Acronym lanquoh (old: rolinoh)
Name pentacontihexa-hecatonicosihexa-pentacosiheptacontihexa-exic heptacomb,
rectified pentacontihexahecatonicosihexaexic heptacomb,
Gosset heptacomb 03,3,1
Confer
general polytopal classes:
Coxeter-Elte-Gosset polytopes  

Incidence matrix according to Dynkin symbol

o3o3o3x3o3o3o *d3o   (N → ∞)

. . . . . . .    . | 2520N      32 |     48     48     16 |     32     72     24     32     24 |     8     48    16     48    36     8    16 |    12    4    32   24    12   24    4 |    8   6    8  16   6 |   2 4 4
-------------------+-------+--------+----------------------+------------------------------------+---------------------------------------------+---------------------------------------+-----------------------+--------
. . . x . . .    . |     2 | 40320N |      3      3      1 |      3      9      3      3      3 |     1      9     3      9     9     1     3 |     3    1     9    9     3    9    1 |    3   3    3   9   3 |   1 3 3
-------------------+-------+--------+----------------------+------------------------------------+---------------------------------------------+---------------------------------------+-----------------------+--------
. . o3x . . .    . |     3 |      3 | 40320N      *      * |      2      3      1      0      0 |     1      6     2      3     3     0     0 |     3    1     6    6     1    3    0 |    3   3    2   6   1 |   1 3 2
. . . x3o . .    . |     3 |      3 |      * 40320N      * |      0      3      0      2      1 |     0      3     0      6     3     1     2 |     1    0     6    3     3    6    1 |    2   1    3   6   3 |   1 2 3
. . . x . . . *d3o |     3 |      3 |      *      * 13440N |      0      0      3      0      3 |     0      0     3      0     9     0     3 |     0    1     0    9     0    9    1 |    0   3    0   9   3 |   0 3 3
-------------------+-------+--------+----------------------+------------------------------------+---------------------------------------------+---------------------------------------+-----------------------+--------
. o3o3x . . .    .      4 |      6 |      4      0      0 | 20160N      *      *      *      * |     1      3     1      0     0     0     0 |     3    1     3    3     0    0    0 |    3   3    1   3   0 |   1 3 1
. . o3x3o . .    .      6 |     12 |      4      4      0 |      * 30240N      *      *      * |     0      2     0      2     1     0     0 |     1    0     4    2     1    2    0 |    2   1    2   4   1 |   1 2 2
. . o3x . . . *d3o      6 |     12 |      4      0      4 |      *      * 10080N      *      * |     0      0     2      0     3     0     0 |     0    1     0    6     0    3    0 |    0   3    0   6   1 |   0 3 2
. . . x3o3o .    .      4 |      6 |      0      4      0 |      *      *      * 20160N      * |     0      0     0      3     0     1     1 |     0    0     3    0     3    3    1 |    1   0    3   3   3 |   1 1 3
. . . x3o . . *d3o      6 |     12 |      0      4      4 |      *      *      *      * 10080N |     0      0     0      0     3     0     2 |     0    0     0    3     0    6    1 |    0   1    0   6   3 |   0 2 3
-------------------+-------+--------+----------------------+------------------------------------+---------------------------------------------+---------------------------------------+-----------------------+--------
o3o3o3x . . .    .      5 |     10 |     10      0      0 |      5      0      0      0      0 | 4032N      *     *      *     *     *     * |     3    1     0    0     0    0    0 |    3   3    0   0   0 |   1 3 0
. o3o3x3o . .    .     10 |     30 |     20     10      0 |      5      5      0      0      0 |     * 12096N     *      *     *     *     * |     1    0     2    1     0    0    0 |    2   1    1   2   0 |   1 2 1
. o3o3x . . . *d3o     10 |     30 |     20      0     10 |      5      0      5      0      0 |     *      * 4032N      *     *     *     * |     0    1     0    3     0    0    0 |    0   3    0   3   0 |   0 3 1
. . o3x3o3o .    .     10 |     30 |     10     20      0 |      0      5      0      5      0 |     *      *     * 12096N     *     *     * |     0    0     2    0     1    1    0 |    1   0    2   2   1 |   1 1 2
