TT22 dissections, like TT2 dissections, dissect two shapes to two shapes using T strips. These dissections are a little more complicated, so we start with an example.
Here are the strips for triangle and pentagon:
Here is the overlay:
The strips are overlaid with an area of overlap equal to a single shape. Note how the edges of the triangle strip pass through the blue anchor points of the pentagon strip and the edges of the pentagon strip pass through the blue anchor points of the triangle strip. The central red anchor points coincide. There are at most eight possible ways of combining the strips.
But what is different about TT22 dissections is that this is not enough. Each piece appears twice, but we have only dissected half of each shape. We have to overlay the strips a second time to now dissect the other half of each shape. We now throw away half the pieces of the overlapping areas to get the final dissection:
Below are some more examples: