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Although trivial as a polytope, it appears as the edges of polygons and other higher dimensional polytopes. [5] It is used in the definition of uniform prisms like Schläfli symbol { }×{p}, or Coxeter diagram as a Cartesian product of a line segment and a regular polygon. [6]
Toggle Polytope elements subsection. 1.1 Polygon ... Five-dimensional space, ... Polytope families • Regular polytope • List of regular polytopes and compounds
5-polytopes may be classified based on properties like "convexity" and "symmetry".A 5-polytope is convex if its boundary (including its cells, faces and edges) does not intersect itself and the line segment joining any two points of the 5-polytope is contained in the 5-polytope or its interior; otherwise, it is non-convex.
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.
The bifurcating graph of the D 5 family contains the 5-orthoplex, as well as a 5-demicube which is an alternated 5-cube. Each reflective uniform 5-polytope can be constructed in one or more reflective point group in 5 dimensions by a Wythoff construction , represented by rings around permutations of nodes in a Coxeter diagram .
There are no regular compounds in five or six dimensions. There are three known seven-dimensional compounds (16, 240, or 480 7-simplices), and six known eight-dimensional ones (16, 240, or 480 8-cubes or 8-orthoplexes).
This category contains polytopes of 5-space, and honeycombs of 4-space. Pages in category "5-polytopes" The following 67 pages are in this category, out of 67 total. ...
It is a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.. There are 23 Uniform 5-polytopes (uniform 5-polytopes) that can be constructed from the D 5 symmetry of the demipenteract, 8 of which are unique to this family, and 15 are shared within the penteractic family.