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searching for Convex polytope 32 found (135 total)

Toric manifold (204 words) [view diff] exact match in snippet view article find links to article

compact torus which is locally standard with the orbit space a simple convex polytope. The aim is to do combinatorics on the quotient polytope and obtain

Feasible region (1,110 words) [view diff] exact match in snippet view article find links to article

subset thereof). In linear programming problems, the feasible set is a convex polytope: a region in multidimensional space whose boundaries are formed by

Permutoassociahedron (635 words) [view diff] exact match in snippet view article find links to article

work on the Knizhnik–Zamolodchikov equations. It was constructed as a convex polytope by Victor Reiner and Günter M. Ziegler. When n = 2 {\displaystyle n=2}

Peter McMullen (755 words) [view diff] exact match in snippet view article find links to article

Research papers McMullen, P. (1970), "The maximum numbers of faces of a convex polytope", Mathematika, 17 (2): 179–184, doi:10.1112/s0025579300002850, MR 0283691

H-vector (2,250 words) [view diff] exact match in snippet view article find links to article

important special case occurs when Δ is the boundary of a d-dimensional convex polytope. For k = 0, 1, …, d, let h k = ∑ i = 0 k ( − 1 ) k − i ( d − i k −

Convex cap (1,603 words) [view diff] case mismatch in snippet view article find links to article

convex shapes. In general it can be thought of as the intersection of a convex Polytope with a half-space. A cap, C {\displaystyle C} can be defined as the

Facet (geometry) (314 words) [view diff] case mismatch in snippet view article

Regular Polytopes, Dover, p. 95 Matoušek, Jiří (2002), "5.3 Faces of a Convex Polytope", Lectures in Discrete Geometry, Graduate Texts in Mathematics, vol

Hirsch conjecture (1,370 words) [view diff] exact match in snippet view article find links to article

Leal's counterexample also disproves this conjecture. The graph of a convex polytope P {\displaystyle P} is any graph whose vertices are in bijection with

K-vertex-connected graph (772 words) [view diff] exact match in snippet view article find links to article

tree of triconnected components. The 1-skeleton of any k-dimensional convex polytope forms a k-vertex-connected graph (Balinski's theorem). As a partial

Shelling (topology) (454 words) [view diff] no match in snippet view article

building (in the sense of Tits), is shellable. The boundary complex of a (convex) polytope is shellable. Note that here, shellability is generalized to the case

Separation oracle (1,626 words) [view diff] exact match in snippet view article find links to article

K=\{x|Ax\leq b\}} . Such a set is called a convex polytope. A strong separation oracle for a convex polytope can be implemented, but its run-time depends

Schur–Horn theorem (2,908 words) [view diff] exact match in snippet view article find links to article

~ ) {\displaystyle \Phi ({\mathcal {O}}_{\tilde {\lambda }})} is a convex polytope. A matrix A ∈ H ( n ) {\displaystyle A\in {\mathcal {H}}(n)} is fixed

Geometric graph theory (934 words) [view diff] exact match in snippet view article find links to article

polyhedron is a planar graph, and the skeleton of any k-dimensional convex polytope is a k-connected graph. Conversely, Steinitz's theorem states that

Dehn–Sommerville equations (780 words) [view diff] exact match in snippet view article find links to article

an interpretation of the components of the h-vector of a simplicial convex polytope P in terms of the projective toric variety X associated with (the dual

Minkowski's second theorem (843 words) [view diff] exact match in snippet view article find links to article

defined by g(bj) = λj. The lower bound is proved by considering the convex polytope 2n with vertices at ±bj/ λj, which has an interior enclosed by K and

Gram–Euler theorem (673 words) [view diff] exact match in snippet view article find links to article

faces. Let P {\displaystyle P} be an n {\displaystyle n} -dimensional convex polytope. For each k-face F {\displaystyle F} , with k = dim ⁡ ( F ) {\displaystyle

Heptadecagon (1,825 words) [view diff] exact match in snippet view article find links to article

heptadecagon is the Petrie polygon for one higher-dimensional regular convex polytope, projected in a skew orthogonal projection: Arthur Jones, Sidney A

Convex position (545 words) [view diff] exact match in snippet view article find links to article

points in dimension 4 not projectively equivalent to the vertices of a convex polytope", Combinatorial geometries (Luminy, 1999), European Journal of Combinatorics

Fulkerson Prize (1,965 words) [view diff] exact match in snippet view article find links to article

theorems on the classification problem of configuration varieties and convex polytope varieties," O. Ya. Viro (ed.), Topology and Geometry-Rohlin Seminar

Schläfli orthoscheme (1,057 words) [view diff] exact match in snippet view article find links to article

unsolved in higher dimensions. Hadwiger's conjecture implies that every convex polytope can be dissected into orthoschemes. Coxeter identifies various orthoschemes

Cutting-plane method (1,546 words) [view diff] exact match in snippet view article find links to article

feasible solution. Geometrically, this solution will be a vertex of the convex polytope consisting of all feasible points. If this vertex is not an integer

Convex analysis (2,607 words) [view diff] exact match in snippet view article find links to article

A 3-dimensional convex polytope. Convex analysis includes not only the study of convex subsets of Euclidean spaces but also the study of convex functions

Arrangement of hyperplanes (1,806 words) [view diff] exact match in snippet view article find links to article

regions or chambers, each of which is either a bounded region that is a convex polytope, or an unbounded region that is a convex polyhedral region which goes

Hans Duistermaat (1,724 words) [view diff] exact match in snippet view article find links to article

ISBN 90-393-2551-0. Duistermaat, Hans (2001). "The universal barrier function of a convex polytope". Circumspice. Various Papers in Around Mathematics in Honour of Arnoud

Bounding volume (2,301 words) [view diff] exact match in snippet view article find links to article

a k-DOP is the Boolean intersection of k bounding slabs and is a convex polytope containing the object (in 2-D a polygon; in 3-D a polyhedron). A 2-D

Manifold (9,536 words) [view diff] exact match in snippet view article find links to article

manifold is its Euler characteristic. Leonhard Euler showed that for a convex polytope in the three-dimensional Euclidean space with V vertices (or corners)

Zonoid (756 words) [view diff] exact match in snippet view article find links to article

approximated arbitrarily closely (in Hausdorff distance) by a zonotope, a convex polytope formed from the Minkowski sum of finitely many line segments. In particular

K-set (geometry) (1,881 words) [view diff] exact match in snippet view article

dimensions that are in convex position, that is, are the vertices of some convex polytope, the number of k {\displaystyle k} -sets is Θ ( ( n − k ) k ) {\displaystyle

Knaster–Kuratowski–Mazurkiewicz lemma (2,396 words) [view diff] exact match in snippet view article find links to article

the KKMS theorem from simplices to polytopes. Let P be any compact convex polytope. Let Faces ( P ) {\displaystyle {\textrm {Faces}}(P)} be the set of

Universal vertex (1,942 words) [view diff] exact match in snippet view article find links to article

ISBN 978-0-8176-8363-4 Klee, Victor (1964), "On the number of vertices of a convex polytope", Canadian Journal of Mathematics, 16: 701–720, doi:10.4153/CJM-1964-067-6

Barycentric coordinate system (8,177 words) [view diff] exact match in snippet view article find links to article

coordinates. More abstractly, generalized barycentric coordinates express a convex polytope with n vertices, regardless of dimension, as the image of the standard

List of unsolved problems in mathematics (20,026 words) [view diff] exact match in snippet view article find links to article

parallelohedron? Does every higher-dimensional tiling by translations of convex polytope tiles have an affine transformation taking it to a Voronoi diagram