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András Bezdek - On fat polygons and polyhedra
| ANDRÁS BEZDEK, The Mathematical Institute of the Hungarian Academy of Science, Budapest, Auburn University, Auburn, Alabama 36849-5310, USA | |
| On fat polygons and polyhedra |
(Joint work with Ferenc Fodor)
We investigate the problem of finding the polygons (polyhedra resp.)
with n vertices and of diameter 1 which have the largest possible
width w(n) (W(n) resp). We prove that 
and
and in general 
. In the later upper bound equality holds if n has an odd
divisor greater than 1 and in this case a polygon 
is
extremal if and only if it has equal sides and it is inscribed in a
Reuleaux polygon of constant width 1, so that the vertices of the
Reuleaux polygon are also vertices of .
eo@camel.math.ca
