Corpus ID: 227227595

Space vectors forming rational angles.

@article{Kedlaya2020SpaceVF,
  title={Space vectors forming rational angles.},
  author={Kiran S. Kedlaya and A. Kolpakov and B. Poonen and M. Rubinstein},
  journal={arXiv: Metric Geometry},
  year={2020}
}
  • Kiran S. Kedlaya, A. Kolpakov, +1 author M. Rubinstein
  • Published 2020
  • Mathematics
  • arXiv: Metric Geometry
  • We classify all sets of nonzero vectors in $\mathbb{R}^3$ such that the angle formed by each pair is a rational multiple of $\pi$. The special case of four-element subsets lets us classify all tetrahedra whose dihedral angles are multiples of $\pi$, solving a 1976 problem of Conway and Jones: there are $2$ one-parameter families and $59$ sporadic tetrahedra, all but three of which are related to either the icosidodecahedron or the $B_3$ root lattice. The proof requires the solution in roots of… CONTINUE READING
    1 Citations

    Figures and Tables from this paper

    References

    SHOWING 1-10 OF 53 REFERENCES
    Rational angles in plane lattices
    • 1
    • Highly Influential
    Classical 6j{symbols and the tetrahedron
    • 124
    • PDF
    On Regular Polytopes
    • 366
    • PDF
    On linear relations between roots of unity
    • 115
    Which Tetrahedra Fill Space
    • 73
    • PDF
    Solving algebraic equations in roots of unity.
    • 6
    • PDF
    The Number of Intersection Points Made by the Diagonals of a Regular Polygon
    • 48
    • PDF