Editing Kepler–Poinsot polyhedron (section)

===Conway's operational terminology===

[[John Horton Conway|John Conway]] defines the Kepler–Poinsot polyhedra as ''greatenings'' and ''stellations'' of the convex solids.<br>
In his [[Stellation#Naming stellations|naming convention]], the [[small stellated dodecahedron]] is just the ''stellated dodecahedron''.

{| class="wikitable"
| icosahedron (I)
| dodecahedron (D)
|-
| great dodecahedron (gD)
| stellated dodecahedron (sD)
|-
| great icosahedron (gI)
| great stellated dodecahedron (sgD = gsD)
|}

''Stellation'' changes pentagonal faces into pentagrams. (In this sense stellation is a unique operation, and not to be confused with the more general [[stellation]] described below.)

''Greatening'' maintains the type of faces, shifting and resizing them into parallel planes.

{| class="wikitable collapsible collapsed" style="text-align: center;"
!colspan="7"| Conway relations illustrated
|-
|-
! diagram
| 
[[File:Relationship among regular star polyhedra (green and violet).png|450px]]
<small><br>The polyhedra in this section are shown with the same [[midsphere|midradius]].</small>
|-
!style="color:#e57500"| stellation
|
{|
|
{{multiple image
 | align = right  | width = 200
 | image1 = Skeleton 12, size s.png | caption1 = <span style="color: #a13870;">'''D'''</span>
 | image2 = Skeleton St12, size s.png | caption2 = <span style="color: #a13870;">'''sD'''</span>
}}
|
{{multiple image
 | align = right  | width = 200
 | image1 = Skeleton Gr12, size s.png | caption1 = <span style="color: #007400;">'''gD'''</span>
 | image2 = Skeleton GrSt12, size s.png | caption2 = <span style="color: #007400;">sgD = '''gsD'''</span>
}}
|}

|-
!style="color:#00a7e1"| greatening
|
{| style="width: 100%;"
| [[File:Skeleton pair 12 and greatening, size s.png|thumb|center|200px|<span style="color: #a13870;">'''D'''</span> and <span style="color: #007400;">'''gD'''</span>]]
| [[File:Skeleton pair 20 and greatening, size s.png|thumb|center|200px|<span style="color: #007400;">'''I'''</span> and <span style="color: #a13870;">'''gI'''</span>]]
| [[File:Skeleton pair St12 and greatening, size s.png|thumb|center|200px|<span style="color: #a13870;">'''sD'''</span> and <span style="color: #007400;">'''gsD'''</span>]]
|}

|-
!style="color:#00cb00"| duality
|
{| style="width: 100%;"
| [[File:Skeleton pair 12-20, size s.png|thumb|center|200px|<span style="color: #a13870;">'''D'''</span> and <span style="color: #007400;">'''I'''</span>]]
| [[File:Skeleton pair Gr12 and dual, size s.png|thumb|center|200px|<span style="color: #007400;">'''gD'''</span> and <span style="color: #a13870;">'''sD'''</span>]]
| [[File:Skeleton pair Gr20 and dual, size s.png|thumb|center|200px|<span style="color: #a13870;">'''gI'''</span> and <span style="color: #007400;">'''gsD'''</span>]]
|}

|}