Sterication

Truncation operators

1. t_0,1 or t: Truncation - applied to polygons and higher. A truncation removes vertices, and inserts a new facet in place of each former vertex. Faces are truncated, doubling their edges. (The term, coined by Kepler, comes from Latin truncare 'to cut off'.)
   • There are higher truncations also: bitruncationt_1,2 or 2t, tritruncationt_2,3 or 3t, quadritruncationt_3,4 or 4t, quintitruncationt_4,5 or 5t, etc.
2. t_0,2 or rr: Cantellation - applied to polyhedra and higher. It can be seen as rectifying its rectification. A cantellation truncates both vertices and edges and replaces them with new facets. Cells are replaced by topologically expanded copies of themselves. (The term, coined by Johnson, is derived from the verb cant, like bevel, meaning to cut with a slanted face.)
   • There are higher cantellations also: bicantellationt_1,3 or r2r, tricantellationt_2,4 or r3r, quadricantellationt_3,5 or r4r, etc.
   • t_0,1,2 or tr: Cantitruncation - applied to polyhedra and higher. It can be seen as truncating its rectification. A cantitruncation truncates both vertices and edges and replaces them with new facets. Cells are replaced by topologically expanded copies of themselves. (The composite term combines cantellation and truncation)
     • There are higher cantellations also: bicantitruncationt_1,2,3 or t2r, tricantitruncationt_2,3,4 or t3r, quadricantitruncationt_3,4,5 or t4r, etc.
3. t_0,3: Runcination - applied to Uniform 4-polytope and higher. Runcination truncates vertices, edges, and faces, replacing them each with new facets. 4-faces are replaced by topologically expanded copies of themselves. (The term, coined by Johnson, is derived from Latin runcina 'carpenter's plane'.)
   • There are higher runcinations also: biruncinationt_1,4, triruncinationt_2,5, etc.
4. t_0,4 or 2r2r: Sterication - applied to Uniform 5-polytopes and higher. Sterication truncates vertices, edges, faces, and cells, replacing each with new facets. 5-faces are replaced by topologically expanded copies of themselves. (The term, coined by Johnson, is derived from Greek stereos 'solid'.)
   • There are higher sterications also: bistericationt_1,5 or 2r3r, tristericationt_2,6 or 2r4r, etc.
   • t_0,2,4 or 2t2r: Stericantellation - applied to Uniform 5-polytopes and higher.
     • There are higher sterications also: bistericantellationt_1,3,5 or 2t3r, tristericantellationt_2,4,6 or 2t4r, etc.
5. t_0,5: Pentellation - applied to Uniform 6-polytopes and higher. Pentellation truncates vertices, edges, faces, cells, and 4-faces, replacing each with new facets. 6-faces are replaced by topologically expanded copies of themselves. (Pentellation is derived from Greek pente 'five'.)
   • There are also higher pentellations: bipentellationt_1,6, tripentellationt_2,7, etc.
6. t_0,6 or 3r3r: Hexication - applied to Uniform 7-polytopes and higher. Hexication truncates vertices, edges, faces, cells, 4-faces, and 5-faces, replacing each with new facets. 7-faces are replaced by topologically expanded copies of themselves. (Hexication is derived from Greek hex 'six'.)
   • There are higher hexications also: bihexication: t_1,7 or 3r4r, trihexication: t_2,8 or 3r5r, etc.
   • t_0,3,6 or 3t3r: Hexiruncinated - applied to Uniform 7-polytopes and higher.
     • There are also higher hexiruncinations: bihexiruncinated: t_1,4,7 or 3t4r, trihexiruncinated: t_2,5,8 or 3t5r, etc.
7. t_0,7: Heptellation - applied to Uniform 8-polytopes and higher. Heptellation truncates vertices, edges, faces, cells, 4-faces, 5-faces, and 6-faces, replacing each with new facets. 8-faces are replaced by topologically expanded copies of themselves. (Heptellation is derived from Greek hepta 'seven'.)
   • There are higher heptellations also: biheptellationt_1,8, triheptellationt_2,9, etc.
8. t_0,8 or 4r4r: Octellation - applied to Uniform 9-polytopes and higher.
9. t_0,9: Ennecation - applied to Uniform 10-polytopes and higher.