  The traditional approach to fixing the parameters of the Skyrme model
requires the energy of a spinning Skyrmion to reproduce the nucleon and delta
masses. The standard Skyrme parameters, which are used almost exclusively, fix
the pion mass to its experimental value and fit the two remaining Skyrme
parameters by approximating the spinning Skyrmion as a rigid body. In this
paper we remove the rigid body approximation and perform numerical calculations
which allow the spinning Skyrmion to deform and break spherical symmetry. The
results show that if the pion mass is set to its experimental value then the
nucleon and delta masses can not be reproduced for any values of the Skyrme
parameters; the commonly used Skyrme parameters are simply an artifact of the
rigid body approximation. However, if the pion mass is taken to be
substantially larger than its experimental value then the nucleon and delta
masses can be reproduced. This result has a significant effect on the structure
of multi-Skyrmions.
