Doubling the tessellation of octagons and squares gives a quasiperiodic tiling of eight-fold rotational symmetry, which makes an interesting kaleidoscope. Here is a sample result:
Finally, I want to show you a result using the quasiperiodic tiling that doubles the tessellation of dodecagons and triangles.
I am leaving it at that. You see, we could use any quasiperiodic tiling to define a kaleidoscope. But being without a concrete application for these images I have more interesting things to do.