These tessellations are, well not cheap knockoffs, but certainly simple variations of some boxy tessellations demonstrated by John McKeever. He describes them as originating with Kenneth Kawamura, but I somehow suspect that their ultimate inventor is Chris Palmer.
A left-handed boxy tessellation ... there are spiral arms connecting
each square to its nearest neighbors.
its reverse is composed of interlocking waterbomb bases, just like
the underside of the symmetric Kawasaki rose tessellation.
Squares counter-rotating. Notice that as the size of the square
element shrinks, the spontaneous curvature of the model increases.
and a different view
Stacked up, they look kind of nice:
Each of these tessellations can be made iso area by inverting half of
the I-beam shaped sinks that surround the square elements. The tessellation
no longer has a spontaneous curvature ... iso-area symmetry would make
it impossible for the model to decide which way to curve. Only the
middle tessellation has been converted to iso-area goodness.
Here is a detail shot of the middle, iso-area fold:
As advertised, the back-side of this fold looks (almost) the same:
There is no need to keep going with squares: here are some boxy
triangle tessellations which wind up putting octahedra and tetrahedra on
different faces of the paper.
The above fold from the back is even more dramatic. I don't even
have to say this isn't an iso-are fold, right?