Minimal-Volume Equiangular Hyperbolic $4$-Polytopes

We study finite-volume convex hyperbolic $4$-polytopes whose dihedral angles are all equal to a fixed strictly acute angle $α$. Put $α_0=\arccos(1/3)$ and $α_1=\arccos(1/4)$. We first show that the class is empty for $α<α_0$. For $α_0\leqα<α_1$, the unique polytope of minimum volume is the regular h