Results 121 to 129 of about 19,164 (129)

Three-Dimensional Manifolds Defined by Coloring a Simple Polytope

Mathematical Notes, 2001
Let \(P\) be a simple convex \(d\)-polytope, that is, each vertex is contained in precisely \(d\)~facets. For each proper coloring~\(\chi\) of the dual graph~\(\Gamma^*(P)\) of~\(P\) with \(s\)~colors the author defines a \(d\)-dimensional manifold~\(\mathcal Z(P,\chi)\) with a natural action of the elementary abelian group \(\mathbb Z_2^s\), whose ...
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Bruns-Gubeladze K-theory defined by some three-dimensional polytopes

Russian Journal of Mathematical Physics, 2015
Bruns and Gubeladze defined a new version of algebraic \(K\)-theory for a commutative ring \(R\) (with unit) and a polytope \(P\) which satisfies certain properties, and which was denoted as \(K_i(R,P)\), \(i\geq2\). Here, the author studies some particular cases of not Col-divisible balanced three-dimensional polytopes, such as the pentagonal pyramid \
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On the structure of faces of three-dimensional polytopes

Izvestiya: Mathematics, 2005
In Euclidean three-space, we consider two-dimensional polyhedra that are homeomorphic to closed surfaces. The structure of an arbitrary face of such a polyhedron is studied in detail. In particular, we prove the following main theorem. If a two-dimensional polyhedron lies in Euclidean three-space and is isometric to the surface of a convex three ...
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Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions

Proceedings of the Steklov Institute of Mathematics, 2019
This paper is devoted to study hyperbolic 3-polytopes of finite volume with all dihedral angles equal to 90\degree. One of the main results is that the operation of truncating the ideal vertices (at infinity) establishes a bijection from the set of right-angled hyperbolic 3-polytopes to the set of strongly cyclically 4-edge-connected 3-polytopes other ...
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Construction of Three-Dimensional Cubature Formulae with Points on Regular and Semi-Regular Polytopes

1987
A method of constructing three-dimensional cubature formulae of arbitrary degree for some three-dimensional regions is presented. We search for formulae with points as vertices of a series of regular polytopes. The radii of the circumscribing spheres and the weights (the same for all points on the same polytope) can be computed from a nonlinear system ...
Ann Haegemans, Ronald Cools
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Three-Dimensional Stress Analysis of Mountain Ranges: A Novel Approach Using Marching Volume Polytopes Algorithm and Finite Cell Method 

The negative feedback between relief formation due to valley incision, increasing topographic stress towards a critical stress state dependent on rock strength, and consequently relief-destroying (and stress-reducing) landslides determines the geometry of alpine landscapes.
Viktor Haunsperger, Jörg Robl, Andreas Schröder, Stefan Hergarten   +3 more
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Three-dimensional polytopes inscribed in and circumscribed about compact convex sets. II

2002
As in the preceding paper [part I, St. Petersbg. Math. J. 12, No. 4, 507-518 (2001; Zbl 0988.52016)], the author investigates the problem of inscribing polytopes into convex bodies. The main result here is that a regular octahedron can be inscribed into an arbitrary smooth convex body. There have been quite a few attempts to prove this result.
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The lower bound for the volume of a three-dimensional convex polytope

2019
In this paper, we provide a lower bound for the volume of a three-dimensional smooth integral convex polytope having interior lattice points. Our formula has a quite simple form compared with preliminary results. Therefore, we can easily utilize it for other beneficial purposes.
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Three-dimensional polytopes

1996
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