One of the main features of crystallization theory relies on the purely combinatorial nature of the representing objects, which makes them particularly suitable for computer manipulation. This fact allows a computational approach to the study of PL n-manifolds, which has been performed by means of several functions, collected in a unified program, called DUKE III. DUKE III allows automatic manipulation of edge-coloured graphs representing PL n-manifolds (code computation, checking possible isomorphism between edge-coloured graphs, construction of boundary graph, checking bipartition, connectedness, rigidity and planarity conditions, combinatorial moves, invariants computation...). Furthermore, DUKE III allows automatic recognition of orientable 3-manifolds triangulated by at most 30 coloured tetrahedra and of non-orientable 3-manifolds triangulated by at most 26 coloured tetrahedra (by making use of existing electronic archives of all rigid bipartite crystallizations up to 30 vertices and non-bipartite ones up to 26 vertices, due to the same research team).
DUKE III: A program to handle edge-coloured graphs representing PL n-dimensional manifolds / Casali, Maria Rita; Cristofori, Paola. - ELETTRONICO. - (2007).