  The skewer of a pair of skew lines in space is their common perpendicular. To
configuration theorems of plane projective geometry involving points and lines
(such as Pappus or Desargues) there correspond configuration theorems in space:
points and lines in the plane are replaced by lines is space, the incidence
between a line and a point translates as the intersection of two lines at right
angle, and the operations of connecting two points by a line or by intersecting
two lines at a point translate as taking the skewer of two lines. These
configuration theorems hold in elliptic, Euclidean, and hyperbolic geometries.
This correspondence principle extends to plane configuration theorems involving
polarity. For example, the theorem that the three altitudes of a triangle are
concurrent corresponds to the Petersen-Morley theorem that the common normals
of the opposite sides of a space right-angled hexagon have a common normal. We
define analogs of plane circles (they are 2-parameter families of lines in
space) and extend the correspondence principle to plane theorems involving
circles. We also discuss the skewer versions of the Sylvester problem: given a
finite collection of pairwise skew lines such that the skewer of any pair
intersects at least one other line at right angle, do all the line have to
share a skewer? The answer is positive in the elliptic and Euclidean
geometries, but negative in the hyperbolic one.
