Acronym ...
Name hyperbolic o3o3o3o4s3s pentacomb
Circumradius sqrt[-(2+sqrt(5))] = 2.058171 i

This para-compact hyperbolic tesselation uses the sadit in the sense of an infinite horoteron as one of its facet types.


Incidence matrix according to Dynkin symbol

o3o3o3o4s3s   (N,M → ∞)

demi( . . . . . . ) | 48NM     10    10 |    5    30    30 |    10   10    20    40 |    5  10    5    25 |   1   5    6
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . . . o4s .   |    2 | 240NM     * |    0     6     2 |     3    1     6     6 |    3   3    2     6 |   1   3    2
sefa( . . . . s3s ) |    2 |     * 240NM |    1     0     4 |     0    4     0     6 |    0   6    0     4 |   0   4    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . . . . s3s   |    3 |     0     3 | 80NM     *     *      0    4     0     0 |    0   6    0     0 |   0   4    0
sefa( . . o3o4s . ) |    3 |     3     0 |    * 480NM     * |     1    0     2     1 |    2   1    1     2 |   1   2    1
sefa( . . . o4s3s ) |    3 |     1     2 |    *     * 480NM |     0    1     0     3 |    0   3    0     3 |   0   3    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . . o3o4s .       4 |     6     0 |    0     4     0 | 120NM    *     *     * |    2   1    0     0 |   1   2    0
      . . . o4s3s      12 |     6    24 |    8     0    12 |     * 40NM     *     * |    0   3    0     0 |   0   3    0
sefa( . o3o3o4s . )     4 |     6     0 |    0     4     0 |     *    * 240NM     * |    1   0    1     1 |   1   1    1
sefa( . . o3o4s3s )     4 |     3     3 |    0     1     3 |     *    *     * 480NM |    0   1    0     2 |   0   2    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      . o3o3o4s .       8 |    24     0 |    0    32     0 |     8    0     8     0 | 30NM   *    *     * |   1   1    0
      . . o3o4s3s      96 |   144   288 |   96    96   288 |    24   24     0    96 |    * 5NM    *     * |   0   2    0
sefa( o3o3o3o4s . )     5 |    10     0 |    0    10     0 |     0    0     5     0 |    *   * 48NM     * |   1   0    1
sefa( . o3o3o4s3s )     5 |     6     4 |    0     4     6 |     0    0     1     4 |    *   *    * 240NM |   0   1    1
--------------------+------+-------------+------------------+------------------------+---------------------+-------------
      o3o3o3o4s .      16 |    80     0 |    0   160     0 |    40    0    80     0 |   10   0   16     0 | 3NM   *    *
      . o3o3o4s3s     24M |   72M   96M |  32M   96M  144M |   24M  12M   24M   96M |   3M   M    0   24M |   * 10N    *
sefa( o3o3o3o4s3s )     6 |    10     5 |    0    10    10 |     0    0     5    10 |    0   0    1     5 |   *   * 48NM

starting figure: o3o3o3o4x3x

s3s3s4o3o3o   (N,M,K → ∞)

