What arrangement of 8 legs will have the most vaginas between them, assuming that vaginas will only appear between legs that are distance x apart?
Actually, too easy a puzzle, the following arrangement seems to be the most effective yieldings fourteen váginias:
Presumably, this solution also extends infinitely, with 7 legs being a hexagon, then further legs layering gradually to make larger hexagons.
Anyone got better geometric puzzles?
Unless the pyramid tips are zero distance apart, then it will still be >x.
A valid solution if you're working on a purely mathematical basis, but if that solution is valid then it's also valid to have a 0-dimensional Ariel where all legs are the same distance apart and lie on the same point, giving a total of 36 vaginias.
Pentagonal bipyramid of legs: Uses 7 legs, and if she is 3D (Only external vaginas) then she has 15 vaginas, and the last leg tacked on anywhere can bring that up to 18; the same number as the hexagonal bipyramid solution, but it works with a "realistic" being.
If we consider Ariel as a 4D being or allow her to have internal vaginas, she can have 19 vaginas by counting the fact that the two tips of the pyramid are x distance apart.
If she is both 4D and can have internal vaginas, we can place the 8th leg in such a way that she has 20 vaginas (in the middle of one of the tetrahedrons formed by the pentagonal bipyramid, displaced in the W dimension just far enough to make a 5-simplex.)
She does not need to have internal vaginas for this solution to count if she is 5 dimensional, bringing the current maximum (discounting the 0D solution) to 20 vaginas.
Maybe there's more...
For nD cubic space where the sides loop at whatever distance is convenient, the number of possible vaginas increases massively.
Just throwing out a guess here, I think the maximum possible number of vaginas for such space is 3*n plus the optimal solution for n-1 dimensions. it is definitely at least that, maybe more. Imagine!