This euclidean honeycomb uses trat (for cells) in the sense of an infinite horohedron. Even honeycomb slabs, like tratap, are being used herein.

Incidence matrix according to Dynkin symbol

xoo3oxo3oox3*a &#x   (N → ∞)   → pw. heights = sqrt(2/3) = 0.816497

o..3o..3o..3*a     & | 3N ♦  6  6 |  3  3  9  9  6 | 1  6  4  4 12 | 2  7
---------------------+----+-------+----------------+---------------+-----
x.. ... ...        & |  2 | 9N  * |  1  1  1  1  0 | 1  2  1  1  1 | 2  2
oo.3oo.3oo.3*a &#x & |  2 |  * 9N |  0  0  2  2  2 | 0  2  1  1  5 | 1  4
---------------------+----+-------+----------------+---------------+-----
x..3o.. ...        & |  3 |  3  0 | 3N  *  *  *  * | 1  1  0  1  0 | 2  1
x.. ... o..3*a     & |  3 |  3  0 |  * 3N  *  *  * | 1  1  1  0  0 | 2  1
xo. ... ...    &#x & |  3 |  1  2 |  *  * 9N  *  * | 0  1  1  0  1 | 1  2
... ox. ...    &#x & |  3 |  1  2 |  *  *  * 9N  * | 0  1  0  1  1 | 1  2
ooo3ooo3ooo3*a &#x   |  3 |  0  3 |  *  *  *  * 6N | 0  0  0  0  3 | 0  3
---------------------+----+-------+----------------+---------------+-----
x..3o..3o..3*a     & ♦  N | 3N  0 |  N  N  0  0  0 | 3  *  *  *  * | 2  0
xo.3ox. ...    &#x & ♦  6 |  6  6 |  1  1  3  3  0 | * 3N  *  *  * | 1  1
xo. ... oo.3*a &#x & ♦  4 |  3  3 |  0  1  3  0  0 | *  * 3N  *  * | 1  1
... ox.3oo.    &#x & ♦  4 |  3  3 |  1  0  0  3  0 | *  *  * 3N  * | 1  1
xoo ... ...    &#x & ♦  4 |  1  5 |  0  0  1  1  2 | *  *  *  * 9N | 0  2
---------------------+----+-------+----------------+---------------+-----
xo.3ox.3oo.3*a &#x & ♦ 2N | 6N 3N | 2N 2N 3N 3N  0 | 2  N  N  N  0 | 3  *
xoo3oxo ...    &#x & ♦  7 |  6 12 |  1  1  6  6  6 | 0  1  1  1  6 | * 3N