This self-dual polytope's matrix is identical to its 180 degree rotation.{{sfn|Coxeter|1973|p=12|loc=§1.8. Configurations}} The ''k''-faces can be read as rows left of the diagonal, while the ''k''-figures are read as rows after the diagonal.<ref>{{cite web | url=https://bendwavy.org/klitzing/incmats/pen.htm | title=Pen }}</ref>
[[File:Symmetrical 5-set Venn diagram.svg|thumb|Grünbaum's rotationally symmetrical 5-set Venn diagram, 1975]]
{| class=wikitable
|-
!Element||''k''-face||f<sub>''k''</sub>
!f<sub>0</sub>
!f<sub>1</sub>
!f<sub>2</sub>
!f<sub>3</sub>
!''k''-figs
|- align=right
|align=left bgcolor=#ffffe0 |<!--. . . .-->{{CDD|node_x|2|node_x|2|node_x|2|node_x}}||( )
|rowspan=1|f<sub>0</sub>
|bgcolor=#e0ffe0|5
|  bgcolor=#e0e0e0|4
|  bgcolor=#ffffff|6
|  bgcolor=#e0e0e0|4
|[[Tetrahedron|{3,3}]]
|- align=right
|align=left bgcolor=#ffffe0 |<!--x . . .-->{{CDD|node_1|2|node_x|2|node_x|2|node_x}}||{ }
|rowspan=1|f<sub>1</sub>
|  bgcolor=#e0e0e0|2
|bgcolor=#e0ffe0|10
|  bgcolor=#e0e0e0|3
|  bgcolor=#ffffff|3
|[[Triangle|{3}]]
|- align=right
|align=left bgcolor=#ffffe0 |<!--x3o . .-->{{CDD|node_1|3|node|2|node_x|2|node_x}}||[[triangle|{3}]]
|rowspan=1|f<sub>2</sub>
|  bgcolor=#ffffff|3
|  bgcolor=#e0e0e0|3
|bgcolor=#e0ffe0|10
|  bgcolor=#e0e0e0|2
|{ }
|- align=right
|align=left bgcolor=#ffffe0 |<!--x3o3o .-->{{CDD|node_1|3|node|3|node|2|node_x}}||[[Tetrahedron|{3,3}]]
|rowspan=1|f<sub>3</sub>
|  bgcolor=#e0e0e0|4
|  bgcolor=#ffffff|6
|  bgcolor=#e0e0e0|4
|bgcolor=#e0ffe0|5
|( )
|}
All these elements of the 5-cell are enumerated in [[Branko Grünbaum]]'s [[Venn diagram]] of 5 points, which is literally an illustration of the regular 5-cell in [[#Projections|projection]] to the plane.