. . o3x3o . . *d3o     24 |     96 |     32     32     32 |      0      8      8      0      8 |     *      *     *      * 3780N     *     * |     0    0     0    2     0    2    0 |    0   1    0   4   1 |   0 2 2
. . . x3o3o3o    .      5 |     10 |      0     10      0 |      0      0      0      5      0 |     *      *     *      *     * 4032N     * |     0    0     0    0     3    0    1 |    0   0    3   0   3 |   1 0 3
. . . x3o3o . *d3o     10 |     30 |      0     20     10 |      0      0      0      5      5 |     *      *     *      *     *     * 4032N |     0    0     0    0     0    3    1 |    0   0    0   3   3 |   0 1 3
-------------------+-------+--------+----------------------+------------------------------------+---------------------------------------------+---------------------------------------+-----------------------+--------
o3o3o3x3o . .    .     15 |     60 |     60     20      0 |     30     15      0      0      0 |     6      6     0      0     0     0     0 | 2016N    *     *    *     *    *    * |    2   1    0   0   0 |   1 2 0
o3o3o3x . . . *d3o     15 |     60 |     60      0     20 |     30      0     15      0      0 |     6      0     6      0     0     0     0 |     * 672N     *    *     *    *    * |    0   3    0   0   0 |   0 3 0
. o3o3x3o3o .    .     20 |     90 |     60     60      0 |     15     30      0     15      0 |     0      6     0      6     0     0     0 |     *    * 4032N    *     *    *    * |    1   0    1   1   0 |   1 1 1
. o3o3x3o . . *d3o     80 |    480 |    320    160    160 |     80     80     80      0     40 |     0     16    16      0    10     0     0 |     *    *     * 756N     *    *    * |    0   1    0   2   0 |   0 2 1
. . o3x3o3o3o    .     15 |     60 |     20     60      0 |      0     15      0     30      0 |     0      0     0      6     0     6     0 |     *    *     *    * 2016N    *    * |    0   0    2   0   1 |   1 0 2
. . o3x3o3o . *d3o     80 |    480 |    160    320    160 |      0     80     40     80     80 |     0      0     0     16    10     0    16 |     *    *     *    *     * 756N    * |    0   0    0   2   1 |   0 1 2
. . . x3o3o3o *d3o     15 |     60 |      0     60     20 |      0      0      0     30     15 |     0      0     0      0     0     6     6 |     *    *     *    *     *    * 672N |    0   0    0   0   3 |   0 0 3
-------------------+-------+--------+----------------------+------------------------------------+---------------------------------------------+---------------------------------------+-----------------------+--------
o3o3o3x3o3o .    .     35 |    210 |    210    140      0 |    105    105      0     35      0 |    21     42     0     21     0     0     0 |     7    0     7    0     0    0    0 | 576N   *    *   *   * |   1 1 0
o3o3o3x3o . . *d3o    240 |   1920 |   1920    640    640 |    960    480    480      0    160 |   192    192   192      0    60     0     0 |    32   32     0   12     0    0    0 |    * 63N    *   *   * |   0 2 0
. o3o3x3o3o3o    .     35 |    210 |    140    210      0 |     35    105      0    105      0 |     0     21     0     42     0    21     0 |     0    0     7    0     7    0    0 |    *   * 576N   *   * |   1 0 1
. o3o3x3o3o . *d3o    720 |   6480 |   4320   4320   2160 |   1080   2160   1080   1080   1080 |     0    432   216    432   270     0   216 |     0    0    72   27     0   27    0 |    *   *    * 56N   * |   0 1 1
. . o3x3o3o3o *d3o    240 |   1920 |    640   1920    640 |      0    480    160    960    480 |     0      0     0    192    60   192   192 |     0    0     0    0    32   12   32 |    *   *    *   * 63N |   0 0 2
-------------------+-------+--------+----------------------+------------------------------------+---------------------------------------------+---------------------------------------+-----------------------+--------
o3o3o3x3o3o3o    .     70 |    560 |    560    560      0 |    280    420      0    280      0 |    56    168     0    168     0    56     0 |    28    0    56    0    28    0    0 |    8   0    8   0   0 | 72N * *
o3o3o3x3o3o . *d3o  10080 | 120960 | 120960  80640  40320 |  60480  60480  30240  20160  20160 | 12096  24192 12096  12096  7560     0  4032 |  4032 2016  4032 1512     0  756    0 |  576 126    0  56   0 |   * N *
