This honeycomb as a total can not be made uniform: The mere alternated faceting (here starting at grothaph) e.g. would use edges of 3 different sizes: |sefa(s3s)| = x(6,2) = h = sqrt(3) = 1.732051, |s2s| = x(4,2) = q = sqrt(2) = 1.414214 and |sefa(s6s)| = x(12,2) = t = sqrt[2+sqrt(3)] = 1.931852 (refering to elements of s∞o2s3s6s here).

Incidence matrix according to Dynkin symbol

s∞o2s3s6s   (N → ∞)

demi( . . . . . ) | 6N |  2  2  2  1  2  2 |  1 1   6   6   6 |  2  2 2  5
------------------+----+-------------------+------------------+-----------
      s 2 s . .   |  2 | 6N  *  *  *  *  * |  0 0   2   2   0 |  1  1 0  2  q
      s 2 . s .   |  2 |  * 6N  *  *  *  * |  0 0   2   0   2 |  1  0 1  2  q
      s 2 . . s   |  2 |  *  * 6N  *  *  * |  0 0   0   2   2 |  0  1 1  2  q
        . s 2 s   |  2 |  *  *  * 3N  *  * |  0 0   0   4   0 |  0  2 0  2  q
sefa( . . s3s . ) |  2 |  *  *  *  * 6N  * |  1 0   2   0   0 |  2  0 0  1  h
sefa( . . . s6s ) |  2 |  *  *  *  *  * 6N |  0 1   0   0   2 |  0  0 2  1  t
------------------+----+-------------------+------------------+-----------
      . . s3s .   |  3 |  0  0  0  0  3  0 | 2N *   *   *   * |  2  0 0  0  h3o
      . . . s6s   |  6 |  0  0  0  0  0  6 |  * N   *   *   * |  0  0 2  0  t6o
sefa( s 2 s3s . ) |  3 |  1  1  0  0  1  0 |  * * 12N   *   * |  1  0 0  1  oh&#q
sefa( s 2 s 2 s ) |  3 |  1  0  1  1  0  0 |  * *   * 12N   * |  0  1 0  1  q3o
sefa( s 2 . s6s ) |  3 |  0  1  1  0  0  1 |  * *   *   * 12N |  0  0 1  1  ot&#q
------------------+----+-------------------+------------------+-----------
      s 2 s3s .   |  6 |  3  3  0  0  6  0 |  2 0   6   0   0 | 2N  * *  *  ho3oh&#q oct variant
      s 2 s 2 s   |  4 |  2  0  2  2  0  0 |  0 0   0   4   0 |  * 3N *  *  q-tet
      s 2 . s6s   | 12 |  0  6  6  0  0 12 |  0 2   0   0  12 |  *  * N  *  to6ot&#q hap variant
sefa( s∞o2s3s6s ) |  5 |  2  2  2  1  1  1 |  0 0   2   2   2 |  *  * * 6N  tridpy variant

starting figure: x∞o x3x6x