Acronym trat
Name triangular tiling,
Delone complex of hexagonal lattice

 x3o6o x3o3o3*a `©`
Vertex figure [36]
Dual hexat
External

Incidence matrix according to Dynkin symbol

```x3o6o   (N→∞)

. . . | N |  6 |  6
------+---+----+---
x . . | 2 | 3N |  2
------+---+----+---
x3o . | 3 |  3 | 2N
```

```x3o3o3*a    (N→∞)

. . .    | N |  6 | 3 3
---------+---+----+----
x . .    | 2 | 3N | 1 1
---------+---+----+----
x3o .    | 3 |  3 | N *
x . o3*a | 3 |  3 | * N
```

```s6o3o    (N→∞)

demi( . . . ) | N |  6 | 3 3
--------------+---+----+----
sefa( s6o . ) | 2 | 3N | 1 1
--------------+---+----+----
s6o .   ♦ 3 |  3 | N *
sefa( s6o3o ) | 3 |  3 | * N
```

```s3s6o    (N→∞)

demi( . . . ) | 3N |  4  2 |  2 1  3
--------------+----+-------+--------
sefa( s3s . ) |  2 | 6N  * |  1 0  1
sefa( . s6o ) |  2 |  * 3N |  0 1  1
--------------+----+-------+--------
s3s .   ♦  3 |  3  0 | 2N *  *
. s6o   ♦  3 |  0  3 |  * N  *
sefa( s3s6o ) |  3 |  2  1 |  * * 3N
```

```s3s3s3*a   (N→∞)

demi( . . .    ) | 3N |  2  2  2 | 1 1 1  3
-----------------+----+----------+---------
sefa( s3s .    ) |  2 | 3N  *  * | 1 0 0  1
sefa( s . s3*a ) |  2 |  * 3N  * | 0 1 0  1
sefa( . s3s    ) |  2 |  *  * 3N | 0 0 1  1
-----------------+----+----------+---------
s3s .      ♦  3 |  3  0  0 | N * *  *
s . s3*a   ♦  3 |  0  3  0 | * N *  *
. s3s      ♦  3 |  0  0  3 | * * N  *
sefa( s3s3s3*a ) |  3 |  1  1  1 | * * * 3N
```