The correspondence of stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in higher dimensions is the lack of a higher-dimensional equivalent of the Ernst poten- tial. This thesis will propose such a generalized Ernst potential, point out where the rod structure of the space-time can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein field equations in higher dimensions from the rod structure, other asymptotic data, and the requirement of a regular axis. Examples in five dimensions are studied and necessary tools are developed, in particular rules for the transition between different adaptations of the patching matrix and rules for the elimination of conical singularities.

L'étude des espaces-temps plats singuliers munis d'une surface de Cauchy polyédrale est motivée par leur rôle de model jouet de gravité quantique proposé par Deser, Jackiw et 'T Hooft. Cette thèse porte sur les paramétrisations de certaines classes d'espaces-temps plat singuliers : les espaces-temps plats avec particules massives et BTZ Cauchy-compacts maximaux. Deux paramétrisations sont proposées, l'une reposant sur une extension du théorème de Mess aux espaces-temps plats avec BTZ et la surface de Penner-Epstein, l'autre reposant sur une généralisation du théorème d'Alexandrov aux espaces-temps plats avec particules massives et BTZ. Ce travail propose également une amorce de cadre théorique permettant de considérer des espaces-temps singuliers plus généraux. / The study of singular flat spacetimes with polyhedral Cauchy-surfaces is motivated by the quantum gravity toy model role they play in the seminal work of Deser, Jackiw and 'T Hooft. This thesis study parametrisations of classes of singular flat spacetimes : Cauchy-compact maximal flat spacetimes with massive and BTZ-like singularities. Two parametrisations are constructed. The first is based on an extension of Mess theorem to flat spacetimes with BTZ and Penner-Epstein convex hull construction. The second is based on a generalisation of Alexandrov polyhedron theorem to radiant Cauchy-compact flat spacetimes with massive and BTZ-like singularities. This work also initiate a wider theoretical background that encompass singular spacetimes.