I didn't know that it had been eliminated from IDTA, but ISTD still uses it, as do most dancers.

To Dave: The reverse-ness of the Reverse Wave comes from two things: (1) The fact that it begins w/ 1-3 Reverse Turn, and (2) The fact that the three back steps [can] curve slightly to the left.

However, if you were to dance three more back steps, the curve would be to the right. If you were to dance a series of measures of consecutive back steps in Foxtrot, every other measure would cancel out the rotation of the last, so you're no longer dancing a "Reverse" or "Natural" anything... and in this case, we just call it a "Wave".

There is certainly such a thing as a "Natural Wave", but most people avoid the terminology because it's so similar to "Natural Weave" (note that the Reverse version of the Weave is not called Reverse Weave, but rather a "Basic Weave"). Therefore, the most common terminology for anything other than the book version is simply called "Wave".

Sincerely,
Jonathan Atkinson