A regular pentagon sits on a plane. It "moves one cell over" by flipping over an edge. Because pentagons don't tessellate, a single point may be covered by many different cells, kind of like parallel universes. What interesting kinds of cellular automata are possible? What approximations of circles and ellipses (Newtonian orbits) happen? How many orbits til the pentagons coincide again?
Repeat, with regular tetrahedra in space; an adventure, because the dihedral angle is not a rational multiple of pi.
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