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Figure 1: HOP sphere representation of vector vortex beams. In contrast to the complexity and challenges of producing OAM beams and vector vortex beams from lasers, the control of polarization or SAM ...

This tan paper cut and glued model has thirty-six equal isosceles triangles for sides. Eighteen of these are around the middle, facing in opposite directions as in an antiprism. Nine at each end form ...

In a pair of papers posted online this month, a Ukrainian mathematician has solved two high-dimensional versions of the centuries-old “sphere packing” problem. In dimensions eight and 24 (the latter ...

A sphere is a sphere, right? Yes, if you mean a globe or a beach ball – what mathematicians call a two-dimensional sphere – but not if you are talking about a sphere in seven dimensions. Now the ...