Fermat Space is the solution set in the field of complex numbers of Fermat's famous "last theorem" (that the formula a^n +b^n = c^n has no rational solutions). The surface is projected from the 4-dimensional complex projective space CP^2 into 3 dimensions to create the model. This 3-lobed model is for the solutions for n=3, the mesh is for clarity and to reduce cost. The graphics were developed by Andrew J. Hanson of Indiana University, plotted in Mathematica, and thickened in Blender.
Fermat Space is closely related to the 6-dimensional Calabi-Yau space, which represents the 6 'hidden' dimensions of 10-dimensional string theory. The C-Y space is the solution set of the Fermat Space with n=5. In other words, C-Y space is the solution set of a degree five polynomial (n=5) with complex variables.