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( xux3xoo5/2xo(-x)&#xt, by 2peppy )   → both heights = 1/2

reduced( o..3o..5/2o.  .         | 60  *  * |  2  2  1  0  0  0 |  2  2  2  2  0  0  0  0 | 1  2  2  0 0
         .o.3.o.5/2.o  .         |  * 12  * |  0  0  5  5  0  0 |  0  0 10  5  5  0  0  0 | 0  5  5  1 0
         ..o3..o5/2..  o         |  *  * 60 |  0  0  0  1  2  2 |  0  0  2  0  2  1  2  1 | 0  1  2  1 1
---------------------------------+----------+-------------------+-------------------------+-------------
         x.. ...   ..  .         |  2  0  0 | 60  *  *  *  *  * |  1  1  1  0  0  0  0  0 | 1  1  1  0 0
reduced( ... x..   ..  .     & ) |  2  0  0 |  * 60  *  *  *  * |  1  1  0  1  0  0  0  0 | 1  1  1  0 0
reduced( oo.3oo.5/2oo  . &#x   ) |  1  1  0 |  *  * 60  *  *  * |  0  0  2  2  0  0  0  0 | 0  2  2  0 0
         .oo3.oo5/2.o  o &#x     |  0  1  1 |  *  *  * 60  *  * |  0  0  2  0  2  0  0  0 | 0  1  2  1 0
         ..x ...   ..  .         |  0  0  2 |  *  *  *  * 60  * |  0  0  1  0  0  1  1  0 | 0  1  1  0 1
         ... ...   ..(-x)        |  0  0  2 |  *  *  *  *  * 60 |  0  0  0  0  1  0  1  1 | 0  0  1  1 1
---------------------------------+----------+-------------------+-------------------------+-------------
         x..3x..   ..  .         |  6  0  0 |  3  3  0  0  0  0 | 20  *  *  *  *  *  *  * | 1  1  0  0 0
         x.. ...   x.  .         |  4  0  0 |  2  2  0  0  0  0 |  * 30  *  *  *  *  *  * | 1  0  1  0 0
         xux ...   ..  . &#xt    |  2  2  2 |  1  0  2  2  1  0 |  *  * 60  *  *  *  *  * | 0  1  1  0 0
reduced( ... xo.   ..  . &#x & ) |  2  1  0 |  0  1  2  0  0  0 |  *  *  * 60  *  *  *  * | 0  1  1  0 0
         ... ...   .o(-x)&#x     |  0  1  2 |  0  0  0  2  0  1 |  *  *  *  * 60  *  *  * | 0  0  1  1 0
         ..x3..o   ..  .         |  0  0  3 |  0  0  0  0  3  0 |  *  *  *  *  * 20  *  * | 0  1  0  0 1
         ..x ...   ..(-x)        |  0  0  4 |  0  0  0  0  2  2 |  *  *  *  *  *  * 30  * | 0  0  1  0 1
         ... ..o5/2..(-x)        |  0  0  5 |  0  0  0  0  0  5 |  *  *  *  *  *  *  * 12 | 0  0  0  1 1  {5/2}
---------------------------------+----------+-------------------+-------------------------+-------------
reduced( x..3x..5/2x.  .       ) | 60  0  0 | 60 60  0  0  0  0 | 20 30  0  0  0  0  0  0 | 1  *  *  * *  ri
         xux3xoo   ..  . &#xt    |  6  3  3 |  3  3  6  3  3  0 |  1  0  3  3  0  1  0  0 | * 20  *  * *  tut
         xux ...   xo(-x)&#xt    |  4  2  4 |  2  2  4  4  2  2 |  0  1  2  2  2  0  1  0 | *  * 30  * *  ebot
         ... .oo5/2.o(-x)&#x     |  0  1  5 |  0  0  0  5  0  5 |  0  0  0  0  5  0  0  1 | *  *  * 12 *  stappy
         ..x3..o5/2..(-x)        |  0  0 60 |  0  0  0  0 60 60 |  0  0  0  0  0 20 30 12 | *  *  *  * 1  qrid