P.L.-spheres, convex polytopes, and stress

DOI10.1007/BF02711516zbMath0856.52009MaRDI QIDQ1913692

Carl W. Lee

Publication date: 17 February 1997

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

zbMATH Keywords

weightsconvex polytopestresssimplicial complexface ringinfinitesimal motionsface-vectorsp.l. spheres

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05)

Related Items

A geometric lower bound theorem, Bipartite Rigidity, Weights on polytopes, Hodge theory for combinatorial geometries, Toric chordality, Lifting degenerate simplices with a single volume constraint, Reconstructing simplicial polytopes from their graphs and affine 2-stresses, Stable sets in flag spheres, Rigidity and volume preserving deformation on degenerate simplices, FAQ on the g-theorem and the hard Lefschetz theorem for face rings, On traces of \(d\)-stresses in the skeletons of lower dimensions of piecewise-linear \(d\)-manifolds, Fully Inverse Parametric Linear/Quadratic Programming Problems via Convex Liftings, Stable sets in flag spheres, The stresses on centrally symmetric complexes and the lower bound theorems, Higher chordality: From graphs to complexes, Projective background of the infinitesimal rigidity of frameworks, A homological interpretation of skeletal ridigity, Valuations and Tensor Weights on Polytopes, Equilibrium stressability of multidimensional frameworks

Cites Work

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• Rigidity and the lower bound theorem. I
• Shellings of simplicial balls and p.l. manifolds with boundary
• Characterization of f-vectors of families of convex sets in \({\mathbb{R}}^ d\). I: Necessity of Eckhoff's conditions
• The number of faces of a simplicial convex polytope
• The number of faces of polytope pairs and unbounded polyhedra
• Rigidity and the Alexandrov-Fenchel inequality
• Cohen-Macaulay quotients of polynomial rings
• Hilbert functions of graded algebras
• On simple polytopes
• Skeletal rigidity of simplicial complexes. I
• Weights on polytopes
• The minimum number of vertices of a simple polytope
• A proof of the lower bound conjecture for convex polytopes
• Introduction to Toric Varieties. (AM-131)
• The Upper Bound Conjecture and Cohen-Macaulay Rings
• The maximum numbers of faces of a convex polytope
• A generalized lower‐bound conjecture for simplicial polytopes
• Schälbare Cohen-Macaulay-Komplexe und ihre Parametrisierung. (Shellable Cohen-Macaulay complexes and their parametrization)