# convex polytope

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## convex polytope

[¦kän‚veks ′päl·i‚tōp]
(mathematics)
A bounded, convex subset of an n-dimensional space enclosed by a finite number of hyperplanes.
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It is based on the premise that the composite limit state will form a convex polytope.
The PI has recently developed an approach to attack some problems in connection with the famous conjecture due to Fuglede (1974), concerning the characterization of domains which admit orthogonal Fourier bases in terms of their possibility to tile the space by translations, and in relation with the theory of multiple tiling by translates of a convex polytope, or by a function.
A DOP is a convex polytope containing the object, constructed by taking a number k of appropriately oriented planes at infinity and bringing it closer to the object until they collide.
Note that any convex polytope can be written in the form [[PI].
The convexity theorem of Atiyah  and Guillemin-Sternberg  implies that [mu](M) is a convex polytope in [R.
5] shows that every arrangement of spheres (and hence every central arrangemen of hyperplanes) is combinatorially equivalent to some convex polytope,  proved that there is a relation between the number of lattice point on a sphere and the volume of it.
T](n) can be realized as the skeleton of an (n - 3)-dimensional convex polytope called the associahedron.
If attention is restricted to the types of queries described in the Elicitation Queries section previously, the space U is conveniently characterized by a set of linear constraints on utility function parameters; if each parameter is bounded, U is simply a convex polytope in utility parameter space (see figure 3a).
However, a program's state-space is not always convex; in fact, most (exact) fixpoint computations are composed of a potentially large number of disjuncts, each defining a convex polytope.
They include (i) computing the smallest enclosing ellipsoid of a point set,(7)(ii) computing the largest ellipsoid (or ball) inscribed inside a convex polytope in [R.
This set is a convex polytope (Figure 1) whose vertices are (0,0,0), (1,0,0), (0,1,0), (1,1,1).
j] (F) denote the set of all j-dimensional faces of a convex polytope F.

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