Let $b\gt a\gt 0$ be constants. Define $P_n(a,b)$ to be the set of all $(x_1,\ldots,x_n)\in\mathbb{R}^n$ satisfying $$ |c_1 x_1 + \cdots + c_n x_n| \le 1$$ for every choice of $c_1,\ldots,c_n\in\lbrace a,b\rbrace$.

This is a finite convex polytope and I wonder if it has been studied and perhaps has a name.

The vertices are rather few, $n(n+1)$ in total, consisting of all permutations of the points $$ \Bigl(-\frac{1}{b}, 0,\ldots,0\Bigr),~~ \Bigl(\frac{1}{b}, 0,\ldots,0\Bigr),~~ \Bigl(-\frac{1}{b-a},\frac{1}{b-a},0,\ldots,0\Bigr). $$