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* [[Hirsch conjecture]], in mathematical programming and polyhedral combinatorics ...

...and '''combinatorial geometry''' are branches of [[geometry]] that study [[Combinatorics|combinatorial]] properties and constructive methods of [[discrete mathemati *[[Polyhedral combinatorics]] ...

...d (along edges) to become the [[face (geometry)|face]]s of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and [[solid geometry]] in g An early instance of polyhedral nets appears in the works of [[Albrecht Dürer]], whose 1525 book ''A Course ...

...f combinatorial optimization problems, under the framework of [[polyhedral combinatorics]].<ref>{{harv|Aardal|Weismantel|1997}}</ref> * {{citation | contribution=Polyhedral combinatorics: An annotated bibliography | first1 = Karen | last1 = Aardal | author1-link ...

In some areas of mathematics, such as [[polyhedral combinatorics]], a polytope is by definition [[convex set|convex]]. In this setting, ther A '''cell''' is a [[polyhedron|polyhedral]] element ('''3-face''') of a 4-dimensional polytope or 3-dimensional tesse ...

...ial set]] appearing in modern simplicial [[homotopy theory]]. The purely [[Combinatorics|combinatorial]] counterpart to a simplicial complex is an [[abstract simpli ...) [[simplicial polytope]]s this coincides with the meaning from polyhedral combinatorics. ...

...ontributions to the fields of [[combinatorial optimization]], [[polyhedral combinatorics]], [[discrete mathematics]] and the theory of computing. He was the recipie ...gs on defining a class of algorithms that could run more efficiently. Most combinatorics scholars, during this time, were not focused on algorithms. However Edmonds ...

'''Combinatorics''' is an area of [[mathematics]] primarily concerned with [[counting]], bot ...theory]], which by itself has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in ...

[[File:Polyhedral-cone.png|thumb|Convex cone generated by the conic combination of the three === Polyhedral and finitely generated cones === ...

In [[geometry]] and [[combinatorics]], an '''arrangement of hyperplanes''' is an [[arrangement (space partition ...[[polytope]], or an unbounded region that is a convex [[polyhedron#General|polyhedral]] region which goes off to infinity. ...

...for theorems. The geometry of a toric variety is fully determined by the [[combinatorics]] of its associated fan, which often makes computations far more tractable. ...limit points of punctured curves, we obtain a lattice fan, a collection of polyhedral rational cones. The cones of highest dimension correspond precisely to the ...

...er hard problems in graph theory: writing in the ''[[Electronic Journal of Combinatorics]]'', Miroslav Chladný and Martin Škoviera state that | journal = [[Electronic Journal of Combinatorics]] ...

..., a [[polyhedral cylinder]] (infinite [[prism (geometry)|prism]]), and a [[polyhedral cone]] (infinite [[cone]]) defined by three or more half-spaces passing thr ...epresented as a sum of a ''bounded polytope'' and a [[Convex cone|''convex polyhedral cone'']].<ref>{{Cite book|last=Motzkin|first=Theodore|title=Beitrage zur Th ...

| journal = [[Graphs and Combinatorics]] | title = On polyhedral realization with isosceles triangles ...

...matics]], and more specifically in [[algebraic topology]] and [[polyhedral combinatorics]], the '''Euler characteristic''' (or '''Euler number''', or '''Euler&ndash ...d]] [[plane graph]]s by the same <math>\ V - E + F\ </math> formula as for polyhedral surfaces, where {{mvar|F}} is the number of faces in the graph, including t ...

** [[W. R. Pulleyblank]], Polyhedral combinatorics (pp.&nbsp;371–446); ...

...deltahedra, which can be used in the applications of chemistry as in the [[polyhedral skeletal electron pair theory]] and [[chemical compound]]s. There are infin ...xample, they are categorized as the ''closo'' polyhedron in the study of [[polyhedral skeletal electron pair theory]].{{sfnp|Kharas|Dahl|1988|p=[https://books.go ...

| journal = [[Graphs and Combinatorics]] | volume = 16 | issue = 4 | pages = 467–495| doi = 10.1007/s003730070009| ...onjecture to be false by finding [[Snark (graph theory)|snarks]] that have polyhedral embeddings on high-genus orientable surfaces.<ref>{{citation ...

...ic) automorphism group of the quartic. In this way the geometry reduces to combinatorics. ...the quartic and containing the first English translation of Klein's paper. Polyhedral models with tetrahedral symmetry most often have [[convex hull]] a [[trunca ...

...rface]] such that all [[facet (geometry)|facets]] are [[triangle]]s. The [[combinatorics|combinatorial]] study of such arrangements of triangles (or, more generally * [[Polyhedral surface]] ...