  We applied a method of symmetry reduction to the gas dynamics equations with
a special form of the equation of state. This equation of state is a pressure
represented as the sum of a density and an entropy functions. The symmetry Lie
algebra of the system is 12-dimensional. One, two and three-dimensional
subalgebras were considered. In this article, four-dimensional subalgebras are
considered for the first time. Specifically, invariants are calculated for 50
four-dimensional subalgebras. Using invariants of one of the subalgebras, a
symmetry reduction of the original system is calculated. The reduced system is
a partially invariant submodel because one gas-dynamic function cannot be
expressed in terms of the invariants. The submodel leads to two families of
exact solutions, one of which describes the isochoric motion of the media, and
the other solution specifies an arbitrary blow-up surface. For the first family
of solutions, the particle trajectories are parabolas or rays; for the second
family of solutions, the particles move along cubic parabolas or straight
lines. From each point of the blow-up surface, particles fly out at different
speeds and end up on a straight line at any other fixed moment in time. A
description of the motion of particles for each family of solutions is given.
