@article{10860,
  abstract     = {A tight frame is the orthogonal projection of some orthonormal basis of Rn onto Rk. We show that a set of vectors is a tight frame if and only if the set of all cross products of these vectors is a tight frame. We reformulate a range of problems on the volume of projections (or sections) of regular polytopes in terms of tight frames and write a first-order necessary condition for local extrema of these problems. As applications, we prove new results for the problem of maximization of the volume of zonotopes.},
  author       = {Ivanov, Grigory},
  issn         = {1496-4287},
  journal      = {Canadian Mathematical Bulletin},
  keywords     = {General Mathematics, Tight frame, Grassmannian, zonotope},
  number       = {4},
  pages        = {942--963},
  publisher    = {Canadian Mathematical Society},
  title        = {{Tight frames and related geometric problems}},
  doi          = {10.4153/s000843952000096x},
  volume       = {64},
  year         = {2021},
}