A Monte Carlo generator has been constructed to simulate the reaction
e^+ e^- \to \gamma + 4 \pi, where the photon is assumed to be observed
in the detector. Isospin relations between the amplitudes governing
tau decays into four pions and electron positron annihilation into
four pions respectively have been found which allow to determine all
four modes after the amplitude for the \pi^+ \pi^- 2 \pi^0 channel has
been fixed. The kinematic breaking of these isospin relations as a
consequence of the \pi^- -- \pi^0 mass difference has also been
investigated. The program is constructed in analogy to an earlier one
simulating e^+ e^- \to \gamma + 2 \pi. However, it does not include
final state radiation from the charged pions. Additional collinear
photon radiation has been incorporated with the technique of structure
functions. Predictions are presented for cms energies of 1GeV, 3GeV
and 10GeV, corresponding to the energies of DAPHNE, BEBC and of
B-meson factories. Using this program it is demonstrated that, even
after applying realistic cuts, the event rates are sufficiently high
to allow for a precise measurement of R(Q^2) in the region of Q
between approximately 1GeV and 2.5GeV. The model predictions are
compared to recent data from electron positron colliders and agreement
is obtained within the relatively large errors.