  While a generic smooth Ribaucour sphere congruence admits exactly two
envelopes, a discrete R-congruence gives rise to a 2-parameter family of
discrete enveloping surfaces. The main purpose of this paper is to gain
geometric insights into this ambiguity. In particular, discrete R-congruences
that are enveloped by discrete channel surfaces and discrete Legendre maps with
one family of spherical curvature lines are discussed.
