Acronym ...
Name hyperbolic order 3 trigonal-horocyclic tiling
 
Circumradius sqrt(-3)/4 = 0.433013 i
Vertex figure [(3,∞)3]

Incidence matrix according to Dynkin symbol

x3o3o∞*a   (N,M → ∞)

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

o3o∞s   (N,M → ∞)

demi( . . . ) | NM |   6 |  3  3
--------------+----+-----+------
sefa( . o∞s ) |  2 | 3NM |  1  1
--------------+----+-----+------
      . o∞s   |  M |   M | 3N  *
sefa( o3o∞s ) |  3 |   3 |  * NM

starting figure: o3oinfinx

s∞s∞s∞*a   (N,M → ∞)

demi( . . .    ) | NM |  2  2  2 | 1 1 1  3
-----------------+----+----------+---------
sefa( s∞s .    ) |  2 | NM  *  * | 1 0 0  1
sefa( s . s∞*a ) |  2 |  * NM  * | 0 1 0  1
sefa( . s∞s    ) |  2 |  *  * NM | 0 0 1  1
-----------------+----+----------+---------
      s∞s .      |  M |  M  0  0 | N * *  *
      s . s∞*a   |  M |  0  M  0 | * N *  *
      . s∞s      |  M |  0  0  M | * * N  *
sefa( s∞s∞s∞*a ) |  3 |  1  1  1 | * * * NM

starting figure: x∞x∞x∞*a

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