Acronym ...
Name hyperbolic o3o4s4o tesselation

This non-Wythoffian but still uniform non-compact hyperbolic tesselation uses the squat in the sense of an infinite horohedron for some of its cells. – Its vertex figure is a close relative to co, in fact it is xox3ouo&#qt.


Incidence matrix according to Dynkin symbol

o3o4s4o   (N,M,K → ∞)

demi( . . . . ) | 2NM |   6   3 |   6  12 |  2  3   6
----------------+-----+---------+---------+----------
      . o4s .   |   2 | 6NM   * |   2   2 |  1  1   2
      . . s4o   |   2 |   * 3NM |   0   4 |  0  2   2
----------------+-----+---------+---------+----------
sefa( o3o4s . ) |   3 |   3   0 | 4NM   * |  1  0   1
sefa( . o4s4o ) |   4 |   2   2 |   * 6NM |  0  1   1
----------------+-----+---------+---------+----------
      o3o4s .      4 |   6   0 |   4   0 | NM  *   *
      . o4s4o      M |   M   M |   0   M |  * 6N   *
sefa( o3o4s4o )    6 |   6   3 |   2   3 |  *  * 2NM

starting figure: o3o4x4o

s4o4s4o   (N,M,K → ∞)

demi( . . . . ) | 2NMK |   1    4    2    2 |    8    6    4 |   2   2   1    6
----------------+------+--------------------+----------------+-----------------
      s4o . .   |    2 | NMK    *    *    * |    4    0    0 |   2   0   0    2
      s . s .   |    2 |   * 4NMK    *    * |    2    2    0 |   1   1   0    1
      . o4s .   |    2 |   *    * 2NMK    * |    2    0    2 |   1   0   1    2
      . . s4o   |    2 |   *    *    * 2NMK |    0    2    2 |   0   1   1    2
----------------+------+--------------------+----------------+-----------------
sefa( s4o4s . ) |    4 |   1    2    1    0 | 4NMK    *    * |   1   0   0    1
sefa( s . s4o ) |    3 |   0    2    0    1 |    * 4NMK    * |   0   1   0    1
sefa( . o4s4o ) |    4 |   0    0    2    2 |    *    * 2NMK |   0   0   1    1
----------------+------+--------------------+----------------+-----------------
      s4o4s .      2M |   M   2M    M    0 |   2M    0    0 | 2NK   *   *    *
      s . s4o       4 |   0    4    0    2 |    0    4    0 |   * NMK   *    *
      . o4s4o       K |   0    0    K    K |    0    0    K |   *   * 2NM    *
sefa( s4o4s4o )     6 |   1    4    2    2 |    2    2    1 |   *   *   * 2NMK

starting figure: x4o4x4o

s4o4s *b3o   (N,M → ∞)

demi( . . .    . ) | 4NM |   3   3   3 |   12   3   3 |  3  1  1   6
-------------------+-----+-------------+--------------+-------------
      s4o .    .   |   2 | 6NM   *   * |    2   2   0 |  1  1  0   2
      s 2 s    .   |   2 |   * 6NM   * |    4   0   0 |  2  0  0   2
      . o4s    .   |   2 |   *   * 6NM |    2   0   2 |  1  0  1   2
-------------------+-----+-------------+--------------+-------------
sefa( s4o4s    . ) |   4 |   1   2   1 | 12NM   *   * |  1  0  0   1
sefa( s4o . *b3o ) |   3 |   3   0   0 |    * 4NM   * |  0  1  0   1
sefa( . o4s *b3o ) |   3 |   0   0   3 |    *   * 4NM |  0  0  1   1
-------------------+-----+-------------+--------------+-------------
      s4o4s    .   |  2M |   M  2M   M |   2M   0   0 | 6N  *  *   *
      s4o . *b3o   |   4 |   6   0   0 |    0   4   0 |  * NM  *   *
      . o4s *b3o   |   4 |   0   0   6 |    0   0   4 |  *  * NM   *
sefa( s4o4s *b3o ) |   6 |   3   3   3 |    3   1   1 |  *  *  * 4NM

starting figure: x4o4x *b3o

© 2004-2019
top of page