. o3o3x3o3o3o *d3o  10080 | 120960 |  80640 120960  40320 |  20160  60480  20160  60480  30240 |     0  12096  4032  24192  7560 12096 12096 |     0    0  4032  756  4032 1512 2016 |    0   0  576  56 126 |   * * N
or
. . . . . . .    .    | 1260N      32 |     96    16 |     64     72     48 |    16     96    32    36 |    24    8    32   48 |   16  12  16 |   2 8
----------------------+-------+--------+--------------+----------------------+--------------------------+-----------------------+--------------+------
. . . x . . .    .    |     2 | 20160N |      6     1 |      6      9      6 |     2     18     6     9 |     6    2     9   18 |    6   6   9 |   1 6
----------------------+-------+--------+--------------+----------------------+--------------------------+-----------------------+--------------+------
. . o3x . . .    .  & |     3 |      3 | 40320N     * |      2      3      1 |     1      9     2     3 |     4    1     6    9 |    5   4   6 |   1 5
. . . x . . . *d3o    |     3 |      3 |      * 6720N |      0      0      6 |     0      0     6     9 |     0    2     0   18 |    0   6   9 |   0 6
----------------------+-------+--------+--------------+----------------------+--------------------------+-----------------------+--------------+------
. o3o3x . . .    .  &      4 |      6 |      4     0 | 20160N      *      * |     1      3     1     0 |     3    1     3    3 |    4   3   3 |   1 4
. . o3x3o . .    .         6 |     12 |      8     0 |      * 15120N      * |     0      4     0     1 |     2    0     4    4 |    4   2   4 |   1 4
. . o3x . . . *d3o  &      6 |     12 |      4     4 |      *      * 10080N |     0      0     2     3 |     0    1     0    9 |    0   4   6 |   0 5
----------------------+-------+--------+--------------+----------------------+--------------------------+-----------------------+--------------+------
o3o3o3x . . .    .  &      5 |     10 |     10     0 |      5      0      0 | 4032N      *     *     * |     3    1     0    0 |    3   3   0 |   1 3
. o3o3x3o . .    .  &     10 |     30 |     30     0 |      5      5      0 |     * 12096N     *     * |     1    0     2    1 |    3   1   2 |   1 3
. o3o3x . . . *d3o  &     10 |     30 |     20    10 |      5      0      5 |     *      * 4032N     * |     0    1     0    3 |    0   3   3 |   0 4
. . o3x3o . . *d3o        24 |     96 |     64    32 |      0      8     16 |     *      *     * 1890N |     0    0     0    4 |    0   2   4 |   0 4
----------------------+-------+--------+--------------+----------------------+--------------------------+-----------------------+--------------+------
o3o3o3x3o . .    .  &     15 |     60 |     80     0 |     30     15      0 |     6      6     0     0 | 2016N    *     *    * |    2   1   0 |   1 2
o3o3o3x . . . *d3o  &     15 |     60 |     60    20 |     30      0     15 |     6      0     6     0 |     * 672N     *    * |    0   3   0 |   0 3
. o3o3x3o3o .    .        20 |     90 |    120     0 |     30     30      0 |     0     12     0     0 |     *    * 2016N    * |    2   0   1 |   1 2
. o3o3x3o . . *d3o  &     80 |    480 |    480   160 |     80     80    120 |     0     16    16    10 |     *    *     * 756N |    0   1   2 |   0 3
----------------------+-------+--------+--------------+----------------------+--------------------------+-----------------------+--------------+------
o3o3o3x3o3o .    .  &     35 |    210 |    350     0 |    140    105      0 |    21     63     0     0 |     7    0     7    0 | 576N   *   * |   1 1
o3o3o3x3o . . *d3o  &    240 |   1920 |   2560   640 |    960    480    640 |   192    192   192    60 |    32   32     0   12 |    * 63N   * |   0 2
. o3o3x3o3o . *d3o       720 |   6480 |   8640  2160 |   2160   2160   2160 |     0    864   432   270 |     0    0    72   54 |    *   * 28N |   0 2
----------------------+-------+--------+--------------+----------------------+--------------------------+-----------------------+--------------+------
o3o3o3x3o3o3o    .        70 |    560 |   1120     0 |    560    420      0 |   112    336     0     0 |    56    0    56    0 |   16   0   0 | 36N *
o3o3o3x3o3o . *d3o  &  10080 | 120960 | 201600 40320 |  80640  60480  50400 | 12096  36288 16128  7560 |  4032 2016  4032 2268 |  576 126  56 |   * N

© 2004-2024
top of page