  The 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.
