A dihedral angle is the angle between two intersecting planes. In chemistry it is the angle between planes through two sets of three atoms, having two atoms in common. In solid geometry it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimension, a dihedral angle represents the angle between two hyperplanes. == Mathematical background == When the two intersecting planes are described in terms of Cartesian coordinates by the two equations a 1 x ...

In geometry, the cyclohedron or Bott–Taubes polytope is a certain (n − 1)-dimensional polytope that is useful in studying knot invariants.The configuration space of n distinct points on the circle S1 is an n-dimensional manifold, which can be compactified into a manifold with corners by allowing the points to approach each other. This compactification can be factored as S 1 × W n {\displaystyle S^{1}\times W_{n}} , where Wn is the...

In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module and the restriction maps F(U) →F(V) are compatible with the restriction maps O(U) →O(V): the restriction of fs is the restriction of f times that of s for any f in O(U) and s in F(U). The standard case is when X is a scheme and O its structure sheaf. If O is the constant sheaf Z _ {\displaystyle {\underline {\mathbf...