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polyhedral

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polyhedral
polyhedral, a. (pɒlɪˈhiːdrəl, -ˈhɛdrəl) Also polyedral. [f. Gr. πολύεδρος (Plut.) (f. πολυ-, poly- + ἕδρα base, side of a solid figure) + -al1.] 1. Of the form of a polyhedron; having many faces or sides, as a solid figure or body.1811 Pinkerton Petralogy I. 324 A granular serpentine,..which..splits... Oxford English Dictionary
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Polyhedral
Polyhedral convex function Polyhedral dice Polyhedral dual Polyhedral formula Polyhedral graph Polyhedral group Polyhedral model Polyhedral net Polyhedral number Polyhedral pyramid Polyhedral prism Polyhedral space Polyhedral skeletal electron pair theory Polyhedral symbol Polyhedral symmetry Polyhedral wikipedia.org
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Polyhedral group
In geometry, the polyhedral group is any of the symmetry groups of the Platonic solids. (The Polyhedral Groups. §3.5, pp. 46–47) External links Polyhedra wikipedia.org
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Polyhedral homology manifold, but not topological manifold. Let $K$ be a simplicial complex given by a set of vertices $V(K)$ and a distinguished set $S(K)$ (the simplexes) of finite non-empty subsets of $V(K)$. Given...
You can't do this in dimension $2$, but you can do it in dimension $4$. First, start with a triangulated homology $3$-sphere $S$, such as the Poincare homology sphere. Let $M=\Sigma S$. This is a homology manifold but is not a manifold. It is more or less constructed to have the property of a homolo...
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Polyhedral symbol
The polyhedral symbol is sometimes used in coordination chemistry to indicate the approximate geometry of the coordinating atoms around the central atom The polyhedral symbol can be used in naming of compounds, in which case it is followed by the configuration index. wikipedia.org
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Polyhedron in $E^n$ with infinitely many sides must contain a side that is a polyhedral wedge So this is from Ratcliffe's text on hyperbolic manifolds. In it there is a part of a proof where he just states that for a ...
That hypothesis already implies that there is at least **ONE** side which is a polyhedral wedge.
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Polyhedral complex
Polyhedral complexes generalize simplicial complexes and arise in various areas of polyhedral geometry, such as tropical geometry, splines and hyperplane Examples Tropical varieties are polyhedral complexes satisfying a certain balancing condition. wikipedia.org
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Dual of a polyhedral cone A general polyhedral cone $\mathcal{P} \subseteq \mathbb{R}^n$ can be represented as either $\mathcal{P} = \\{x \in \mathbb{R}^n : Ax \geq 0 \\}$ or $\mathcal{P} = \\{V x : x \in \mathbb{R}_+...
It's quite non-trivial to prove that your two definitions of polyhedral cone are equivalent. _+^k\\} =\\{y\in\Bbb R^n:x^RV^Ty\ge0\ \forall x\in \Bbb R_+^k\\}=\\{y\in\Bbb R^n:V^Ty\ge0\\}$$ so that $\mathcal{P}^*$ meets your first definition of polyhedral
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Polyhedral space
Polyhedral space is a certain metric space. In the sequel all polyhedral spaces are taken to be Euclidean polyhedral spaces. wikipedia.org
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The maximum of several affine functions is a polyhedral function A function $f: \mathbb{R}^n \mapsto (-\infty,\infty]$ is polyhedral if its **epigraph** is a polyhedral, i.e. $$\text{epi}f=\\{(x,t)\in \mathbb{R}^{n+...
A function is polyhedral if its epigraph is a finite intersection of closed halfspaces. 2.
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Polyhedral graph
Hamiltonicity and shortness Tait conjectured that every cubic polyhedral graph (that is, a polyhedral graph in which each vertex is incident to exactly Tutte, the polyhedral but non-Hamiltonian Tutte graph. wikipedia.org
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The difference between polyhedral complex and support of a polyhedral complex? A polyhedral complex is a collection of polyhedra such that intersection of any two polyhedron is a face of of both the polyhedron or empt...
A polyhedral complex is a _set_ of polyhedra. Its support is their _union_. All of these are different polyhedral complexes, but they have the same support.
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Polyhedral combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the Research in polyhedral combinatorics falls into two distinct areas. wikipedia.org
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Polyhedral graph such that every vertex has degree $2k$, for some $k > 2$ Is there any polyhedral graph such that every vertex has degree even greater than 4?
If a graph's every vertex has degree of at least $6$, then it cannot be planar graph because it needs to satisfy Euler's formula. See this MO question's comment by Noam Elkies for details.
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Centered polyhedral number
The centered polyhedral numbers are a class of figurate numbers, each formed by a central dot, surrounded by polyhedral layers with a constant number of wikipedia.org
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