Acronym	tha
Name	trigonal hemiapeirogonal tesselation
	©
Vertex figure	[3,∞,3/2,∞]/0
Colonel of regiment	that
External links

This looks like a that, where only the triangles are present.

Incidence matrix according to Dynkin symbol

x3o3/2x∞*a   (N,M → ∞)

. .   .    | 3NM |   2   2 |  1  1  2
-----------+-----+---------+---------
x .   .    |   2 | 3NM   * |  1  0  1
. .   x    |   2 |   * 3NM |  0  1  1
-----------+-----+---------+---------
x3o   .    |   3 |   3   0 | NM  *  *
. o3/2x    |   3 |   0   3 |  * NM  *
x .   x∞*a ♦  2M |   M   M |  *  * 3N

or
. .   .      | 3NM |   4 |   2  2
-------------+-----+-----+-------
x .   .    & |   2 | 6NM |   1  1
-------------+-----+-----+-------
x3o   .    & |   3 |   3 | 2NM  *
x .   x∞*a   ♦   M |   M |   * 6N