Acronym	rath
Name	hyperbolic rectified (order 6) tetrahedral honeycomb
	©
Circumradius	1 i
Vertex figure	©
External links

This non-compact hyperbolic tesselation uses trat in the sense of an infinite horohedron as one of its cell types.

Incidence matrix according to Dynkin symbol

o3x3o6o   (N,M → ∞)

. . . . | NM ♦  12 |   6  12 |  6  2
--------+----+-----+---------+------
. x . . |  2 | 6NM |   1   2 |  2  1
--------+----+-----+---------+------
o3x . . |  3 |   3 | 2NM   * |  2  0
. x3o . |  3 |   3 |   * 4NM |  1  1
--------+----+-----+---------+------
o3x3o . ♦  6 |  12 |   4   4 | NM  *
. x3o6o ♦  M |  3M |   0  2M |  * 2N

o3x3o3o3*b   (N,M → ∞)

. . . .    | 2NM ♦   12 |   6   6   6 |  3  3  2
-----------+-----+------+-------------+---------
. x . .    |   2 | 12NM |   1   1   1 |  1  1  1
-----------+-----+------+-------------+---------
o3x . .    |   3 |    3 | 4NM   *   * |  1  1  0
. x3o .    |   3 |    3 |   * 4NM   * |  1  0  1
. x . o3*b |   3 |    3 |   *   * 4NM |  0  1  1
-----------+-----+------+-------------+---------
o3x3o .    ♦   6 |   12 |   4   4   0 | NM  *  *
o3x . o3*b ♦   6 |   12 |   4   0   4 |  * NM  *
. x3o3o3*b ♦   M |   3M |   0   M   M |  *  * 4N