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searching for Convex polytope 30 found (101 total)

alternate case: convex polytope

Barycentric subdivision (1,622 words) [view diff] exact match in snippet view article find links to article

triangles, a convex polyhedron into tetrahedra, or, in general, a convex polytope into simplices with the same dimension, by connecting the barycenters
Expansion (geometry) (537 words) [view diff] exact match in snippet view article
creates a uniform polytope, but the operation can be applied to any convex polytope, as demonstrated for polyhedra in Conway polyhedron notation. For polyhedra
Toric variety (1,304 words) [view diff] exact match in snippet view article find links to article
cones into cones of nonsingular toric varieties. The fan of a rational convex polytope in N consists of the cones over its proper faces. The toric variety
Kostant's convexity theorem (1,870 words) [view diff] exact match in snippet view article find links to article
self-adjoint matrices with given eigenvalues Λ = (λ1, ..., λn) is the convex polytope with vertices all permutations of the coordinates of Λ. Kostant used
Toric manifold (193 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 (1,093 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
H-vector (1,722 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 −
Schur–Horn theorem (2,209 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
K-vertex-connected graph (515 words) [view diff] exact match in snippet view article find links to article
graph is called triconnected. The 1-skeleton of any k-dimensional convex polytope forms a k-vertex-connected graph (Balinski's theorem, Balinski 1961)
Facet (geometry) (255 words) [view diff] case mismatch in snippet view article
Geometry, Graduate Texts in Mathematics, 212, Springer, 5.3 Faces of a Convex Polytope, p. 86. De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco (2010)
Convex analysis (969 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
Gram–Euler theorem (219 words) [view diff] exact match in snippet view article find links to article
polytopes. Let P {\displaystyle P} be an n {\displaystyle n} -dimensional convex polytope. For each cell E {\displaystyle E} , let dim ⁡ ( E ) {\displaystyle
Hirsch conjecture (1,375 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
Ehrhart polynomial (2,218 words) [view diff] exact match in snippet view article find links to article
positive integers t. The Ehrhart polynomial of the interior of a closed convex polytope P can be computed as: L ( int ⁡ ( P ) , t ) = ( − 1 ) d L ( P , − t
Geometric graph theory (915 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
Balinski's theorem (405 words) [view diff] exact match in snippet view article find links to article
method for finding the minimum or maximum of a linear function on a convex polytope (the linear programming problem). The simplex method starts at an arbitrary
Heptadecagon (1,248 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
Peter McMullen (530 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
Face (geometry) (991 words) [view diff] case mismatch in snippet view article
Geometry, Graduate Texts in Mathematics, 212, Springer, 5.3 Faces of a Convex Polytope, p. 86. Cromwell, Peter R. (1999), Polyhedra, Cambridge University
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 (840 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
Fulkerson Prize (1,754 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
Cutting-plane method (1,183 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
Connectivity (graph theory) (2,035 words) [view diff] exact match in snippet view article
theorem states that the polytopal graph (1-skeleton) of a k-dimensional convex polytope is a k-vertex-connected graph. Steinitz's previous theorem that any
Arrangement of hyperplanes (1,804 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
Bounding volume (2,235 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 (9,856 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)
K-set (geometry) (1,649 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-sets is Θ((n-k)k), which follows from arguments used
Regular icosahedron (3,218 words) [view diff] exact match in snippet view article find links to article
a positive defect for folding in four dimensions (in general for a convex polytope in n dimensions, at least three facets must meet at a peak and leave
Barycentric coordinate system (5,857 words) [view diff] exact match in snippet view article find links to article
simplex. More abstractly, generalized barycentric coordinates express a convex polytope with n vertices, regardless of dimension, as the image of the standard