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It can also be called a regular hexdeca-8-tope or hexadecazetton, being an 8-dimensional polytope constructed from 16 regular facets. It is a part of an infinite family of polytopes, called hypercubes. The dual of an 8-cube can be called an 8-orthoplex and is a part of the infinite family of cross-polytopes.
In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube. There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square faces of the 8-cube.
In 8-dimensional geometry, there are 256 uniform polytopes with B 8 symmetry. There are two regular forms, the 8-orthoplex and 8-cube , with 16 and 256 vertices respectively. The 8-demicube is added with half the symmetry.
The topology of any given 8-polytope is defined by its Betti numbers and torsion coefficients. [1]The value of the Euler characteristic used to characterise polyhedra does not generalize usefully to higher dimensions, and is zero for all 8-polytopes, whatever their underlying topology.
Hypercubes or measure polytopes, including the square and the cube. Orthoplexes or cross polytopes, including the square and regular octahedron . Dimensions two, three and four include regular figures which have fivefold symmetries and some of which are non-convex stars, and in two dimensions there are infinitely many regular polygons of n ...
A polytope in eight dimensions is called an 8-polytope. The most studied are the regular polytopes, of which there are only three in eight dimensions: the 8-simplex, 8-cube, and 8-orthoplex. A broader family are the uniform 8-polytopes, constructed from fundamental symmetry domains of reflection, each domain defined by a Coxeter group.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.
In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube. There are unique 8 degrees of rectifications, the zeroth being the 8-cube, and the 7th and last being the 8-orthoplex. Vertices of the rectified 8-cube are located at the edge-centers of the 8-cube.