  There exist cubical transition systems containing cubes having an arbitrarily
large number of faces. A regular transition system is a cubical transition
system such that each cube has the good number of faces. The categorical and
homotopical results of regular transition systems are very similar to the ones
of cubical ones. A complete combinatorial description of fibrant cubical and
regular transition systems is given. One of the two appendices contains a
general lemma of independant interest about the restriction of an adjunction to
a full reflective subcategory.
