# Henry Segerman

I am a postdoctoral mathematician. My mathematical research is in 3-dimensional geometry and topology, and concepts from those areas often appear in my work. Other artistic interests involve procedural generation, self reference, ambigrams and puzzles. These sculptures were designed with the assistance of Saul Schleimer.

These three (actually four) objects are representations of regular 4-dimensional polytopes, the analogues of the 3-dimensional regular polyhedra. The edges of the polytopes are first radially projected onto the unit sphere in 4-dimensional Euclidean space, then stereographically projected into our 3-dimensional Euclidean space so they can be 3D printed. Only the parts of the polytope within the hemihypersphere furthest from the projection point are printed, but one can imagine reflecting across the equatorial 2-sphere to recover the whole of the polytope. The 120-cell and 600-cell are shown, which have 120 dodecahedral facets and 600 tetrahedral facets respectively. These two polytopes are dual to each other, which means that the vertices of one correspond to the 3-dimensional facets of the other, and vice versa. This is illustrated in the third object, which is simply copies of the two other objects occupying the same space, interlinking with each other.