In 2025 B. Klein came up with this non-convex regular-faced bistratic lace tower, thereby pointing out that ebots can be used for facets in a non-trivial way too.

Incidence matrix according to Dynkin symbol

reduced( xux3xoo3xo(-x)&#xt, by 2thah )   → both heights = 0

         o..3o..3o.  .        | 24 * * |  1  1  1  1  0  0 | 1 1 1  1  1  1  0 0 0 | 1 1 1 1 0
         .o.3.o.3.o  .        |  * 4 * |  0  0  0  6  3  0 | 0 0 0  6  3  3  3 0 0 | 0 3 3 1 1
reduced( ..o3..o3..  o      ) |  * * 6 |  0  0  0  0  2  4 | 0 0 0  4  0  0  4 2 2 | 0 2 4 0 2
------------------------------+--------+-------------------+-----------------------+----------
         x.. ... ..  .        |  2 0 0 | 12  *  *  *  *  * | 1 1 0  1  0  0  0 0 0 | 1 1 1 0 0
         ... x.. ..  .        |  2 0 0 |  * 12  *  *  *  * | 1 0 1  0  1  0  0 0 0 | 1 1 0 1 0
         ... ... x.  .        |  2 0 0 |  *  * 12  *  *  * | 0 1 1  0  0  1  0 0 0 | 1 0 1 1 0
         oo.3oo.3oo  . &#x    |  1 1 0 |  *  *  * 24  *  * | 0 0 0  1  1  1  0 0 0 | 0 1 1 1 0
         .oo3.oo3.o  o &#x    |  0 1 1 |  *  *  *  * 12  * | 0 0 0  2  0  0  2 0 0 | 0 1 2 0 1
reduced( ..x ... ..  .    & ) |  0 0 2 |  *  *  *  *  * 12 | 0 0 0  1  0  0  1 1 1 | 0 1 2 0 1
------------------------------+--------+-------------------+-----------------------+----------
         x..3x.. ..  .        |  6 0 0 |  3  3  0  0  0  0 | 4 * *  *  *  *  * * * | 1 1 0 0 0
         x.. ... x.  .        |  4 0 0 |  2  0  2  0  0  0 | * 6 *  *  *  *  * * * | 1 0 1 0 0
         ... x..3x.  .        |  6 0 0 |  0  3  3  0  0  0 | * * 4  *  *  *  * * * | 1 0 0 1 0  (*)
         xux ... ..  . &#xt   |  2 2 2 |  1  0  0  2  2  1 | * * * 12  *  *  * * * | 0 1 1 0 0
         ... xo. ..  . &#x    |  2 1 0 |  0  1  0  2  0  0 | * * *  * 12  *  * * * | 0 1 0 1 0  (*)
         ... ... xo  . &#x    |  2 1 0 |  0  0  1  2  0  0 | * * *  *  * 12  * * * | 0 0 1 1 0  (*)
         ... ... .o(-x)&#x    |  0 1 2 |  0  0  0  0  2  1 | * * *  *  *  * 12 * * | 0 0 1 0 1
reduced( ..x3..o ..  .    & ) |  0 0 3 |  0  0  0  0  0  3 | * * *  *  *  *  * 4 * | 0 1 0 0 1
reduced( ..x ... ..(-x)     ) |  0 0 4 |  0  0  0  0  0  4 | * * *  *  *  *  * * 3 | 0 0 2 0 0
------------------------------+--------+-------------------+-----------------------+----------
         x..3x..3x.  .        | 24 0 0 | 12 12 12  0  0  0 | 4 6 4  0  0  0  0 0 0 | 1 * * * *  toe
         xux3xoo ..  . &#xt   |  6 3 3 |  3  3  0  6  3  3 | 1 0 0  3  3  0  0 1 0 | * 4 * * *  tut
         xux ... xo(-x)&#xt   |  4 2 4 |  2  0  2  4  4  4 | 0 1 0  2  0  2  2 0 1 | * * 6 * *  ebot
         ... xo.3xo  . &#x    |  6 1 0 |  0  3  3  6  0  0 | 0 0 1  0  3  3  0 0 0 | * * * 4 *  hippy (degenerate in turn)
         ... .oo3.o(-x)&#x    |  0 1 3 |  0  0  0  0  3  3 | 0 0 0  0  0  0  3 1 0 | * * * * 4  tet

(*) all are coplanar