The mere alternated faceting (here starting at tassiph) e.g. would use edges of 3 different sizes: |s2s| = x(4,2) = q = sqrt(2) = 1.414214 resp. |sefa(s4x)| = x(8,3) = w = 1+sqrt(2) = 2.414214, besides the remaining unit edges (refering to elements of s∞o2x4s4x 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 square trapezobiprisms then would become square biprisms, which have an internal dihedral angle of 180°. In fact, this rescaled structure then happens to be quite similar to chon in its 3-coloring of the underlying squat: on the red squares there are stacks of monostratic square prisms (cube), on the yellow ones there are stacks of bistratic square biprisms, based on all the even layers, and on the blue ones there are also stacks of bistratic square biprisms, based on all the odd layers.

Incidence matrix according to Dynkin symbol

s∞o2s4x4o   (N → ∞)

demi( . . . . . ) | 4N |  2  2  2 | 1  2  8 |  4 3
------------------+----+----------+---------+-----
demi( . . . x . ) |  2 | 4N  *  * | 1  1  2 |  2 2  x
      s 2 s . .   |  2 |  * 4N  * | 0  0  4 |  2 2  q
sefa( . . s4x . ) |  2 |  *  * 4N | 0  1  2 |  2 1  w
------------------+----+----------+---------+-----
demi( . . . x4o ) |  4 |  4  0  0 | N  *  * |  0 2  x4o
      . . s4x .   |  4 |  2  0  2 | * 2N  * |  2 0  x2w
sefa( s 2 s4x . ) |  4 |  1  2  1 | *  * 8N |  1 1  xw&#q
------------------+----+----------+---------+-----
      s 2 s4x .   |  8 |  4  4  4 | 0  2  4 | 2N *  xw2wx&#q recta
sefa( s∞o2s4x4o ) | 12 |  8  8  4 | 2  0  8 |  * N  xwx4ooo&#qt square trapezobiprisms

starting figure: x∞o x4x4o

s∞o2x4s4x   (N → ∞)

demi( . . . . . ) | 4N |  1  1  2  1  1 | 1 1 1  4  4 | 2 2 3
------------------+----+----------------+-------------+------
demi( . . x . . ) |  2 | 2N  *  *  *  * | 1 1 0  2  0 | 2 0 2  x
demi( . . . . x ) |  2 |  * 2N  *  *  * | 1 0 1  0  2 | 0 2 2  x
      s 2 . s .   |  2 |  *  * 4N  *  * | 0 0 0  2  2 | 1 1 2  q
sefa( . . x4s . ) |  2 |  *  *  * 2N  * | 0 1 0  2  0 | 2 0 1  w
sefa( . . . s4x ) |  2 |  *  *  *  * 2N | 0 0 1  0  2 | 0 2 1  w
------------------+----+----------------+-------------+------
demi( . . x . x ) |  4 |  2  2  0  0  0 | N * *  *  * | 0 0 2  x4o
      . . x4s .   |  4 |  2  0  0  2  0 | * N *  *  * | 2 0 0  x2w
      . . . s4x   |  4 |  0  2  0  0  2 | * * N  *  * | 0 2 0  x2w
sefa( s 2 x4s . ) |  4 |  1  0  2  1  0 | * * * 4N  * | 1 0 1  xw&#q
sefa( s 2 . s4x ) |  4 |  0  1  2  0  1 | * * *  * 4N | 0 1 1  xw&#q
------------------+----+----------------+-------------+------
      s 2 x4s .   |  8 |  4  0  4  4  0 | 0 2 0  4  0 | N * *  xw2wx&#q recta
      s 2 . s4x   |  8 |  0  4  4  0  4 | 0 0 2  0  4 | * N *  xw2wx&#q recta
sefa( s∞o2x4s4x ) | 12 |  4  4  8  2  2 | 2 0 0  4  4 | * * N  xwx4ooo&#qt square trapezobiprisms

starting figure: x∞o x4x4x