  We study infinitesimal conformal deformations of a triangulated surface in
Euclidean space and investigate the change in its extrinsic geometry. A
deformation of vertices is conformal if it preserves length cross-ratios. On
one hand, conformal deformations generalize deformations preserving edge
lengths. On the other hand, there is a one-to-one correspondence between
infinitesimal conformal deformations in space and infinitesimal isometric
deformations of the stereographic image on the sphere. The space of
infinitesimal conformal deformations can be parametrized in terms of the change
in dihedral angles, which is closely related to the Schl\"{a}fli formula.
