In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges and vertices, creating new facets in place of the original face, edge, and vertex centers. It is a higher order truncation operation, following cantellation, and truncation. It is represented by an extended Schläfli symbol t0,3{p,q,...}. This operation only exists for 4polytopes {p,q,r} or higher. This operation is dualsymmetric for regular uniform 4polytopes and 3space convex uniform honeycombs. Runcinated 4polytopes/honeycombs forms:
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