This hexagon-with-dents is a tile which, I think, tiles the plane in a necessarily aperiodic way:

     ________  __ 
    /        \/  \__
   _\              /
  /                \
 /                  \
/                    \
\                    /
 \                  _\
  \                /
  /_              /
    \_/\_________/

Is is essentially the Socolar–Taylor tile. I'm rather surprised that this tile does not appear in the paper of Socolar and Taylor, and that it also doesn't appear in Wikipedia's list of aperiodic sets of tiles.

Did I miss something?
Am I maybe wrong to claim that this tile tiles the plane in a necessarily aperiodic way?

Question: Does the above tile tile the plane in a necessarily aperiodic way?

This hexagon-with-dents is a tile which, I think, tiles the plane in a necessarily aperiodic way:

     ________  __ 
    /        \/  \__
   _\              /
  /                \
 /                  \
/                    \
\                    /
 \                  _\
  \                /
  /_              /
    \_/\_________/

This is essentially the Socolar–Taylor tile. I'm rather surprised that this tile does not appear in the paper of Socolar and Taylor, and that it also doesn't appear in Wikipedia's list of aperiodic sets of tiles.

Did I miss something?
Am I maybe wrong to claim that this tile tiles the plane in a necessarily aperiodic way?

Question: Does the above tile tile the plane in a necessarily aperiodic way?