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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.
The regular skew polyhedron {4,5| 4} can be realized within the 5-cube, with its 32 vertices, 80 edges, and 40 square faces, and the other 40 square faces of the 5-cube become square holes. This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex .
This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.. There are 23 uniform 5-polytopes that can be constructed from the D 5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.
In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube. There are 8 unique degrees of runcinations of the 5-cube, along with permutations of truncations and cantellations. Four are more simply constructed relative to the 5-orthoplex.
Pages in category "5-polytopes" The following 67 pages are in this category, out of 67 total. ... Steric 5-cubes; Steric tesseractic honeycomb;
The 5-cube and 5-orthoplex are the regular forms in the B 5 family. 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 ...
In 5-dimensional geometry, the 5-cube 5-orthoplex compound [1] is a polytope compound composed of a regular 5-cube and dual regular 5-orthoplex. [2] A compound polytope is a figure that is composed of several polytopes sharing a common center.
This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.. There are 23 uniform polytera (uniform 5-polytope) that can be constructed from the D 5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.