Crown-shy Nova Plexus
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A crown-shy interpretation of the the classical Nova Plexus puzzle.
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Take the configuration of the rods of the famous Nova Plexus.
Let the rods repel each other while maintaining the tetrahedral symmetry.
Stop when the nearest five rods are equally far away.
Congraduations,
you rediscover the Tetra Cage.
Compute the contour of the equation
D(x, 1st-rod)⁻¹⁰ = r⁻¹⁰ + D(x, 2nd-rod)⁻¹⁰ + D(x, 3rd-rod)⁻¹⁰ + ...,
where D is the distance and r is a radius we like.
(In this case, r is the smallest distance between rods.)
When x is far away from the other rods,
this equation degenerates into
D(x, 1st-rod)⁻¹⁰ = r⁻¹⁰,
which defines a cylinder.
When 10 is replaced by very large integers,
our equation converges to
D(x, 1st-rod) = min{r, D(x, 2nd-rod), D(x, 3rd-rod), ...},
which defines a Voronoi boundary.
As a result,
this defines cylinders that are shy when they get too close to each other.
For more crown-shy puzzles, check out my collection.