  We consider thorny spheres, that is 2-dimensional compact surfaces which are
everywhere locally isometric to a round sphere $S^2$ except for a finite number
of isolated points where they have conical singularities. We use thorny spheres
to generate, from a spherically symmetric solution of the Einstein equations,
new solutions which describe spacetimes pierced by an arbitrary number of
infinitely thin cosmic strings radially directed. Each string produces an angle
deficit proportional to its tension, while the metric outside the strings is a
locally spherically symmetric solution. We prove that there can be arbitrary
configurations of strings provided that the directions of the strings obey a
certain equilibrium condition. In general this equilibrium condition can be
written as a force-balance equation for string forces defined in a flat 3-space
in which the thorny sphere is isometrically embedded, or as a constraint on the
product of holonomies around strings in an alternative 3-space that is flat
except for the strings. In the case of small string tensions, the constraint
equation has the form of a linear relation between unit vectors directed along
the string axes.
