  Define the augmented square twist origami crease pattern to be the classic
square twist crease pattern with one crease added along a diagonal of the
twisted square. In this paper we fully describe the rigid foldability of this
new crease pattern. Specifically, the extra crease allows the square twist to
rigidly fold in ways the original cannot. We prove that there are exactly four
non-degenerate rigid foldings of this crease pattern from the unfolded state.
