Would you care to expand this problem to include hanging baskets? The scenario here would be to find the balanced solutions for (b,n,k) where b is the number of baskets with n holes each.

]]>There is a sequence of polyhedra which begin with a dodecahedron and whose limiting shape is an icosahedron and these can be projected to a sphere.

there’s the 120-cell, again to be projected on the three sphere, as well as the other polychora in R4.

there’s the polytope associated with E8, again to be projected onto a sphere.

There are hyperboloids crossed by rulings which are Lorenz invariant.

there’s the Klein quartic. eek?

symmetry with respect to more complicated discrete subgroups of SO(n,R) feels like it might have a representation theoretic flavor

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