  The groups QF, QT, and QV are groups of quasi-automorphisms of the infinite
binary tree. Their names indicate a similarity with Thompson's well-known
groups F, T, and V.
  We will use the theory of diagram groups over semigroup presentations to
prove that all of the above groups (and several generalizations) have type
F-infinity. Our proof uses certain types of hybrid diagrams, which have
properties in common with both planar diagrams and braided diagrams. The
diagram groups defined by hybrid diagrams also act properly and isometrically
on CAT(0) cubical complexes.
