2015 Joint Mathematics Meetings

# Henry Segerman and Will Segerman

## Artists

## Statement

Henry Segerman is an assistant professor in the Department of Mathematics at Oklahoma State University. His mathematical research is in 3-dimensional geometry and topology, and concepts from those areas often appear in his work. Other artistic interests involve procedural generation, self reference, ambigrams and puzzles. Will Segerman is a self-employed sculptor in analogue and digital media. He works from his home/office/workshop in Brighton, UK. His current main source of income is as a virtual milliner.

## Artworks

This sculpture was inspired by a question of Vi Hart. This seems to be the first physical object with the quaternion group as its symmetry group. The quaternion group {1,i,j,k,-1,-i,-j,-k} is not a subgroup of the symmetries of 3D space, but is a subgroup of the symmetries of 4D space. The monkey was designed in a 3D cube, viewed as one of the 8 cells of a hypercube. The quaternion group moves the monkey to the other seven cells. We radially project the monkeys onto the 3-sphere, the unit sphere in 4D space, then stereographically project to 3D space. The distortion in the sizes of the monkeys comes only from this last step - otherwise all eight monkeys are identical. The animation shows the result of rotating the monkeys in the 3-sphere.