abstract polytope in a sentence
1) To define an abstract polytope , a few preliminary concepts are needed.
2) This equivalence is what is encapsulated in the concept of an abstract polytope .
3) The concept of "vertex figure" is also defined differently for an abstract polytope .
abstract polytope example sentences
4) Throughout this article, "polytope" means " abstract polytope " - unless stated otherwise.5) When an abstract polytope is regular, its automorphism group is isomorphic to a quotient of a Coxeter group.
6) The exchange maps and the flag action in particular can be used to prove that "any" abstract polytope is a quotient of some regular polytope.
7) From the definition of an abstract polytope , it can be proven that there is a unique flag differing from "Ψ" by a rank "i" element, and the same otherwise.
8) In general, an abstract polytope is called "locally X" if its facets and vertex figures are, topologically, either spheres or "X", but not both spheres.
9) In fact, every abstract polytope with "v" vertices has at least one realisation, as the vertices of a ("v" − 1)-dimensional simplex.
10) Formally, an abstract polytope is defined to be "regular" if its automorphism group acts transitively on the set of its flags.
11) Properties, particularly measurable ones, of traditional polytopes such as angles, edge-lengths, skewness, and convexity "have no meaning for an abstract polytope ".
12) A geometric polytope is understood to be a "realization" of the abstract polytope , such that there is a one-to-one mapping from the abstract elements to the geometric.
13) An abstract polytope is defined as a partially ordered set (poset), whose elements are the polytope's faces (vertices, edges, faces etc.) ordered by "containment".
14) An abstract polytope is a partially ordered set (poset) of elements whose partial ordering obeys certain rules of incidence (connectivity) and ranking.
15) An abstract polyhedron is an abstract polytope having the following ranking:
use abstract polytope in a sentence
16) Thus the corresponding incidence matrix of this abstract polytope may be shown as:17) As stated above, this concept of an abstract polytope is very general, and includes:
18) An abstract polytope is a partially ordered set, whose elements we call "faces", satisfying the 4 axioms:
19) Abstract polytope
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