The non-regular hexagons {(h,H,H)²} are diagonally elongated squares. Its vertex angles are h = 90° resp. H = 135°.

Incidence matrix according to Dynkin symbol

((oqQ3xxx3wxx4xux))&#zxt   → heights = 0, Q=2q = 2.828427
(tegum sum of (x,w,x)-grit, (q,x,x,u)-gidpith, and (Q,x,x,x)-gidpith)

  o..3o..3o..4o..        | 192   *   * |   2  1   2   0   0   0   0   0   0 |  1  2  1   2   2  0   0   0  0  0  0 |  1  1  1  2  0 0
  .o.3.o.3.o.4.o.        |   * 384   * |   0  0   1   1   1   1   0   0   0 |  0  0  1   1   1  1   1   1  0  0  0 |  0  1  1  1  1 0
  ..o3..o3..o4..o        |   *   * 384 |   0  0   0   0   0   1   1   1   1 |  0  0  0   0   1  0   1   1  1  1  1 |  0  0  1  1  1 1
-------------------------+-------------+------------------------------------+--------------------------------------+-----------------
  ... x.. ... ...        |   2   0   0 | 192  *   *   *   *   *   *   *   * |  1  1  0   1   0  0   0   0  0  0  0 |  1  1  0  1  0 0
  ... ... ... x..        |   2   0   0 |   * 96   *   *   *   *   *   *   * |  0  2  0   0   2  0   0   0  0  0  0 |  1  0  1  2  0 0
  oo.3oo.3oo.4oo.  &#x   |   1   1   0 |   *  * 384   *   *   *   *   *   * |  0  0  1   1   1  0   0   0  0  0  0 |  0  1  1  1  0 0
  ... .x. ... ...        |   0   2   0 |   *  *   * 192   *   *   *   *   * |  0  0  0   1   0  1   1   0  0  0  0 |  0  1  0  1  1 0
  ... ... .x. ...        |   0   2   0 |   *  *   *   * 192   *   *   *   * |  0  0  1   0   0  1   0   1  0  0  0 |  0  1  1  0  1 0
  .oo3.oo3.oo4.oo  &#x   |   0   1   1 |   *  *   *   *   * 384   *   *   * |  0  0  0   0   1  0   1   1  0  0  0 |  0  0  1  1  1 0
  ... ..x ... ...        |   0   0   2 |   *  *   *   *   *   * 192   *   * |  0  0  0   0   0  0   1   0  1  1  0 |  0  0  0  1  1 1
  ... ... ..x ...        |   0   0   2 |   *  *   *   *   *   *   * 192   * |  0  0  0   0   0  0   0   1  1  0  1 |  0  0  1  0  1 1
  ... ... ... ..x        |   0   0   2 |   *  *   *   *   *   *   *   * 192 |  0  0  0   0   1  0   0   0  0  1  1 |  0  0  1  1  0 1
-------------------------+-------------+------------------------------------+--------------------------------------+-----------------
  o..3x.. ... ...        |   3   0   0 |   3  0   0   0   0   0   0   0   0 | 64  *  *   *   *  *   *   *  *  *  * |  1  1  0  0  0 0
  ... x.. ... x..        |   4   0   0 |   2  2   0   0   0   0   0   0   0 |  * 96  *   *   *  *   *   *  *  *  * |  1  0  0  1  0 0
((oq. ... wx. ...))&#zx  |   2   4   0 |   0  0   4   0   2   0   0   0   0 |  *  * 96   *   *  *   *   *  *  *  * |  0  1  1  0  0 0  {(h,H,H)2}
  ... xx. ... ...  &#x   |   2   2   0 |   1  0   2   1   0   0   0   0   0 |  *  *  * 192   *  *   *   *  *  *  * |  0  1  0  1  0 0
  ... ... ... xux  &#xt  |   2   2   2 |   0  1   2   0   0   2   0   0   1 |  *  *  *   * 192  *   *   *  *  *  * |  0  0  1  1  0 0
  ... .x.3.x. ...        |   0   6   0 |   0  0   0   3   3   0   0   0   0 |  *  *  *   *   * 64   *   *  *  *  * |  0  1  0  0  1 0
  ... .xx ... ...  &#x   |   0   2   2 |   0  0   0   1   0   2   1   0   0 |  *  *  *   *   *  * 192   *  *  *  * |  0  0  0  1  1 0
  ... ... .xx ...  &#x   |   0   2   2 |   0  0   0   0   1   2   0   1   0 |  *  *  *   *   *  *   * 192  *  *  * |  0  0  1  0  1 0
  ... ..x3..x ...        |   0   0   6 |   0  0   0   0   0   0   3   3   0 |  *  *  *   *   *  *   *   * 64  *  * |  0  0  0  0  1 1
  ... ..x ... ..x        |   0   0   4 |   0  0   0   0   0   0   2   0   2 |  *  *  *   *   *  *   *   *  * 96  * |  0  0  0  1  0 1
  ... ... ..x4..x        |   0   0   8 |   0  0   0   0   0   0   0   4   4 |  *  *  *   *   *  *   *   *  *  * 48 |  0  0  1  0  0 1
-------------------------+-------------+------------------------------------+--------------------------------------+-----------------
  o..3x.. ... x..        ♦   6   0   0 |   6  3   0   0   0   0   0   0   0 |  2  3  0   0   0  0   0   0  0  0  0 | 32  *  *  *  * *
((oq.3xx.3wx. ...))&#zx  ♦  12  24   0 |  12  0  24  12  12   0   0   0   0 |  4  0  6  12   0  4   0   0  0  0  0 |  * 16  *  *  * *
((oqQ ... wxx4xux))&#zxt ♦   8  16  16 |   0  4  16   0   8  16   0   8   8 |  0  0  4   0   8  0   0   8  0  0  2 |  *  * 24  *  * *
  ... xxx ... xux  &#xt  ♦   4   4   4 |   2  2   4   2   0   4   2   0   2 |  0  1  0   2   2  0   2   0  0  1  0 |  *  *  * 96  * *
  ... .xx3.xx ...  &#x   ♦   0   6   6 |   0  0   0   3   3   6   3   3   0 |  0  0  0   0   0  1   3   3  1  0  0 |  *  *  *  * 64 *
  ... ..x3..x4..x        ♦   0   0  48 |   0  0   0   0   0   0  24  24  24 |  0  0  0   0   0  0   0   0  8 12  6 |  *  *  *  *  * 8