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The cuboctahedron, r{4,3}, is an example. Hypertruncation A form of truncation that goes past the rectification, inverting the original edges, and causing self-intersections to appear. Quasitruncation A form of truncation that goes even farther than hypertruncation where the inverted edge becomes longer than the original edge. It can be ...
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.
In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. Intuitively, it may be regarded as footballs (or soccer balls) that are typically patterned with white hexagons and black pentagons.
For example, the augmented truncated tetrahedron is a Johnson solid constructed from a truncated tetrahedron by attaching triangular cupola onto its hexagonal face. [9] The triakis truncated tetrahedron is a polyhedron constructed from a truncated tetrahedron by adding three tetrahedrons onto its triangular faces, as interpreted by the name ...
In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices. [1] Coxeter labels an alternation by a prefixed h, standing for hemi or half. Because alternation reduces all polygon faces to half as many sides, it can only be applied to ...
Truncation of positive real numbers can be done using the floor function. Given a number x ∈ R + {\displaystyle x\in \mathbb {R} _{+}} to be truncated and n ∈ N 0 {\displaystyle n\in \mathbb {N} _{0}} , the number of elements to be kept behind the decimal point, the truncated value of x is
The truncated dodecahedron is constructed from a regular dodecahedron by cutting all of its vertices off, a process known as truncation. [1] Alternatively, the truncated dodecahedron can be constructed by expansion: pushing away the edges of a regular dodecahedron, forming the pentagonal faces into decagonal faces, as well as the vertices into triangles. [2]
The truncation involves cutting away corners; to preserve symmetry, the cut is in a plane perpendicular to the line joining a corner to the center of the polyhedron and is the same for all corners, and an example can be found in truncated icosahedron constructed by cutting off all the icosahedron's vertices, having the same symmetry as the ...