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

Incidence matrix according to Dynkin symbol

xxo3xox3oxx3*a &#x   (N → ∞)   → pw. heights = sqrt(2/3) = 0.816497

o..3o..3o..3*a     & | 9N |  2  2   4 |  2  1  1  4  3  3  2 | 1  3  3  2  5 | 2  4
---------------------+----+-----------+----------------------+---------------+-----
x.. ... ...        & |  2 | 9N  *   * |  1  1  0  1  0  1  0 | 1  1  2  1  1 | 2  2
... x.. ...        & |  2 |  * 9N   * |  1  0  1  1  1  0  0 | 1  2  1  1  1 | 2  2
oo.3oo.3oo.3*a &#x & |  2 |  *  * 18N |  0  0  0  1  1  1  1 | 0  1  1  1  3 | 1  3
---------------------+----+-----------+----------------------+---------------+-----
x..3x.. ...        & |  6 |  3  3   0 | 3N  *  *  *  *  *  * | 1  1  1  0  0 | 2  1
x.. ... o..3*a     & |  3 |  3  0   0 |  * 3N  *  *  *  *  * | 1  0  1  1  0 | 2  1
... x..3o..        & |  3 |  0  3   0 |  *  * 3N  *  *  *  * | 1  1  0  1  0 | 2  1
xx. ... ...    &#x & |  4 |  1  1   2 |  *  *  * 9N  *  *  * | 0  1  1  0  1 | 1  2
... xo. ...    &#x & |  3 |  0  1   2 |  *  *  *  * 9N  *  * | 0  1  0  1  1 | 1  2
... ... ox.    &#x & |  3 |  1  0   2 |  *  *  *  *  * 9N  * | 0  0  1  1  1 | 1  2
ooo3ooo3ooo3*a &#x   |  3 |  0  0   3 |  *  *  *  *  *  * 6N | 0  0  0  0  3 | 0  3
---------------------+----+-----------+----------------------+---------------+-----
x..3x..3o..3*a     & ♦ 3N | 3N 3N   0 |  N  N  N  0  0  0  0 | 3  *  *  *  * | 2  0
xx.3xo. ...    &#x & ♦  9 |  3  6   6 |  1  0  1  3  3  0  0 | * 3N  *  *  * | 1  1
xx. ... ox.3*a &#x & ♦  9 |  6  3   6 |  1  1  0  3  0  3  0 | *  * 3N  *  * | 1  1
... xo.3ox.    &#x & ♦  6 |  3  3   6 |  0  1  1  0  3  3  0 | *  *  * 3N  * | 1  1
xxo ... ...    &#x & ♦  5 |  1  1   6 |  0  0  0  1  1  1  2 | *  *  *  * 9N | 0  2
---------------------+----+-----------+----------------------+---------------+-----
xx.3xo.3ox.3*a &#x & ♦ 6N | 6N 6N  6N | 2N 2N 2N 3N 3N 3N  0 | 2  N  N  N  0 | 3  *
xxo3xox ...    &#x & ♦ 12 |  6  6  18 |  1  1  1  6  6  6  6 | 0  1  1  1  6 | * 3N