4 problems

Haase–Ziegler's conjecture. These are all the empty $4$-simplices of width larger than two.

Let $d$ be a positive integer such that $d+1$ is prime. Consider empty $d$-simplices modulo unimodular equivalence that admit a unimodular symmetry acting transitively on vertices,…

A cyclotomic simplex is an empty lattice simplex associated with the cyclotomic construction; two lattice simplices are considered equivalent modulo unimodular equivalence. Let $d$…

Mori–Mori–Morrison classification conjecture. The classification of all such infinite families is complete.