Acronym buffy
Name diacositetracont-dischiliahectohexacont-myriaheptachiliadiacosioctaconta-zetton,
rectified bif:  t1(12,4),
birectified bay:  t2(21,4),
tetrarectified fy:  t4(41,2),
Gosset polytope 04,2,1
Circumradius sqrt(15) = 3.872983
Confer
general polytopal classes:
Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

o3o3x3o *c3o3o3o3o

. . . .    . . . . | 483840       30 |      30      15      60 |      10      15      60      30      60 |      5     20     30      60      30      30 |    10     20     30     30     15      6 |   10     10    15      6     3 |   5     2    3
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
. . x .    . . . . |      2 | 7257600 |       2       1       4 |       1       2       8       4       6 |      1      4      8      12       6       4 |     4      6     12      8      4      1 |    6      4     8      2     1 |   4     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
. o3x .    . . . . |      3 |       3 | 4838400       *       * |       1       1       4       0       0 |      1      4      4       6       0       0 |     4      6      6      4      0      0 |    6      4     4      1     0 |   4     1    1
. . x3o    . . . . |      3 |       3 |       * 2419200       * |       0       2       0       4       0 |      1      0      8       0       6       0 |     4      0     12      0      4      0 |    6      0     8      0     1 |   4     0    2
. . x . *c3o . . . |      3 |       3 |       *       * 9676800 |       0       0       2       1       3 |      0      1      2       6       3       3 |     1      3      6      6      3      1 |    3      3     6      2     1 |   3     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x .    . . . .       4 |       6 |       4       0       0 | 1209600       *       *       *       * |      1      4      0       0       0       0 |     4      6      0      0      0      0 |    6      4     0      0     0 |   4     1    0
. o3x3o    . . . .       6 |      12 |       4       4       0 |       * 1209600       *       *       * |      1      0      4       0       0       0 |     4      0      6      0      0      0 |    6      0     4      0     0 |   4     0    1
. o3x . *c3o . . .       6 |      12 |       4       0       4 |       *       * 4838400       *       * |      0      1      1       3       0       0 |     1      3      3      3      0      0 |    3      3     3      1     0 |   3     1    1
. . x3o *c3o . . .       6 |      12 |       0       4       4 |       *       *       * 2419200       * |      0      0      2       0       3       0 |     1      0      6      0      3      0 |    3      0     6      0     1 |   3     0    2
. . x . *c3o3o . .       4 |       6 |       0       0       4 |       *       *       *       * 7257600 |      0      0      0       2       1       2 |     0      1      2      4      2      1 |    1      2     4      2     1 |   2     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o    . . . .      10 |      30 |      20      10       0 |       5       5       0       0       0 | 241920      *      *       *       *       *      4      0      0      0      0      0 |    6      0     0      0     0 |   4     0    0
o3o3x . *c3o . . .      10 |      30 |      20       0      10 |       5       0       5       0       0 |      * 967680      *       *       *       * |     1      3      0      0      0      0 |    3      3     0      0     0 |   3     1    0
. o3x3o *c3o . . .      24 |      96 |      32      32      32 |       0       8       8       8       0 |      *      * 604800       *       *       * |     1      0      3      0      0      0 |    3      0     3      0     0 |   3     0    1
. o3x . *c3o3o . .      10 |      30 |      10       0      20 |       0       0       5       0       5 |      *      *      * 2903040       *       * |     0      1      1      2      0      0 |    1      2     2      1     0 |   2     1    1
. . x3o *c3o3o . .      10 |      30 |       0      10      20 |       0       0       0       5       5 |      *      *      *       * 1451520       * |     0      0      2      0      2      0 |    1      0     4      0     1 |   2     0    2
. . x . *c3o3o3o .       5 |      10 |       0       0      10 |       0       0       0       0       5 |      *      *      *       *       * 2903040 |     0      0      0      2      1      1 |    0      1     2      2     1 |   1     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o *c3o . . .      80 |     480 |     320     160     160 |      80      80      80      40       0 |     16     16     10       0       0       0 | 60480      *      *      *      *      * |    3      0     0      0     0 |   3     0    0
o3o3x . *c3o3o . .      20 |      90 |      60       0      60 |      15       0      30       0      15 |      0      6      0       6       0       0 |     * 483840      *      *      *      * |    1      2     0      0     0 |   2     1    0
. o3x3o *c3o3o . .      80 |     480 |     160     160     320 |       0      40      80      80      80 |      0      0     10      16      16       0 |     *      * 181440      *      *      * |    1      0     2      0     0 |   2     0    1
. o3x . *c3o3o3o .      15 |      60 |      20       0      60 |       0       0      15       0      30 |      0      0      0       6       0       6 |     *      *      * 967680      *      * |    0      1     1      1     0 |   1     1    1
. . x3o *c3o3o3o .      15 |      60 |       0      20      60 |       0       0       0      15      30 |      0      0      0       0       6       6 |     *      *      *      * 483840      * |    0      0     2      0     1 |   1     0    2
. . x . *c3o3o3o3o       6 |      15 |       0       0      20 |       0       0       0       0      15 |      0      0      0       0       0       6 |     *      *      *      *      * 483840 |    0      0     0      2     1 |   0     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o *c3o3o . .     720 |    6480 |    4320    2160    4320 |    1080    1080    2160    1080    1080 |    216    432    270     432     216       0 |    27     72     27      0      0      0 | 6720      *     *      *     * |   2     0    0
o3o3x . *c3o3o3o .      35 |     210 |     140       0     210 |      35       0     105       0     105 |      0     21      0      42       0      21 |     0      7      0      7      0      0 |    * 138240     *      *     * |   1     1    0
. o3x3o *c3o3o3o .     240 |    1920 |     640     640    1920 |       0     160     480     480     960 |      0      0     60     192     192     192 |     0      0     12     32     32      0 |    *      * 30240      *     * |   1     0    1
. o3x . *c3o3o3o3o      21 |     105 |      35       0     140 |       0       0      35       0     105 |      0      0      0      21       0      42 |     0      0      0      7      0      7 |    *      *     * 138240     * |   0     1    1
. . x3o *c3o3o3o3o      21 |     105 |       0      35     140 |       0       0       0      35     105 |      0      0      0       0      21      42 |     0      0      0      0      7      7 |    *      *     *      * 69120 |   0     0    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o *c3o3o3o .   10080 |  120960 |   80640   40320  120960 |   20160   20160   60480   30240   60480 |   4032  12096   7560   24192   12096   12096 |   756   4032   1512   4032   2016      0 |   56    576   126      0     0 | 240     *    *
o3o3x . *c3o3o3o3o      56 |     420 |     280       0     560 |      70       0     280       0     420 |      0     56      0     168       0     168 |     0     28      0     56      0     28 |    0      8     0      8     0 |   * 17280    *
. o3x3o *c3o3o3o3o     672 |    6720 |    2240    2240    8960 |       0     560    2240    2240    6720 |      0      0    280    1344    1344    2688 |     0      0     84    448    448    448 |    0      0    14     64    64 |   *     * 2160

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