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- W2891874228 abstract "Interior angle vectors of polytopes are semi-discrete analogs of $f$-vectors that take into account the interior angles at faces measured by spherical volumes. In this context, Gram's relation takes the place of the Euler-Poincare relation as the unique linear relation among the entries of the interior angle vectors. Simple and normalized cone valuations naturally generalize spherical volumes and in this paper we study the associated interior and exterior angle vectors. We show that for any given cone valuation, Gram's relation is the unique linear relation that is satisfied by all generalized interior angle vectors. To show uniqueness, we prove that the angle vectors of a zonotope are independent of the cone valuation and only depend on the combinatorics of the zonotope. In the second part of the paper, we introduce flag-angle vectors as a counterpart to flag-vectors of polytopes. We determine the linear relations on flag-angle vectors and we show a connection to flag-vectors of lattices of flats." @default.
- W2891874228 created "2018-09-27" @default.
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- W2891874228 date "2018-09-04" @default.
- W2891874228 modified "2023-09-27" @default.
- W2891874228 title "Cone valuations, Gram's relation, and flag-angles" @default.
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