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Truncated square is a regular octagon: t {4} = {8} =. Truncated cube. t {4,3} or. Truncated cubic honeycomb. t {4,3,4} or. In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates from Kepler 's names for the Archimedean solids.
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.
The truncated icosahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [5] It has the same symmetry as the regular icosahedron, the icosahedral symmetry, and it also has the property of vertex-transitivity. [6][7] The polygonal faces ...
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 an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [6] It has the same symmetry as the regular icosahedron, the icosahedral symmetry. [7] The polygonal faces that meet for every vertex are one equilateral triangle ...
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 ...
Net. In geometry, the truncated cuboctahedron or great rhombicuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices, and 72 edges. Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the ...
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive —there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent. Uniform polyhedra may be regular (if also face- and edge-transitive), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular (if ...