Editing Kepler–Poinsot polyhedron (section)

===Stellations and facetings===

The [[great icosahedron]] is one of the [[stellation]]s of the [[regular icosahedron|icosahedron]]. (See ''[[The Fifty-Nine Icosahedra]]'')<br>
The three others are all the stellations of the [[regular dodecahedron|dodecahedron]].

The [[great stellated dodecahedron]] is a [[faceting]] of the dodecahedron.<br>
The three others are facetings of the icosahedron.

{| class="wikitable collapsible collapsed" style="text-align: center;"
!colspan="7"| Stellations and facetings
|-
! Convex
|colspan="3"| [[File:Polyhedron 20 big.png|160px]]<br>[[regular icosahedron|icosahedron]]
|colspan="3"| [[File:Polyhedron 12 big.png|160px]]<br>[[regular dodecahedron|dodecahedron]]
|-
! Stellations
|colspan="3"| [[File:Polyhedron great 20.png|90px]]<br>[[great icosahedron|gI]] <small>(the one with yellow faces)</small>
| [[File:Polyhedron great 12.png|90px]]<br>[[great dodecahedron|gD]]
| [[File:Polyhedron great 12 dual.png|90px]]<br>[[small stellated dodecahedron|sD]]
| [[File:Polyhedron great 20 dual.png|90px]]<br>[[great stellated dodecahedron|gsD]]
|-
! Facetings
| [[File:Polyhedron great 20.png|90px]]<br>[[great icosahedron|gI]]
| [[File:Polyhedron great 12.png|90px]]<br>[[great dodecahedron|gD]]
| [[File:Polyhedron great 12 dual.png|90px]]<br>[[small stellated dodecahedron|sD]]
|colspan="3"| [[File:Polyhedron great 20 dual.png|90px]]<br>[[great stellated dodecahedron|gsD]] <small>(the one with yellow vertices)</small>
|}

If the intersections are treated as new edges and vertices, the figures obtained will not be [[regular polyhedron|regular]], but they can still be considered [[stellation]]s.{{Example needed|s|date=December 2018}}

(See also [[List of Wenninger polyhedron models#Stellations of dodecahedron|List of Wenninger polyhedron models]])