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polytope
Durer's Conjecture ★★★
Conjecture Every convex polytope has a non-overlapping edge unfolding.
Cube-Simplex conjecture ★★★
Author(s): Kalai
Conjecture For every positive integer
, there exists an integer
so that every polytope of dimension
has a
-dimensional face which is either a simplex or is combinatorially isomorphic to a
-dimensional cube.
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Continous analogue of Hirsch conjecture ★★
Author(s): Deza; Terlaky; Zinchenko
Conjecture The order of the largest total curvature of the primal central path over all polytopes defined by
inequalities in dimension
is
.
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Average diameter of a bounded cell of a simple arrangement ★★
Author(s): Deza; Terlaky; Zinchenko
Conjecture The average diameter of a bounded cell of a simple arrangement defined by
hyperplanes in dimension
is not greater than
.
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Keywords: arrangement; diameter; polytope
Fat 4-polytopes ★★★
Author(s): Eppstein; Kuperberg; Ziegler
The fatness of a 4-polytope is defined to be
where
is the number of faces of
of dimension
.
Question Does there exist a fixed constant
so that every convex 4-polytope has fatness at most
?
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