Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)

Pages 387–390 Short Papers

*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.

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