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Truncation is a shape operation that intuitively, chops off all the corners of a polytope and exposes all of the polytope's vertex figures[1]. Truncation replaces all vertices with their vertex figures and all facets with their truncated versions. For example, truncating a cube, which has square faces and triangular verfs, will give out a shape whose faces are truncated squares and triangles. Truncating a polygon $ \{p\} $ will give out a polygon with symbol $ \{2p\} $.

Generally when truncating a uniform polytope, the uniform truncation is considered. The uniform truncation of a polytope is the truncated polytope such that all of its facets are uniform. Uniform truncation is represented by ringing the first and second nodes of the Coxeter diagram. Uniform truncation can be represented with the Schläfli symbol operator $ t_{0,1} $.

References

  1. https://web.archive.org/web/20070207021813/http://members.aol.com/Polycell/glossary.html#Truncation
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