  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 the group SO(3), which is also a space
that 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.
