Isocanted Alcoved Polytopes

Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their f -vectors and checking the validity of the following five conjectures: Bárány, unimodality, 3 d , flag and cubical lower bound (CLBC). Isocanted alcoved polytopes are centrally symmetric, almost simple cubical polytopes. They are zonotopes. We show that, for each dimension, there is a unique combinatorial type. In dimension d , an isocanted alcoved polytope has 2 d +1 − 2 vertices, its face lattice is the lattice of proper subsets of [ d + 1] and its diameter is d + 1. They are realizations of d -elementary cubical polytopes. The f -vector of a d -dimensional isocanted alcoved polytope attains its maximum at the integer ⌊ d /3⌋.