Editing 600-cell (section)

=== As a configuration ===
This [[Regular 4-polytope#As configurations|configuration matrix]]{{Sfn|Coxeter|1973|p=12|loc=§1.8. Configurations}} represents the 600-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 600-cell. The non-diagonal numbers say how many of the column's element occur in or at the row's element.

<math>\begin{bmatrix}\begin{matrix}120 & 12 & 30 & 20 \\ 2 & 720 & 5 & 5 \\ 3 & 3 & 1200 & 2 \\ 4 & 6 & 4 & 600 \end{matrix}\end{bmatrix}</math>

Here is the configuration expanded with ''k''-face elements and ''k''-figures. The diagonal element counts are the ratio of the full [[Coxeter group]] order, 14400, divided by the order of the subgroup with mirror removal.
{| class=wikitable
!H<sub>4</sub>||{{CDD|node_1|3|node|3|node|5|node}}
! [[k-face|''k''-face]]||f<sub>''k''</sub>||f<sub>0</sub> || f<sub>1</sub>||f<sub>2</sub>||f<sub>3</sub>||[[vertex figure|''k''-fig]]
!Notes
|- align=right
|H<sub>3</sub> || {{CDD|node_x|2|node|3|node|5|node}} ||( )
!f<sub>0</sub>
|| 120 ||  12 ||   30 ||  20 ||[[icosahedron|{3,5}]] || H<sub>4</sub>/H<sub>3</sub> = 14400/120 = 120
|- align=right
|A<sub>1</sub>H<sub>2</sub> ||{{CDD|node_1|2|node_x|2|node|5|node}} ||{ }
!f<sub>1</sub>
||   2 || 720 ||    5 ||   5 || [[pentagon|{5}]] || H<sub>4</sub>/H<sub>2</sub>A<sub>1</sub> = 14400/10/2 = 720
|- align=right
|A<sub>2</sub>A<sub>1</sub> ||{{CDD|node_1|3|node|2|node_x|2|node}} ||[[equilateral triangle|{3}]]
!f<sub>2</sub>
||   3 ||   3 || 1200 ||   2 || { } || H<sub>4</sub>/A<sub>2</sub>A<sub>1</sub> = 14400/6/2 = 1200
|- align=right
|A<sub>3</sub> ||{{CDD|node_1|3|node|3|node|2|node_x}} ||[[tetrahedron|{3,3}]]
!f<sub>3</sub>
||   4 ||   6 ||    4 || 600|| ( ) || H<sub>4</sub>/A<sub>3</sub> = 14400/24 = 600
|}