mathematics, a polyhedral complex is a set of polyhedra in a real vector space that fit together in a specific way. Polyhedral complexes generalize simplicial...

an irreducible tropical variety if it is the support of a weighted polyhedral complex of pure dimension d that satisfies the zero-tension condition and...

to a unique complex one, and 4-dimensional topology can be studied from the point of view of complex geometry in two variables (complex surfaces), though...

\operatorname {int} \mathbb {Q} =\varnothing .} If X {\displaystyle X} is the complex plane C , {\displaystyle \mathbb {C} ,} then int ⁡ ( { z ∈ C : | z | ≤...

structure to describe polygons in computer graphics Fan, a type of polyhedral complex One of several types of fan-shaped deposits of sediment caused by...

slightly different concept from the boundary of a manifold or of a simplicial complex. For example, the boundary of an open disk viewed as a manifold is empty...

a complex where all facets have the same dimension. For (boundary complexes of) simplicial polytopes this coincides with the meaning from polyhedral combinatorics...

covering dimension Lebesgue's number lemma Polytope Simplex Simplicial complex CW complex Manifold Triangulation Barycentric subdivision Sperner's lemma Simplicial...

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré...

dense in R . {\displaystyle \mathbb {R} .} If X {\displaystyle X} is the complex plane C = R 2 , {\displaystyle \mathbb {C} =\mathbb {R} ^{2},} then cl...

Polyhedral space is a certain metric space. A (Euclidean) polyhedral space is a (usually finite) simplicial complex in which every simplex has a flat...

uniform Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism...

on Rn the basic open sets are the open balls. Similarly, C, the set of complex numbers, and Cn have a standard topology in which the basic open sets are...

uniform Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism...

of polyhedral surfaces or surface meshes from scattered data points, geodesics on polyhedral surfaces, visibility and illumination in polyhedral scenes...

ideal polyhedral decompositions and are used in popular computer software, such as SnapPea. An infinite-dimensional Hilbert space is not a CW complex: it...

and not based on a particular projection Polyhedral maps Polyhedral maps can be folded up into a polyhedral approximation to the sphere, using particular...

of zonotopes is a zonotopal tiling of Z {\displaystyle Z} if it a polyhedral complex with support Z {\displaystyle Z} , that is, if the union of all zonotopes...

holomorphic convexity. The proof method uses an approximation by the polyhedral domain, as in Oka-Weil theorem. Note that the Riemann extension theorem...

uniform Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism...

uniform Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism...

condensed polyhedral oligomeric silsesquioxanes (POSS-mono-ol, POSS-diol and POSS-triol): Hydrogen-bonded interaction and host–guest complex". J. Organomet...

Singularities" (PDF). Coxeter, H. S. M. (1974), "7 The Binary Polyhedral Groups", Regular Complex Polytopes, Cambridge University Press, pp. 73–82. Coxeter...

In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of...

Complex Polytopes, p.413 Coxeter, Complex Regular Polytopes, (1991), 14.6 McMullen's two polyhedral with 84 square faces, pp.166-171 Coxeter, Complex...

Use of the polyhedral model (also called the polytope model) within a compiler requires software to represent the objects of this framework (sets of integer-valued...

that a longer strip would be. The Möbius strip can also be embedded as a polyhedral surface in space or flat-folded in the plane, with only five triangular...

The polyhedral symbol is sometimes used in coordination chemistry to indicate the approximate geometry of the coordinating atoms around the central atom...

dimension n. On the other hand, if we consider the dimension of T(X) as a polyhedral complex, Develin (2006) showed that, with a suitable general position assumption...

shellable. Note that here, shellability is generalized to the case of polyhedral complexes (that are not necessarily simplicial). There is an unshellable triangulation...