2 problems
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Natarajan's two-hands separation conjecture for finite convex-body packings
A finite packing of convex bodies can be moved arbitrarily far without disturbing the others by simultaneous translations. Natarajan's conjecture. In every such packing, a proper s…
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Fejes Tóth–Heppes tetrahedral packing conjecture
There is a finite packing in space consisting of twelve tetrahedra around a rhombic dodecahedron, with the property that no single member can move rigidly without disturbing the ot…