Acronym ..., s∞o2x3x6s
Name alternating bistratic hexat honeycomb

The mere alternated faceting (here starting at grothaph) e.g. would use edges of 3 different sizes: |s2s| = x(4,2) = q = sqrt(2) = 1.414214 resp. |sefa(s6x)| = x(12,3) = e = 1+sqrt(3) = 2.732051, besides the remaining unit edges (refering to elements of s∞o2x3x6s 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 ditriangular trapezobiprisms then would become hexagonal biprisms, which have an internal dihedral angle of 180°. In fact, this rescaled structure then happens to be quite similar to hiph in its 3-coloring of the underlying hexat: on the red hexagons there are stacks of monostratic hexagonal prisms (hip), on the yellow ones there are stacks of bistratic hexagonal biprisms, based on all the even layers, and on the blue ones there are also stacks of bistratic hexagonal biprisms, based on all the odd layers.


Incidence matrix according to Dynkin symbol

s∞o2x3x6s   (N → ∞)

demi( . . . . . ) | 6N |  1  1  2  1 | 1  2 1  4 | 2 3
------------------+----+-------------+-----------+----
demi( . . x . . ) |  2 | 3N  *  *  * | 1  2 0  0 | 0 3  x
demi( . . . x . ) |  2 |  * 3N  *  * | 1  0 1  2 | 2 2  x
      s 2 . . s   |  2 |  *  * 6N  * | 0  1 0  2 | 1 2  q
sefa( . . . x6s ) |  2 |  *  *  * 3N | 0  0 1  2 | 2 1  e=x+h
------------------+----+-------------+-----------+----
demi( . . x3x . ) |  6 |  3  3  0  0 | N  * *  * | 0 2  x3x
      s 2 x 2 s   |  4 |  2  0  2  0 | * 3N *  * | 0 2  x2q
      . . . x6s   |  6 |  0  3  0  3 | *  * N  * | 2 0  x3e
sefa( s 2 . x6s ) |  4 |  0  1  2  1 | *  * * 6N | 1 1  xe&#q
------------------+----+-------------+-----------+----
      s 2 . x6s   | 12 |  0  6  6  6 | 0  0 2  6 | N *  xe3ex&#q ditra
sefa( s∞o2x3x6s ) | 18 |  9  6 12  3 | 2  6 0  6 | * N  xxx3xex&#qt ditriangular trapezobiprism

starting figure: x∞o x3x6x

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