Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their $f$--vectors and checking the validity of the following five conjectures: Barany, 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 $\lfloor d/3\rfloor$.

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等距多胞体

通过热带正态幂等矩阵，我们引入了等距凹形多胞体，计算它们的 $f$--vectors 并检查以下五个猜想的有效性：Barany、unimodality、$3^d$、flag 和立方体下界 (CLBC)。等距凹腔多胞体是中心对称的，几乎是简单的立方体多胞体。它们是带状体。我们表明，对于每个维度，都有一个独特的组合类型。在$d$维上，一个等斜凹形多面体有$2^{d+1}-2$个顶点，它的面格是$[d+1]$的真子集格，它的直径是$d+1$。它们是 $d$--基本立方多胞体的实现。$d$-维等倾壁凹多胞体的$f$--vector 在整数$\lfloor d/3\rfloor$ 处达到最大值。