Delta-matroids are "type B" or "type C" analogues of matroids. I will discuss how to extend a geometric construction related to matroids to delta-matroids. Using this construction, we prove the ultra log-concavity of the number of independent sets of a large class of delta-matroids. This gives inequalities which are new even for matroids. Joint work with Chris Eur, Alex Fink, and Hunter Spink.