This Demonstration depicts what many believe is the simplest and most elegant of these possibilities, a quintic (fifth degree) polynomial in four-dimensional complex projective space. When two of the four complex variables are fixed, the surface that remains can be displayed using ordinary graphics projected from 4D into 3D; in this Demonstration you can interactively alter the 4D viewpoint to see a variety of different aspects of this fundamental shape. The fact that the surface is derived from a quintic polynomial can be perceived directly by noting the five-fold pie-slice arrangements that occur in the color-coded variant of the image of this Calabi-Yau shape.