Acronym ...
Name hyperbolic tetrahexagonal tiling
 
    ©
Circumradius sqrt(-1) = 1 i
Vertex figure [(4,6)2]
External
links
wikipedia

There exists a regular modwrap of this tiling, obtained by identifying every 6th vertex on each hole. Then it allows a representation as infinite skew polyhedron, which happens to be a facial subset of the bitruncated cubical honeycomb.


Incidence matrix according to Dynkin symbol

o4x6o   (N → ∞)

. . . | 6N |   4 |  2  2
------+----+-----+------
. x . |  2 | 12N |  1  1
------+----+-----+------
o4x . |  4 |   4 | 3N  *
. x6o |  6 |   6 |  * 2N

x6o6x   (N → ∞)

. . . | 6N |  2  2 | 1  2 1
------+----+-------+-------
x . . |  2 | 6N  * | 1  1 0
. . x |  2 |  * 6N | 0  1 1
------+----+-------+-------
x6o . |  6 |  6  0 | N  * *
x . x |  4 |  2  2 | * 3N *
. o6x |  6 |  0  6 | *  * N

x3x4o4*a   (N → ∞)

. . .    | 12N |   2   2 |  2  1  1
---------+-----+---------+---------
x . .    |   2 | 12N   * |  1  1  0
. x .    |   2 |   * 12N |  1  0  1
---------+-----+---------+---------
x3x .    |   6 |   3   3 | 4N  *  *
x . o4*a |   4 |   4   0 |  * 3N  *
. x4o    |   4 |   0   4 |  *  * 3N

x3xØx3xØ*a

. . . .    | 12N |  1  1  1  1 |  1  1  1  1
-----------+-----+-------------+------------
x . . .    |   2 | 6N  *  *  * |  1  1  0  0
. x . .    |   2 |  * 6N  *  * |  1  0  1  0
. . x .    |   2 |  *  * 6N  * |  0  1  0  1
. . . x    |   2 |  *  *  * 6N |  0  0  1  1
-----------+-----+-------------+------------
x3x . .    |   6 |  3  3  0  0 | 2N  *  *  *
x . x .    |   4 |  2  0  2  0 |  * 3N  *  *
. x . x    |   4 |  0  2  0  2 |  *  * 3N  *
. . x3x    |   6 |  0  0  3  3 |  *  *  * 2N

© 2004-2019
top of page