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...is a theorem used in studying [[intrinsic metric|intrinsic geometry]] of [[convex surface]]. ...gamma</math> is a unit-speed minimizing [[geodesic]] on the surface of a [[convex body]] ''K'' in [[Euclidean space]] then for any point ''p''&nbsp;&isin;&nb ...

{{Short description|Upper bound on the volume of a convex body containing one lattice point}} ...soon as its volume exceeds <math>2^n</math>. The conjecture states that a convex body ''K'' containing only one lattice point in its interior as its [[Cente ...

...}, [https://books.google.com/books?id=ofrBsl61lq8C&pg=PA67&dq=%22unbounded+convex+polyhedron%22&sig=ACfU3U1Yv3iG-XIn3hiuh84nK2e8UIcdAA#PPA68,M1 p. 68]</ref> ...rives from the fact that the set of all conical sum of vectors defines a [[Convex cone|cone]] (possibly in a lower-dimensional [[Linear subspace|subspace]]). ...

...e=3 April 2023}}</ref><ref>{{cite arXiv |last1=Fritz |first1=Tobias |title=Convex Spaces I: Definition and Examples |year=2009 |class=math.MG |eprint=0903.55 A convex space can be defined as a set <math>X</math> equipped with a binary convex combination operation <math>c_\lambda : X \times X \rightarrow X</math> for ...

...s a kind of a [[convex cone]] that is particularly important in modeling [[convex optimization]] problems.<ref name=":0">{{Cite web |title=MOSEK Modeling Coo ...]] programs. There are many problems that can be described as minimizing a convex function over a power cone.<ref name=":0" /> ...

...vex set that are not exposed points. Therefore, not every convex face of a convex set is an exposed face.]] In [[mathematics]], most commonly in [[convex geometry]], an '''extreme set''' or '''face''' of a set <math>C\subseteq V</math> in ...

...is the [[discrete geometry]] analogue of the concept of [[convex set]] in geometry. ...if any point ''y'' in the [[convex hull]] of ''X'' can be expressed as a [[convex combination]] of the points of ''X'' that are "near" ''y'', where "near" me ...

...osition if they are pairwise disjoint and none of them is contained in the convex hull of the others.{{r|tv05}} ...t solvable in [[polynomial time]] by [[dynamic programming]] for points in convex position.{{r|k80}} ...

...le:Convex polygon trivial triangulation.svg|thumb|Fan triangulation of a [[convex polygon]]]] ...on can be triangulated this way, so this method is usually only used for [[convex polygon]]s.<ref name=Loera2010>{{cite book |last1=Loera |first1=Jesus |last ...

...focuses on problems of reconstructing homogeneous (often [[convex polytope|convex]]) objects from tomographic data (this might be X-rays, projections, sectio A key theorem in this area states that any convex body in <math> E^n</math> can be determined by parallel, coplanar ...

...[[positive semidefinite matrix|positive semidefinite matrices]] forms a [[convex cone]] in {{math|'''R'''^{''n'' &times; ''n''}}}, and a spectrahedr ...01|title=Spectrahedral Shadows|journal=SIAM Journal on Applied Algebra and Geometry|volume=2|pages=26–44|doi=10.1137/17m1118981|doi-access=free}}</ref> ...

...honeycomb''' is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. ...e list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...

.... A classical example is the problem of enumeration of the vertices of a [[convex polytope]] specified by a [[set of linear inequalities]]:<ref>[[Eric W. Wei ...inequalities given the vertices is called ''[[facet enumeration]]'' (see [[convex hull algorithms]]). ...

...that have two or more shortest [[geodesic]]s to <math>p</math>. For every convex polyhedron, and every choice of the point <math>p</math> on its surface, cu ...of the net that do not lie along edges of the polyhedron, as a [[Blooming (geometry)|blooming]] of the polyhedron.{{r|ddhilo}} The unfolded shape of the source ...

[[File:Convex layers halfspace.svg|thumb|The convex layers of a point set and their intersection with a halfplane]] ...polygon]]s having the points as their vertices. The outermost one is the [[convex hull]] of the points and the rest are formed in the same way [[recursion|re ...

...png|thumb|The two distinguished points are examples of extreme points of a convex set that are not exposed]] In mathematics, an '''exposed point''' of a [[convex set]] <math>C</math> is a point <math>x\in C</math> at which some [[continu ...

...convexity'''. Beck proved the following theorem: A Banach space is ''B''-convex [[if and only if]] every sequence of [[statistical independence|independent ...with [[norm (mathematics)|norm]] ||&nbsp;||. ''X'' is said to be '''''B''-convex''' if for some ''ε''&nbsp;&gt;&nbsp;0 and some [[natural number]] ''n'', it ...

...the '''Blaschke sum''' of two polytopes is a polytope that has a [[Facet (geometry)|facet]] parallel to each facet of the two given polytopes, with the same [ Blaschke sums exist and are unique up to [[Translation (geometry)|translation]], as can be proven using the theory of the [[Minkowski proble ...

...ing [[honeycomb (geometry)|honeycomb]]. It can be seen as a [[Runcination (geometry)|runcination]] of the regular [[16-cell honeycomb]], containing [[Rectified ...e list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' Model 122 ...

...honeycomb''' is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. ...e list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' ...