Rendering Pacioli's rhombicuboctahedron

We analyze the glass rhombicuboctahedron (RCO) appearing in a famous painting of Pacioli (1495), considering the extent to which it might agree with a physically correct rendering of a corresponding glass container half-filled with water. This investigation shows that it is unlikely that the painter of the RCO was looking at such a physical object. We then ask what a proper rendering of such an object might look like. Our computer renderings, which take into account multiple internal and external reflections and refractions, yield visual effects that differ strongly from their depictions in the painting. Nevertheless, the painter of the RCO has clearly succeeded in providing a rendering that appears plausible and awe-inspiring to almost all observers