Примеры использования Polytopes на Английском языке и их переводы на Русский язык
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All polytopes of rank≤ 2 are regular.
This definition excludes chiral polytopes.
Thus, unlike real polytopes, no interior can be defined.
These cases exist as alternations of reflective symmetry polytopes.
Hence… we have to consider unitary polytopes as configurations.
An outstanding problem is to find the volume of the Birkhoff polytopes.
Isomorphic polytopes give rise to isomorphic Hasse diagrams, and vice versa.
The duoprisms are proprisms formed from exactly two polytopes.
Some complex polytopes which are not fully regular have also been described.
The idea of Petrie polygons was later extended to semiregular polytopes.
Such polytopes may also be used as facets, yielding forms such as{p, q,… 2… y, z.
Many examples of bounded convex polytopes can be found in the article"polyhedron.
Polytopes may be classified by properties like"convexity" and"symmetry.
By definition, this isotopic property is common to the duals of the uniform polytopes.
Polytopes may be classified based on properties like"convexity" and"symmetry.
These definitions can be extended to higher-dimensional polytopes and tessellations.
Polytopes cannot be seen in three-dimensional space due to their extra dimension.
The 3d conjecture remains open for arbitrary polytopes in higher dimensions.
These complex polytopes have not been systematically explored beyond a few cases.
Edge figures are useful for expressing relations between the elements within regular and uniform polytopes.
Many polytopes lack mirror symmetry, and in that sense form chiral polytopes. .
Their vertex figures are icosahedral pentagonal polytopes of one less dimension.
Uniform polytopes that cannot be created through a Wythoff mirror construction are called non-Wythoffian.
See also polytope families for a table of end-node uniform polytopes associated with these groups.
The six convex and ten star polytopes described are the only solutions to these constraints.
All of these fundamental reflective domains, both simplices and nonsimplices,are often called Coxeter polytopes or sometimes less accurately Coxeter polyhedra.
In three dimensions all Hanner polytopes are combinatorially equivalent to one of these two types of polytopes.
By this definition, even highly-symmetric and enantiomorphic polytopes such as the snub cube are not chiral.
The Schläfli-Hess 4-polytopes are the complete set of 10 regular self-intersecting star polychora four-dimensional polytopes.
Similar objects in dimension 4(or more!) are generally called polytopes though they are often simply called polyhedra.