Acronym ...
Name 2that+∞{3} (?)
Vertex figure 2[3,3/2,3,6,3,6]
Confer
non-Grünbaumian master:
that  
Grünbaumian relatives:
2that  

Looks like 2 incident triangular-hexagonal tilings (that) together with additional coincident triangle pairs, and indeed, vertices and {6} coincide by pairs, edges coincide by 3, and each {3/2} coincides with 3 {3}.


Incidence matrix according to Dynkin symbol

β6β3o   (N → ∞)

both( . . .    ) | 6N |  2  2  2 | 1 1  1  3
-----------------+----+----------+----------
sefa( s6s . (r)) |  2 | 6N  *  * | 1 0  0  1
sefa( s6s . (l)) |  2 |  * 6N  * | 0 1  0  1
sefa( . 3o    ) |  2 |  *  * 6N | 0 0  1  1
-----------------+----+----------+----------
      s6s . (r)    6 |  6  0  0 | N *  *  *
      s6s . (l)    6 |  0  6  0 | * N  *  *
      . 3o        3 |  0  0  3 | * * 2N  *
sefa( 63o    ) |  3 |  1  1  1 | * *  * 6N

starting figure: x6x3o

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