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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.
Toggle Polytope elements subsection. 1.1 Polygon ... Five-dimensional space, ... Polytope families • Regular polytope • List of regular polytopes and compounds
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]
14.8 Five-dimensional regular polytopes and higher. 14.8.1 Tessellations of Euclidean 4-space. ... Vertex, a 0-dimensional element; Edge, a 1-dimensional element;
McMullen conjectures that this list is complete regarding the compact compounds. If any more compact compounds exist, they must involve {4,3,3,5} or {5,3,3,5} being inscribed in {5,3,3,3} (the only case not yet excluded). [8] In five dimensions, there is only one regular hyperbolic honeycomb whose vertices are not at infinity: {3,4,3,3,3}.
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 .
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. ...
A polytope comprises elements of different dimensionality such as vertices, edges, faces, cells and so on. Terminology for these is not fully consistent across different authors. For example, some authors use face to refer to an (n − 1)-dimensional element while others use face to denote a 2-face specifically.