# Vi Hart (VH), Andrea Hawksley (AH), Henry Segerman (HS) and Marc ten Bosch (MtB)

## Artists

## Statement

Vi Hart is a mathemusician and virtual reality artist who likes triangles. Andrea Hawksley is a VR researcher who enjoys finding and creating mathematical patterns in the everyday things around her. Henry Segerman's mathematical research is in 3-dimensional geometry and topology. He is also interested in procedural generation, self reference, ambigrams and puzzles. Marc ten Bosch is an independent game designer and programmer, currently working on games that let you explore and interact with a four-dimensional world. Hypernom can be played at http://hypernom.com.

## Artworks

Hypernom is a virtual reality game. The cells of a regular 4D polytope are radially projected to S^3, the sphere in 4D space, then stereographically projected to 3D space where they are viewed in the headset. The orientation of the headset is given by an element of SO(3), a space which is double covered by S^3. In fact, the headset outputs a point of this double cover: a unit quaternion. The positions of the cells are multiplied by this quaternion before projection to 3D space, which moves the player through S^3. When the player is sufficiently close to a cell, they eat it. The aim of the game is to eat all of the cells of the polytope, which, roughly speaking, is achieved by moving one's head through all possible orientations, twice.