In this paper, we take the advantages of extended superquadrics to represent and recognize the entire set of 36 geons. Extended superquadrics are novel volumetric shape models that include superquadrics as a special case. An extended superquadric model can be deformed in any direction because it extends the exponents of the superquadric model from constants to functions of the latitude and longitude angles in the spherical coordinate system. Thirteen features derived from the extended superquadric parameters are recovered in order to distinguish between all the 36 geon classes. Classification error rates are estimated for the nearest neighbor classifier and the back-propagation neural network. Both simulated data (at different noise levels) and real geon models are tested in our experiments. The results are very encouraging and has significant benefits for an object recognition system.