 

Greg Kuperberg
Circumscribing ConstantWidth Bodies with Polytopes


Published: 
July 9, 1999 
Keywords: 
constant width, convex, strictly convex, inscribed, circumscribed 
Subject: 
52A15 


Abstract
Makeev conjectured that every constantwidth body is inscribed in the
dual difference body of a regular simplex. We prove that homologically,
there are an odd number of such circumscribing bodies in dimension
3, and therefore geometrically there is at least one. We show that
the homological answer is zero in higher dimensions, a result which
is inconclusive for the geometric question. We also give a partial
generalization involving affine circumscription of strictly convex bodies.


Author information
Department of Mathematics, UC Davis, Davis, CA 956168633
greg@math.ucdavis.edu
http://www.math.ucdavis.edu/~greg/

