2015 Joint Mathematics Meetings

Henry Segerman and Will Segerman


Henry Segerman

Associate Professor of Mathematics

Oklahoma State University

Stillwater, Oklahoma, USA




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.


Image for entry 'More fun than a hypercube of monkeys'

More fun than a hypercube of monkeys

22.6 cm x 20.8 cm x 21.4 cm

PA 2200 Plastic, Selective-Laser-Sintered, Computer Animation (on a tablet computer)


Additional info

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.