Acronym	...
Name	2hexat (?)
Vertex figure	[66]/2
Confer	non-Grünbaumian master: hexat

Looks like a double cover of hexat, just that the vertices are identified.

Incidence matrix according to Dynkin symbol

o3o6x6/5*a   (N → ∞)

. . .      | 2N |  6 | 3 3
-----------+----+----+----
. . x      |  2 | 6N | 1 1
-----------+----+----+----
o . x6/5*a |  6 |  6 | N *
. o6x      |  6 |  6 | * N

o3/2o6x6*a   (N → ∞)

.   . .    | 2N |  6 | 3 3
-----------+----+----+----
.   . x    |  2 | 6N | 1 1
-----------+----+----+----
o   . x6*a |  6 |  6 | N *
.   o6x    |  6 |  6 | * N

o3/2o6/5x6/5*a   (N → ∞)

.   .   .      | 2N |  6 | 3 3
---------------+----+----+----
.   .   x      |  2 | 6N | 1 1
---------------+----+----+----
o   .   x6/5*a |  6 |  6 | N *
.   o6/5x      |  6 |  6 | * N