2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132117The purpose of the paper is to construct a polyhedral Markov field in ${\mathbb R}^3$ in analogy with the planar construction of the original Arak (1982) polygonal Markov field. We provide a dynamic construction of the process in terms of evolution of two-dimensional multi-edge systems tracing polyhedral boundaries of the field in three-dimensional time-space. We also give a general algorithm for simulating Gibbsian modifications of the constructed polyhedral field.16 pages, second corrected version, published in the Markov Processes and Related Fields (2006), vol. 12 (1), 43-58, further small correctionsProbability60D05; 60K35, 82B21text