From one of my previous question [Aperiodic set of corner Wang Tile](https://mathoverflow.net/questions/179079/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](https://doi.org/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](https://doi.org/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:)



A possible minimal aperiodic set of corner Wang Tile
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](https://mathoverflow.net/a/164405/1946), 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.


