Acronym	ditatha
Name	ditrigonary trigonal hemiapeirogonal tesselation, alternate triangular tiling
	©
Vertex figure	[(3,∞)3]/2 = [(3/2,∞)3]
Colonel of regiment	trat
External links

This looks like a trat, where every second triangle is missing.

Incidence matrix according to Dynkin symbol

x3o3/2o∞*a   (N,M → ∞)

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

x3o3o∞'*a   (N,M → ∞)

. . .     | NM |   6 |  3  3
----------+----+-----+------
x . .     |  2 | 3NM |  1  1
----------+----+-----+------
x3o .     |  3 |   3 | NM  *
x . o∞'*a ♦  M |   M |  * 3N

x3/2o3/2o∞'*a   (N,M → ∞)

.   .   .     | NM |   6 |  3  3
--------------+----+-----+------
x   .   .     |  2 | 3NM |  1  1
--------------+----+-----+------
x3/2o   .     |  3 |   3 | NM  *
x   .   o∞'*a ♦  M |   M |  * 3N