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A Characterization of Three-Dimensional Convex Polytopes with Five Pairwise Antipodal Vertices
MathematicsConcerning the antipodality properties of finite sets, we focus on convex polytopes in R3 with less than 23 vertices and characterize convex polytopes with 5 vertices that are pairwise antipodal.
Rong Guo +3 more
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Mathematics, 2021 The deformation of a solid due to changing boundary conditions is described by a deformation gradient in Euclidean space. If the deformation process is reversible (conservative), the work done by the changing boundary conditions is stored as potential ...
Odysseas Kosmas +2 more
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Three-Dimensional Classical Groups Acting on Polytopes [PDF]
Discrete & Computational Geometry, 2009 The authors show that any irreducible subgroup \(G\) of \(\mathrm{GL}(V)\), where \(V\) is a three-dimensional vector space over a finite field \(K\), that arises as automorphism group of an abstract regular polytope preserves a non-degenerate symmetric bilinear form \(f\) of \(V\). In any such case \(K\) is of characteristic \(\neq 2\). Moreover, let \
Brooksbank, Peter A. +1 more
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The geometry of structural equilibrium [PDF]
Royal Society Open Science, 2017 Building on a long tradition from Maxwell, Rankine, Klein and others, this paper puts forward a geometrical description of structural equilibrium which contains a procedure for the graphic analysis of stress resultants within general three-dimensional ...
Allan McRobie
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Optimization of Packing Irregular Three-Dimensional Objects
Кібернетика та комп'ютерні технології, 2023 Introduction. Nowadays the irregular packing problem is becoming more important, since effective space management and optimal arrangement of objects are becoming key factors for ensuring efficiency and saving resources in a wide range of applications, e ...
Tetyana Romanova +4 more
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DEFINING SIMPLE nD OPERATIONS BASED ON PRISMATIC nD OBJECTS [PDF]
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2016 An alternative to the traditional approaches to model separately 2D/3D space, time, scale and other parametrisable characteristics in GIS lies in the higher-dimensional modelling of geographic information, in which a chosen set of non-spatial ...
K. Arroyo Ohori, H. Ledoux, J. Stoter
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On Delaunay’s Theorem Classifying Coincidences of Parallelohedra at Faces of Codimension 3
Моделирование и анализ информационных систем, 2013 In 1929 B.N. Delaunay obtained the complete classification of all possible combinatorial coincidence types of parallelohedra at their faces of codimension 3.
A. N. Magazinov
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On the Fine Interior of Three-Dimensional Canonical Fano Polytopes
, 2022 The Fine interior $Δ^{\text{FI}}$ of a $d$-dimensional lattice polytope $Δ$ is a rational subpolytope of $Δ$ which is important for constructing minimal birational models of non-degenerate hypersurfaces defined by Laurent polynomials with Newton polytope $Δ$.
Batyrev, Victor +2 more
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Journal of High Energy Physics, 2022 Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles.
Sebastian Mizera, Simon Telen
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Systematics of perturbatively flat flux vacua
Journal of High Energy Physics, 2022 In this article, we present a systematic analysis of the so-called perturbatively flat flux vacua (PFFV) for the mirror Calabi-Yau (CY) 3-folds ( X ~ 3 $$ {\overset{\sim }{X}}_3 $$ ) with h 1,1( X ~ 3 $$ {\overset{\sim }{X}}_3 $$ ) = 2 arising from the ...
Federico Carta +2 more
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