page_title: Kepler–Poinsot polyhedron
section_title: Conway's operational terminology
hierarchical_section_title: Kepler–Poinsot polyhedron / Relationships among the regular polyhedra / Conway's operational terminology
caption_attribution_description: Regular polyhedra and their greatenings (Conway operation)Part of Skeletons of polyhedra (mostly green and violet) dodecahedron (violet),great dodecahedron (green) icosahedron (green),great icosahedron (violet) stellated dodecahedron (violet),great stellated dodecahedron (green) The images in this set have matching sizes. Please do not overwrite them with cropped versions. This &#32;image was created with POV-Ray. This file was uploaded with Commonist.
context_page_description: In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
  They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures. They can all be seen as three-dimensional analogues of the pentagram in one way or another.
context_section_description: John Conway defines the Kepler–Poinsot polyhedra as greatenings and stellations of the convex solids.
  
  In his naming convention the small stellated dodecahedron is just the stellated dodecahedron.
  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.
caption: I and gI
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