论文标题
空间向量形成理性角度
Space vectors forming rational angles
论文作者
论文摘要
我们将所有一组非零向量分类为$ \ mathbb {r}^3 $，使每对形成的角度是$π$的合理倍数。四元素子集的特殊情况使我们可以对所有四面角进行分类，其二面角是$π$的倍数，解决了1976年的康威和琼斯的问题：$ 2 $ $ $ $ 59 $ 59 $ scoradic tetrahedra，其中三个除外，所有这些都与icosidododecahedecahedecahedecahedecahedecahedechedron or $ bythe $ bythe the y the the y book book boot the boot the the ratt latt。证明需要在$ W（D_6）$ - 对称多项式方程的统一根基中的解决方案，并以$ 105 $单元（以前的记录为$ 12 $ MONEMAILS）。
We classify all sets of nonzero vectors in $\mathbb{R}^3$ such that the angle formed by each pair is a rational multiple of $π$. The special case of four-element subsets lets us classify all tetrahedra whose dihedral angles are multiples of $π$, 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 unity of a $W(D_6)$-symmetric polynomial equation with $105$ monomials (the previous record was $12$ monomials).
