Polytope operations

Polytope operators

Tier 0: Base - the base form of a polytope.

Rectification - rectifies its facets and adds the polytope's vertex figure(s). Puts vertices in each edge. In 2D, it is the same as its dual. (3D and above)

Birectification - birectifies its facets, adds the polytope's vertex figure(s) and rectifies the vertex figure(s). Puts vertices in each face. In 4D, it is the same as its rectified dual and in 3D, it is the same as its dual. (5D and above)

n-rectification - n-rectifies its facets, adds the polytope's vertex figure(s) and (n-1)-rectifies the vertex figure(s). Puts vertices in each n-face. In 2n-D, it is the same as its (n-1)-rectified dual and in (n+1)-D, it is the same as its dual. ((2n+1)D and above)

Tier 1: Truncation - truncates its facets and adds the polytope's vertex figure(s). Cuts off the polytope starting from the vertex figure(s) but at a depth lesser than rectification. (2D and above)

Bitruncation - bitruncates its facets, adds the polytope's vertex figure(s) and truncates the vertex figure(s). Cuts off the polytope starting from the figure(s) greater than rectification but at a depth lesser than birectification. In 3D, it is the same as its truncated dual and in 2D, it is the same as its truncation. (4D and above)

n-truncation - n-truncates its facets, adds the polytope's vertex figure(s) and (n-1)-truncates the vertex figure(s). Cuts off the polytope starting from the figure(s) greater than (n-1)-rectification but at a depth lesser than n-rectification. (2n-D and above)

Cantellation - cantellates its facets, rectifies the vertex figure(s) and adds prisms of the polytope's edge figure(s). Expands the polytope's faces radially from its center. Same as the rectification of rectification. (3D and above)

Bicantellation - bicantellates its facets, cantellates the vertex figure(s) and adds duoprisms based on its faces and the face figure. Same as the rectification of birectification. In 4D, bicantellation is the same as its cantellated dual and in 3D it is the same as its cantellation. (5D and above)

n-cantellation - n-cantellates its facets, (n-1)-cantellates the vertex figure(s) and adds duoprisms based on its n-faces and the n-face figure. Same as the rectification of n-rectification. ((2n+1)D and above)

Runcination - runcinates its facets, birectifies the vertex figure(s), adds prisms of the rectified edge figure(s) and adds duoprisms based on its face - face figure. (4D and above)

Tier 2: Cantitruncation - cantitruncates its facets, truncates the vertex figure(s) and adds prisms of the edge figure(s). (3D and above)

Runcitruncation - runcitruncates its facets, cantellates the vertex figure(s), adds prisms of the rectified edge figure(s) and adds duoprisms based on its truncated face - face figure. In 4D, it is the same as its runcicantellated dual. (4D and above)

Runcicantellation - runcicantellates its facets, bitruncates the vertex figure(s), adds prisms of the truncated edge figure(s) and adds duoprisms based on its face - face figure. In 4D, it is the same as its runcitruncated dual. (4D and above)

Steritruncation - steritruncates its facets, runcinates the vertex figure(s), adds prisms of the birectified edge figure(s) and adds duoprisms based on its truncated face - rectified face figure and another based on its truncated cell - cell figure. (5D and above)