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polyhedron
polyhedron (pɒlɪˈhiːdrən, -ˈhɛdrən) Also polyedron. Pl. -a (rarely -ons). [a. Gr. πολύεδρον a polyhedron, prop. neut. of πολύεδρος adj.: see polyhedral.] Geom. A solid figure contained by many (i.e., usually, more than six) plane faces; a many-sided solid. Hence, a material body having such a form.1... Oxford English Dictionary
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Goldberg polyhedron
A Goldberg polyhedron is a dual polyhedron of a geodesic sphere. A consequence of Euler's polyhedron formula is that a Goldberg polyhedron always has exactly twelve pentagonal faces. wikipedia.org
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Polyhedron | Journal | ScienceDirect.com by Elsevier
Polyhedron publishes original, fundamental, experimental and theoretical work of the highest quality in all the major areas of inorganic chemistry. This includes synthetic chemistry, coordination chemistry, organometallic chemistry, bio…. View full aims & scope. $3480.
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Regular polyhedron - HandWiki
Jun 27, 2023A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex.
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polyhedron
polyhedron/ˌpɔlɪˈhi:drən; ˌpɑlɪ`hidrən/ n(pl ~s or -hedra / -ˈhi:drə; -`hidrə/) solid figure with many (usu seven or more) faces 多面体（通常指至少有七面）. 牛津英汉双解词典
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Waterman polyhedron
(WP) Generalized Waterman polyhedron by Ed Pegg jr of Wolfram various Waterman sphere clusters by Ed Pegg jr of Wolfram app to make 4d waterman polyhedron in Great Stella by Rob Webb Waterman polyhedron app in Matlab needs a workaround as shown on the following reference page Waterman polyhedron in Mupad wikipedia.org
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Flexible polyhedron
Steffen's polyhedron is another non-self-intersecting flexible polyhedron derived from Bricard's octahedra. the Dehn invariant that is also known to stay constant while a polyhedron flexes. wikipedia.org
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Can an empty set satisfy the definition of a polyhedron? Based the definition, a polyhedron satisfies {$x \in \Re^n |Ax \ge b$} . But can an empty set satisfies this? In another word, is an empty set also a polyhedron?
The set $\\{\,x\in\Bbb R^1\mid Ax\ge b\,\\} $, where $A=\begin{pmatrix}1\\\\-1\end{pmatrix}$ and $b=\begin{pmatrix}1\\\1\end{pmatrix}$, is empty.
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Omnitruncated polyhedron
More generally an omnitruncated polyhedron is a bevel operator in Conway polyhedron notation. quasiregular polyhedron. wikipedia.org
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Lower bound on the number of faces of a polyhedron of genus g Is there a lower bound on the number of faces of a polyhedron of topological genus g? For example: it seems very reasonable that $g$ < $F$ i.e. the genus...
Example of polyhedron with 4096 faces and 4097 holes. P. McMullen, C. Schulz, and J.M. Wills.
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Geodesic polyhedron
A geodesic polyhedron is a convex polyhedron made from triangles. creates a new Goldberg polyhedron. wikipedia.org
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Ideal polyhedron - Wikipedia
Animation of an ideal icosahedron in the Klein model of hyperbolic space. In three-dimensional hyperbolic geometry, an ideal polyhedron is a convex polyhedron all of whose vertices are ideal points, points "at infinity" rather than interior to three-dimensional hyperbolic space. It can be defined as the convex hull of a finite set of ideal points.
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Does max { $w^Tx$ subject to $x$ is a point on a given polyhedron } optimize at an extreme point? Is it necessary that the linear program max { $w^Tx$ subject to : $x$ is a point on a given polyhedron } attain its ...
which means that it's on the polyhedron. Some special cases are where an entire face of the polyhedron optimizes the function.
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Semiregular polyhedron - Wikipedia
Definitions. In its original definition, it is a polyhedron with regular polygonal faces, and a symmetry group which is transitive on its vertices; today, this is more commonly referred to as a uniform polyhedron (this follows from Thorold Gosset 's 1900 definition of the more general semiregular polytope ). [1] [2] These polyhedra include:
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CN101342757A - Polyhedron component molding mould - Google Patents
The invention provides a mould for moulding a polyhedral component, which comprises templets (1), fasteners (2) and a rotary component (3). The templets (1) are connected with each other by the rotary component (3); the connected templets (1) can turn relatively; after the templets (1) are folded, the templets are fixed with the fasteners (2).
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