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A support characterization of zonotopes
Author(s) -
Witsenhausen H. S.
Publication year - 1978
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300009219
Subject(s) - mathematics , polytope , subspace topology , characterization (materials science) , convex polytope , quadrilateral , combinatorics , norm (philosophy) , polyhedron , regular polygon , piecewise linear function , convex set , pure mathematics , convex optimization , mathematical analysis , geometry , finite element method , materials science , nanotechnology , physics , political science , law , thermodynamics
A convex polytope is a zonotope, if, and only if, its support function satisfies Hlawka's inequality. It follows that a finite dimensional real space with piecewise linear norm is isometrically isomorphic to a subspace of an L 1 space, if, and only if, it has the quadrilateral property‖ x ‖ + ‖ y ‖ + ‖ z ‖ + ‖ x + y + z ‖ ⩾ ‖ x + y ‖ + ‖ y + z ‖ + ‖ z + x ‖ .