The mere alternated faceting (here starting at thaph) e.g. would use edges of 3 different sizes: |s2s| = x(4,2) = sqrt(2) = 1.414214 resp. |sefa(s6x)| = x(12,3) = 1+sqrt(3) = 2.732051, besides the remaining unit edges (refering to elements of s∞o2o3x6s here).

Even so this snub can be made all unit edged. However then it neither would become uniform nor scaliform, because pairs of the former trapezia would become adjoining coplanar squares, that is the triangular trapezobiprisms then would become triangular biprisms, which have an internal dihedral angle of 180°. In fact, this rescaled structure then happens to be quite similar to thiph in its 2-coloring of the triangles of the underlying that: on the hexagons there are stacks of monostratic hexagonal prisms (hip), on the red triangles there are stacks of bistratic triangular biprisms, based on all the even layers, and on the blue triangles there are also stacks of bistratic triangular biprisms, based on all the odd layers.

Incidence matrix according to Dynkin symbol

s∞o2o3x6s   (N → ∞)

demi( . . . . . ) | 3N |  2  2  2 | 1 2  4 | 4 3
------------------+----+----------+--------+----
demi( . . . x . ) |  2 | 3N  *  * | 1 1  2 | 2 2  x
      s 2 . . s   |  2 |  * 3N  * | 0 0  4 | 2 2  q
sefa( . . . x6s ) |  2 |  *  * 3N | 0 1  2 | 2 1  e=x+h
------------------+----+----------+--------+----
demi( . . o3x . ) |  3 |  3  0  0 | N *  * | 0 2  x3o
      . . . x6s   |  6 |  3  0  3 | * N  * | 2 0  x3e
sefa( s 2 . x6s ) |  4 |  1  2  1 | * * 6N | 1 1  xe&#q
------------------+----+----------+--------+----
      s 2 . x6s   | 12 |  6  6  6 | 0 2  6 | N *  xe3ex&#q ditra
sefa( s∞o2o3x6s ) |  9 |  6  6  3 | 2 0  6 | * N  xex3ooo&#qt triangular biprism variant

starting figure: x∞o o3x6x