Domokos–Horváth–Goriely–Regős conjecture on completely softening polyhedral tilings

A polyhedral tiling is a tiling of Euclidean space by polyhedral cells. A tiling can be completely softened if each of its nodes can be softened using pairwise disjoint bending neighborhoods.

Domokos–Horváth–Goriely–Regős conjecture. Every polyhedral tiling can be completely softened.

Domokos, Goriely, G. Horváth, and Regős proved this for a wide class of polyhedral tilings satisfying a stated combinatorial condition, and conjectured that the condition is unnecessary. The conjecture asks whether all polyhedral tilings admit such a complete softening.