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In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another. It is similar to expansion: it moves the faces apart (outward), and adds a new face between each two adjacent faces; but contrary to expansion, it maintains the original vertices. (Equivalently: it separates the faces by reducing them ...
Uniform truncation are a special case of this with equal edge lengths. The truncated cube, t{4,3}, with square faces becoming octagons, with new triangular faces are the vertices. Antitruncation A reverse shallow truncation, truncated outwards off the original edges, rather than inward. This results in a polytope which looks like the original ...
Tetrahedron, its edge truncation, and the truncated cube Truncating alternating vertices of the cube gives the chamfered tetrahedron , i.e. the edge truncation of the tetrahedron. The truncated triangular trapezohedron is another polyhedron which can be formed from cube edge truncation.
In Euclidean geometry, rectification, also known as critical truncation or complete-truncation, is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points. [1] The resulting polytope will be bounded by vertex figure facets and the rectified facets of the original polytope.
An interesting result of this operation is that self-dual 4-polytope {p,q,p} (and honeycombs) remain cell-transitive after bitruncation. There are 5 such forms corresponding to the five truncated regular polyhedra: t{q,p}.
It is constructed as a chamfer (edge-truncation) of a regular dodecahedron. The pentagons are reduced in size and new hexagonal faces are added in place of all the original edges. Its dual is the pentakis icosidodecahedron. It is also called a truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron.
In geometry, a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex. Cantellation also applies to regular tilings and honeycombs.
Regardless of whether the random variable is bounded above, below, or both, the truncation is a mean-preserving contraction combined with a mean-changing rigid shift, and hence the variance of the truncated distribution is less than the variance of the original normal distribution.