Acronym gyerich
Name parallelly that elongated gyrich
Confer
related CRF honeycombs:
erich   gyrich   6Q3-2S3-ortho   3Q3-S3-2P6-2P3-ortho  

This CRF honeycomb is the elongated form of gyrich or likewise the gyrated form of erich.

Each etobcu could be dissected into pairs of tricu and an equatorial hip. Then this honeycomb would become 3Q3-S3-2P6-2P3-ortho.

As a not rescaled mere alternated faceting (here starting at srothaph) it would use edges of 3 different sizes: |s2s| = x(4,2) = sqrt(2) = q = 1.414214 resp. |sefa(o6s)| = x(6,2) = h = sqrt(3) = 1.732051, besides the remaining unit edges (refering to elements of s∞x2x3o6s here).


Incidence matrix according to Dynkin symbol

s∞x2x3o6s   (N → ∞)

demi( . . . . . ) | 6N |  1  2  2  2 |  2  1  2  1  3  2 | 1 1 1 3
------------------+----+-------------+-------------------+--------
demi( . x . . . ) |  2 | 3N  *  *  * |  2  0  0  0  0  2 | 1 0 1 2  x
demi( . . x . . ) |  2 |  * 6N  *  * |  1  1  1  0  0  0 | 1 0 0 2  x
      s 2 . . s   |  2 |  *  * 6N  * |  0  0  1  0  2  0 | 0 1 0 2  q
sefa( . . . o6s ) |  2 |  *  *  * 6N |  0  0  0  1  1  1 | 0 1 1 1  h
------------------+----+-------------+-------------------+--------
demi( . x x . . ) |  4 |  2  2  0  0 | 3N  *  *  *  *  * | 1 0 0 1  x4o
demi( . . x3o . ) |  3 |  0  3  0  0 |  * 2N  *  *  *  * | 1 0 0 1  x3o
      s 2 x 2 s   |  4 |  0  2  2  0 |  *  * 3N  *  *  * | 0 0 0 2  x2q
      . . . o6s   |  3 |  0  0  0  3 |  *  *  * 2N  *  * | 0 1 1 0  h3o
sefa( s 2 . o6s ) |  3 |  0  0  2  1 |  *  *  *  * 6N  * | 0 1 0 1  oh&#q
sefa( . x 2 o6s ) |  4 |  2  0  0  2 |  *  *  *  *  * 3N | 0 0 1 1  x2h
------------------+----+-------------+-------------------+--------
demi( . x x3o . )   6 |  3  6  0  0 |  3  2  0  0  0  0 | N * * *  x-trip
      s 2 . o6s     6 |  0  0  6  6 |  0  0  0  2  6  0 | * N * *  ho3oh&#q oct variant
      . x 2 o6s     6 |  3  0  0  6 |  0  0  0  2  0  3 | * * N *  x h3o trip variant
sefa( s∞x2x3o6s )  18 |  6 12 12  6 |  3  2  6  0  6  3 | * * * N  xxxx3ohho&#qt etobcu variant

starting figure: x∞x x3o6s

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