A possible minimal aperiodic set of corner Wang Tile

Question

From one of my previous question Aperiodic set of corner Wang Tile (although it is put on hold), I realize there is a systematic way to construct aperiodic corner type of Wang tile from edge type aperiodic Wang Tiles. But what I am more interested in is this:

For edge type of Wang tile, there is common knowledge of a very small set of Wang tile with 13 elements: http://www.sciencedirect.com/science/article/pii/S0012365X96001185 (doi: 10.1016/S0012-365X(96)00118-5 or with 14 elements: http://www.sciencedirect.com/science/article/pii/0012365X9500120L (doi: 10.1016/0012-365X(95)00120-L

It seems there is a competition on this arena of achieving smaller set of aperiodic edge type of Wang tiles. On the other hand, I interested on a documented small set of corner Wang tiles. Do someone know some reference on this? Thank you:)

Answer 1

You could look at the corner types that actually arise in the aperiodic edge-tilings you mention and thereby find small collections of corner-tiles with analogous aperiodic tilings, using the method in my answer to your previous question, which converts edge-tilings to corner-tilings and vice versa. That is, which combinations of corners arise in the aperiodic tilings in the small edge-tile sets that are known? The answer would tell you which kinds of tiles are needed in the translation and thereby provide a upper bound for an answer to your current question.