Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskij space

DOI10.1007/BF01077314zbMath0597.51014MaRDI QIDQ1079190

A. G. Khovanskii

Publication date: 1986

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

Lobachevskij spacetoroidal manifolddiscrete reflection groupintersection of polyhedra by hyperplanes

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Polyhedra and polytopes; regular figures, division of spaces (51M20) Special varieties (14M99) Other geometric groups, including crystallographic groups (20H15) Reflection groups, reflection geometries (51F15) Polytopes and polyhedra (52Bxx)

Related Items

The number of cusps of right-angled polyhedra in hyperbolic spaces, Mirror symmetries of hyperbolic tetrahedral manifolds, Facet-reducing cuts of a convex polytope, Cell decomposition of polytopes by bending, Infinitely many quasi-arithmetic maximal reflection groups, Relatively hyperbolic Coxeter groups with maximal flats of codimension one, Right-angled polyhedra and hyperbolic 3-manifolds, Hamiltonian structure of dynamical systems which solve linear programming problems, On hyperbolic Coxeter polytopes with mutually intersecting facets, Notes on right-angled Coxeter polyhedra in hyperbolic spaces., Counting cusped hyperbolic 3-manifolds that bound geometrically, Virtually special embeddings of integral Lorentzian lattices, Fundamental groups of three-dimensional small covers, Generalized virtual polytopes and quasitoric manifolds, Convex polytopes, Coxeter orbifolds and torus actions

Cites Work

• Unnamed Item
• Toroidal embeddings. I
• Selection of subspaces with special properties in a Banach space and some properties of quasicomplements
• The number of faces of a simplicial convex polytope
• Convexity properties of the moment mapping
• The numbers of faces of simplicial polytopes
• THE GEOMETRY OF TORIC VARIETIES
• Sufficiency of McMullen’s conditions for 𝑓-vectors of simplicial polytopes
• Convexity and Commuting Hamiltonians