The following papers constitute a study of the
precise geometrical nature of the Cuspoid Catastrophes,
the Elliptic, Hyperbolic and Parabolic Umbilics and the
Reduced Double Cusp. Stereographic-pair figures permit
a 3-dimensional realization of the Catastrophe Manifolds of
the Cuspoid Catastrophes when observed through a stereo
viewer. In introducing these precise pictures into the
literature, it is hoped that they will aid in the
application of Catastrophe Theory to the understanding of
complex systems such as those of Biology, Physical
Chemistry, Economics and Sociology.