In mathematics, a cyclic polytope, denoted C(n,d), is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd, where n is greater than d. These polytopes were studied by Constantin Carathéodory, David Gale, Theodore Motzkin, Victor Klee, and others. They play an important role in polyhedral combinatorics: according to the upper bound theorem, proved by Peter McMullen and Richard Stanley, the boundary Δ(n,d) of the cyclic polytope C(n,d) maximizes the number fi of i-dimensional faces among all simplicial spheres of dimension d − 1 with n vertices.
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| - Zyklisches Polytop (de)
- Politopo cíclico (es)
- Cyclic polytope (en)
- Циклический многогранник (ru)
- Циклічний многогранник (uk)
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| - In mathematics, a cyclic polytope, denoted C(n,d), is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd, where n is greater than d. These polytopes were studied by Constantin Carathéodory, David Gale, Theodore Motzkin, Victor Klee, and others. They play an important role in polyhedral combinatorics: according to the upper bound theorem, proved by Peter McMullen and Richard Stanley, the boundary Δ(n,d) of the cyclic polytope C(n,d) maximizes the number fi of i-dimensional faces among all simplicial spheres of dimension d − 1 with n vertices. (en)
- En matemáticas, un politopo cíclico, denotado como C(n,d), es un tipo de politopo convexo formado como la envolvente convexa de n puntos distintos de una curva normal racional en Rd, donde n es mayor que d. Estos politopos fueron estudiados por Constantin Carathéodory, , , Victor Klee y otros. Desempeñan un papel importante en la combinatoria poliédrica: según el , demostrado por Peter McMullen y , el límite Δ(n,d) del politopo cíclico C (n,d) maximiza el número fi de caras de dimensión i entre todos las de dimensión d − 1 con n vértices. (es)
- Ein zyklisches Polytop ist ein konvexes Polytop mit Ecken auf der . Es ist für viele Fragen der kombinatorischen Theorie von Polytopen von großer Bedeutung, unter anderem für das . (de)
- Циклі́чний многогра́нник — опуклий многогранник, вершини якого лежать на кривій в . (uk)
- Циклический многогранник — выпуклый многогранник, вершины которого лежат на кривой в . (ru)
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| - In mathematics, a cyclic polytope, denoted C(n,d), is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd, where n is greater than d. These polytopes were studied by Constantin Carathéodory, David Gale, Theodore Motzkin, Victor Klee, and others. They play an important role in polyhedral combinatorics: according to the upper bound theorem, proved by Peter McMullen and Richard Stanley, the boundary Δ(n,d) of the cyclic polytope C(n,d) maximizes the number fi of i-dimensional faces among all simplicial spheres of dimension d − 1 with n vertices. (en)
- En matemáticas, un politopo cíclico, denotado como C(n,d), es un tipo de politopo convexo formado como la envolvente convexa de n puntos distintos de una curva normal racional en Rd, donde n es mayor que d. Estos politopos fueron estudiados por Constantin Carathéodory, , , Victor Klee y otros. Desempeñan un papel importante en la combinatoria poliédrica: según el , demostrado por Peter McMullen y , el límite Δ(n,d) del politopo cíclico C (n,d) maximiza el número fi de caras de dimensión i entre todos las de dimensión d − 1 con n vértices. (es)
- Ein zyklisches Polytop ist ein konvexes Polytop mit Ecken auf der . Es ist für viele Fragen der kombinatorischen Theorie von Polytopen von großer Bedeutung, unter anderem für das . (de)
- Циклі́чний многогра́нник — опуклий многогранник, вершини якого лежать на кривій в . (uk)
- Циклический многогранник — выпуклый многогранник, вершины которого лежат на кривой в . (ru)
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