Acronym	tratap
Name	triangular tiling antiprism
	©
Vertex figure	©
Confer	related tesselations: octet   gytoh
External links

This euclidean honeycomb uses trat (for cells) in the sense of an infinite horohedron.

The infinite stack of this slab, then blending out those horohedra, would either result in octet or in gytoh.

Incidence matrix according to Dynkin symbol

s2s6o3o   (N → ∞)

demi( . . . . ) | 2N ♦  3  6 |  3  9  3 | 3 1  4
----------------+----+-------+----------+-------
      s2s . .   |  2 | 3N  * |  0  4  0 | 2 0  2
sefa( . s6o . ) |  2 |  * 6N |  1  1  1 | 1 1  1
----------------+----+-------+----------+-------
      . s6o .   |  3 |  0  3 | 2N  *  * | 1 1  0
sefa( s2s6o . ) |  3 |  2  1 |  * 6N  * | 1 0  1
sefa( . s6o3o ) |  3 |  0  3 |  *  * 2N | 0 1  1
----------------+----+-------+----------+-------
      s2s6o .   ♦  6 |  6  6 |  2  6  0 | N *  *
      . s6o3o   ♦  N |  0 3N |  N  0  N | * 2  *
sefa( s2s6o3o ) ♦  4 |  3  3 |  0  3  1 | * * 2N

starting figure: x x6o3o

s2s3s6o   (N → ∞)

demi( . . . . ) | 6N ♦  1  2   4  2 |  2  1   6  3  3 |  2 1 1  4
----------------+----+--------------+-----------------+----------
      s2s . .   |  2 | 3N  *   *  * |  0  0   4  0  0 |  2 0 0  2
      s 2 s .   |  2 |  * 6N   *  * |  0  0   2  2  0 |  1 1 0  2
sefa( . s3s . ) |  2 |  *  * 12N  * |  1  0   1  0  1 |  1 0 1  1
sefa( . . s6o ) |  2 |  *  *   * 6N |  0  1   0  1  1 |  0 1 1  1
----------------+----+--------------+-----------------+----------
      . s3s .   |  3 |  0  0   3  0 | 4N  *   *  *  * |  1 0 1  0
      . . s6o   |  3 |  0  0   0  3 |  * 2N   *  *  * |  0 1 1  0
sefa( s2s3s . ) |  3 |  1  1   1  0 |  *  * 12N  *  * |  1 0 0  1
sefa( s 2 s6o ) |  3 |  0  2   0  1 |  *  *   * 6N  * |  0 1 0  1
sefa( . s3s6o ) |  3 |  0  0   2  1 |  *  *   *  * 6N |  0 0 1  1
----------------+----+--------------+-----------------+----------
      s2s3s .   ♦  6 |  3  3   6  0 |  2  0   6  0  0 | 2N * *  *
      s 2 s6o   ♦  6 |  0  6   0  6 |  0  2   0  6  0 |  * N *  *
      . s3s6o   ♦ 3N |  0  0  6N 3N | 2N  N   0  0 3N |  * * 2  *
sefa( s2s3s6o ) ♦  4 |  1  2   2  1 |  0  0   2  1  1 |  * * * 6N

starting figure: x x3x6o

xo3ox3oo3*a&#x   (N → ∞) → height = sqrt(2/3) = 0.816497

o.3o.3o.3*a    | N * ♦  6  3  0 | 3 3  6  3 0 0 | 1 3 3 1 0
.o3.o3.o3*a    | * N ♦  0  3  6 | 0 0  3  6 3 3 | 0 3 1 3 1
---------------+-----+----------+---------------+----------
x. .. ..       | 2 0 | 3N  *  * | 1 1  1  0 0 0 | 1 1 1 0 0
oo3oo3oo3*a&#x | 1 1 |  * 3N  * | 0 0  2  2 0 0 | 0 2 1 1 0
.. .x ..       | 0 2 |  *  * 3N | 0 0  0  1 1 1 | 0 1 0 1 1
---------------+-----+----------+---------------+----------
x.3o. ..       | 3 0 |  3  0  0 | N *  *  * * * | 1 1 0 0 0
x. .. o.*a     | 3 0 |  3  0  0 | * N  *  * * * | 1 0 1 0 0
xo .. ..   &#x | 2 1 |  1  2  0 | * * 3N  * * * | 0 1 1 0 0
.. ox ..   &#x | 1 2 |  0  2  1 | * *  * 3N * * | 0 1 0 1 0
.o3.x ..       | 0 3 |  0  0  3 | * *  *  * N * | 0 1 0 0 1
.. .x3.o       | 0 3 |  0  0  3 | * *  *  * * N | 0 0 0 1 1
---------------+-----+----------+---------------+----------
x.3o.3o.3*a    ♦ N 0 | 3N  0  0 | N N  0  0 0 0 | 1 * * * *
xo3ox ..   &#x ♦ 3 3 |  3  6  3 | 1 0  3  3 1 0 | * N * * *
xo .. oo3*a&#x ♦ 3 1 |  3  3  0 | 0 1  3  0 0 0 | * * N * *
.. ox3oo   &#x ♦ 1 3 |  0  3  3 | 0 0  0  3 0 1 | * * * N *
.o3.x3.o3*a    ♦ 0 N |  0  0 3N | 0 0  0  0 N N | * * * * 1

or
o.3o.3o.3*a    & | 2N ♦  6  3 |  3  3  9 | 1 3  4
-----------------+----+-------+----------+-------
x. .. ..       & |  2 | 6N  * |  1  1  1 | 1 1  1
oo3oo3oo3*a&#x   |  2 |  * 3N |  0  0  4 | 0 2  2
-----------------+----+-------+----------+-------
x.3o. ..       & |  3 |  3  0 | 2N  *  * | 1 1  0
x. .. o.3*a    & |  3 |  3  0 |  * 2N  * | 1 0  1
xo .. ..   &#x & |  3 |  1  2 |  *  * 6N | 0 1  1
-----------------+----+-------+----------+-------
x.3o.3o.3*a    & ♦  N | 3N  0 |  N  N  0 | 2 *  *
xo3ox ..   &#x   ♦  6 |  6  6 |  2  0  6 | * N  *
xo .. oo3*a&#x & ♦  4 |  3  3 |  0  1  3 | * * 2N