demi( . . . . . . ) | 48NMK      4      6     2      8 |     1     4     12     18     18     12 |     4     6     6     4     24     16     16     4 |    6     4    4    1     20     5     5 |   4    1   1     6
--------------------+-------+---------------------------+-----------------------------------------+----------------------------------------------------+-----------------------------------------+-------------------
      s 2 s . . .   |     2 | 96NMK      *     *      * |     0     0      2      6      0      0 |     1     3     0     0      6      6      0     0 |    3     3    0    0      6     2     0 |   3    1   0     2
      . . s4o . .   |     2 |     * 144NMK     *      * |     0     0      0      2      2      4 |     0     1     1     2      2      4      4     2 |    1     2    2    1      4     2     2 |   2    1   1     2
sefa( s3s . . . . ) |     2 |     *      * 48NMK      * |     1     0      4      0      0      0 |     4     0     0     0      6      0      0     0 |    6     0    0    0      4     0     0 |   4    0   0     1
sefa( . s3s . . . ) |     2 |     *      *     * 192NMK |     0     1      1      0      3      0 |     1     0     3     0      3      0      3     0 |    3     0    3    0      3     0     1 |   3    0   1     1
--------------------+-------+---------------------------+-----------------------------------------+----------------------------------------------------+-----------------------------------------+-------------------
      s3s . . . .   |     3 |     0      0     3      0 | 16NMK     *      *      *      *      *      4     0     0     0      0      0      0     0 |    6     0    0    0      0     0     0 |   4    0   0     0
      . s3s . . .   |     3 |     0      0     0      3 |     * 64NMK      *      *      *      * |     1     0     3     0      0      0      0     0 |    3     0    3    0      0     0     0 |   3    0   1     0
sefa( s3s3s . . . ) |     3 |     1      0     1      1 |     *     * 192NMK      *      *      * |     1     0     0     0      3      0      0     0 |    3     0    0    0      3     0     0 |   3    0   0     1
sefa( s 2 s4o . . ) |     3 |     2      1     0      0 |     *     *      * 288NMK      *      * |     0     1     0     0      1      2      0     0 |    1     2    0    0      2     1     0 |   2    1   0     1
sefa( . s3s4o . . ) |     3 |     0      1     0      2 |     *     *      *      * 288NMK      * |     0     0     1     0      1      0      2     0 |    1     0    2    0      2     0     1 |   2    0   1     1
sefa( . . s4o3o . ) |     3 |     0      3     0      0 |     *     *      *      *      * 192NMK |     0     0     0     1      0      1      1     1 |    0     1    1    1      1     1     1 |   1    1   1     1
--------------------+-------+---------------------------+-----------------------------------------+----------------------------------------------------+-----------------------------------------+-------------------
      s3s3s . . .       12 |     6      0    12     12 |     4     4     12      0      0      0 | 16NMK     *     *     *      *      *      *     * |    3     0    0    0      0     0     0 |   3    0   0     0
      s 2 s4o . .        4 |     4      2     0      0 |     0     0      0      4      0      0 |     * 72NMK     *     *      *      *      *     * |    1     2    0    0      0     0     0 |   2    1   0     0
      . s3s4o . .       12 |     0      6     0     24 |     0     8      0      0     12      0 |     *     * 24NMK     *      *      *      *     * |    1     0    2    0      0     0     0 |   2    0   1     0
      . . s4o3o .        4 |     0      6     0      0 |     0     0      0      0      0      4 |     *     *     * 48NMK      *      *      *     * |    0     1    1    1      0     0     0 |   1    1   1     0
sefa( s3s3s4o . . )      4 |     2      1     1      2 |     0     0      2      1      1      0 |     *     *     *     * 288NMK      *      *     * |    1     0    0    0      2     0     0 |   2    0   0     1
sefa( s 2 s4o3o . )      4 |     3      3     0      0 |     0     0      0      3      0      1 |     *     *     *     *      * 192NMK      *     * |    0     1    0    0      1     1     0 |   1    1   0     1
sefa( . s3s4o3o . )      4 |     0      3     0      3 |     0     0      0      0      3      1 |     *     *     *     *      *      * 192NMK     * |    0     0    1    0      1     0     1 |   1    0   1     1
sefa( . . s4o3o3o )      4 |     0      6     0      0 |     0     0      0      0      0      4 |     *     *     *     *      *      *      * 48NMK |    0     0    0    1      0     1     1 |   0    1   1     1
--------------------+-------+---------------------------+-----------------------------------------+----------------------------------------------------+-----------------------------------------+-------------------
      s3s3s4o . .       96 |    96     48    96    192 |    32    64    192     96     96      0 |    16    24     8     0     96      0      0     0 | 3NMK     *    *    *      *     *     * |   2    0   0     0
      s 2 s4o3o .        8 |    12     12     0      0 |     0     0      0     24      0      8 |     0     6     0     2      0      8      0     0 |    * 24NMK    *    *      *     *     * |   1    1   0     0
      . s3s4o3o .       96 |     0    144     0    288 |     0    96      0      0    288     96 |     0     0    24    24      0      0     96     0 |    *     * 2NMK    *      *     *     * |   1    0   1     0
      . . s4o3o3o        8 |     0     24     0      0 |     0     0      0      0      0     32 |     0     0     0     8      0      0      0     8 |    *     *    * 6NMK      *     *     * |   0    1   1     0
sefa( s3s3s4o3o . )      5 |     3      3     1      3 |     0     0      3      3      3      1 |     0     0     0     0      3      1      1     0 |    *     *    *    * 192NMK     *     * |   1    0   0     1
sefa( s 2 s4o3o3o )      5 |     4      6     0      0 |     0     0      0      6      0      4 |     0     0     0     0      0      4      0     1 |    *     *    *    *      * 48NMK     * |   0    1   0     1
sefa( . s3s4o3o3o )      5 |     0      6     0      4 |     0     0      0      0      6      4 |     0     0     0     0      0      0      4     1 |    *     *    *    *      *     * 48NMK |   0    0   1     1
--------------------+-------+---------------------------+-----------------------------------------+----------------------------------------------------+-----------------------------------------+-------------------
      s3s3s4o3o .      96M |  144M   144M   96M   288M |   32M   96M   288M   288M   288M    96M |   24M   72M   24M   24M   288M    96M    96M     0 |   3M   12M    M    0    96M     0     0 | 2NK    *   *     *
      s 2 s4o3o3o       16 |    32     48     0      0 |     0     0      0     96      0     64 |     0    24     0    16      0     64      0    16 |    0     8    0    2      0    16     0 |   * 3NMK   *     *
      . s3s4o3o3o      24K |     0    72K     0    96K |     0   32K      0      0   144K    96K |     0     0   12K   24K      0      0    96K   24K |    0     0    K   3K      0     0   24K |   *    * 2NM     *
sefa( s3s3s4o3o3o )      6 |     4      6     1      4 |     0     0      4      6      6      4 |     0     0     0     0      6      4      4     1 |    0     0    0    0      4     1     1 |   *    *   * 48NMK

starting figure: x3x3x4o3o3o

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