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Convex bodies equidecomposable by locally discrete groups of isometries
Author(s) -
Gardner R. J.
Publication year - 1985
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/s0025579300010780
Subject(s) - mathematics , partition (number theory) , disjoint sets , combinatorics , polytope , convex polytope , regular polygon , convex body , group (periodic table) , convex analysis , convex hull , geometry , convex optimization , chemistry , organic chemistry
We show that if a polytope K 1 , in ℝ d can be partitioned into a finite number of sets, and these sets can be moved by isometries in a locally discrete group to form a convex body K 2 , then K 2 is a polytope and a similar partition can be made where the sets involved are simplices with disjoint interiors. This gives partial answers to questions of Tarski, Sallee and Wagon.