  We consider the problem of embedding a symmetric configuration with block
size 3 in an orientable surface in such a way that the blocks of the
configuration form triangular faces and there is only one extra large face. We
develop a sufficient condition for such an embedding to exist given any
orientation of the configuration, and show that this condition is satisfied for
all configurations on up to 19 points. We also show that there exists a
configuration on 21 points which is not embeddable in any orientation. As a
by-product, we give a revised table of numbers of configurations, correcting
the published figure for 19 points. We give a number of open questions about
embeddability of configurations on larger numbers of points.
