``Normal'' crystallizations of 3-manifolds (Q788328)

\textit{M. Ferri} and \textit{C. Gagliardi} [Pac. J. Math. 100, 85-103 (1982; Zbl 0517.57003)] demonstrated that two crystallizations represent the same manifold if and only if there is a finite sequence of moves of two types which takes one crystallization to the other. The authors of this paper define a special type of crystallization which they call (0,1,2)- normal and show that every 3-manifold admits such a crystallization. As a result they are able to show that every 3-manifold can be represented as a partition of a positive integer n along with a fixed-point free involutory permutation on \({\mathbb{Z}}_{4n}\).