Editing Platonic solid (section)

=== As a configuration===
The elements of a polyhedron can be expressed in a [[Configuration (polytope)#Higher dimensions|configuration matrix]]. The rows and columns correspond to vertices, edges, and faces. The diagonal numbers say how many of each element occur in the whole polyhedron. The nondiagonal numbers say how many of the column's element occur in or at the row's element. Dual pairs of polyhedra have their configuration matrices rotated 180 degrees from each other.<ref>Coxeter, Regular Polytopes, sec 1.8 Configurations</ref>

{| class=wikitable
! {p,q}
! colspan=5 | Platonic configurations
|- style="vertical-align:top;"
! [[Group order]]: <br/>''g'' = 8''pq''/(4 − (''p'' − 2)(''q'' − 2))
! ''g'' = 24
! colspan=2 | ''g'' = 48
! colspan=2 | ''g'' = 120
|-
|
{| class=wikitable style="margin: auto;"
! !! v !! e !! f
|- align=center
!v
| ''g''/2''q'' || ''q'' || ''q''
|- align=center
! e
| 2 || ''g''/4 || 2
|- align=center
! f
| ''p'' || ''p'' || ''g''/2''p''
|}

| style="background-color:#e0f0e0;" |
{| class=wikitable
|+ {3,3}
|- align=center
| 4 || 3 || 3
|- align=center
| 2 || 6 || 2
|- align=center
| 3 || 3 || 4
|}
| style="background-color:#f0e0e0;" |
{| class=wikitable
|+ {3,4}
|- align=center
| 6 ||  4 || 4
|- align=center
| 2 || 12 || 2
|- align=center
| 3 ||  3 || 8
|}
| style="background-color:#e0e0f0;" |
{| class=wikitable
|+ {4,3}
|- align=center
| 8 ||  3 || 3
|- align=center
| 2 || 12 || 2
|- align=center
| 4 ||  4 || 6
|}
| style="background-color:#f0e0e0" |
{| class=wikitable
|+ {3,5}
|- align=center
| 12 ||  5 ||  5
|- align=center
|  2 || 30 ||  2
|- align=center
|  3 ||  3 || 20
|}
| style="background-color:#e0e0f0;" |
{| class=wikitable
|+ {5,3}
|- align=center
| 20||  3 ||  3
|- align=center
|  2|| 30 ||  2
|- align=center
|  5||  5 || 12
|}
|}