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Reduced spherical polygons

Marek Lassak — 2015

Colloquium Mathematicae

For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere S d we consider the width of C determined by K. By the thickness Δ(C) of C we mean the minimum of the widths of C over all supporting hemispheres K of C. A spherically convex body R S d is said to be reduced provided Δ(Z) < Δ(R) for every spherically convex body Z ⊂ R different from R. We characterize reduced spherical polygons on S². We show that every reduced spherical polygon is of thickness at most π/2. We...

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