Acronym icoy
Name icosayotton,
quadrirectified decayotton,
equatorial cross-section of (vertex first) 1/q-deker,
Gosset polytope 04,4
Circumradius sqrt(5)/2 = 1.118034
Inradius sqrt(5)/6 = 0.372678
Confer
general polytopal classes:
Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

o3o3o3o3x3o3o3o3o

. . . . . . . . . | 252    25 |   50   50 |   50  100   50 |   25  100  100   25 |   5  50  100  50   5 |  10  50  50  10 | 10 25 10 |  5  5
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
. . . . x . . . . |   2 | 3150 |    4    4 |    6   16    6 |    4   24   24    4 |   1  16   36  16   1 |   4  24  24   4 |  6 16  6 |  4  4
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
. . . o3x . . . . |   3 |    3 | 4200    * |    3    4    0 |    3   12    6    0 |   1  12   18   4   0 |   4  18  12   1 |  6 12  3 |  4  3
. . . . x3o . . . |   3 |    3 |    * 4200 |    0    4    3 |    0    6   12    3 |   0   4   18  12   1 |   1  12  18   4 |  3 12  6 |  3  4
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
. . o3o3x . . . .    4 |    6 |    4    0 | 3150    *    * |    2    4    0    0 |   1   8    6   0   0 |   4  12   4   0 |  6  8  1 |  4  2
. . . o3x3o . . .    6 |   12 |    4    4 |    * 4200    * |    0    3    3    0 |   0   3    9   3   0 |   1   9   9   1 |  3  9  3 |  3  3
. . . . x3o3o . .    4 |    6 |    0    4 |    *    * 3150 |    0    0    4    2 |   0   0    6   8   1 |   0   4  12   4 |  1  8  6 |  2  4
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
. o3o3o3x . . . .    5 |   10 |   10    0 |    5    0    0 | 1260    *    *    * |   1   4    0   0   0 |   4   6   0   0 |  6  4  0 |  4  1
. . o3o3x3o . . .   10 |   30 |   20   10 |    5    5    0 |    * 2520    *    * |   0   2    3   0   0 |   1   6   3   0 |  3  6  1 |  3  2
. . . o3x3o3o . .   10 |   30 |   10   20 |    0    5    5 |    *    * 2520    * |   0   0    3   2   0 |   0   3   6   1 |  1  6  3 |  2  3
. . . . x3o3o3o .    5 |   10 |    0   10 |    0    0    5 |    *    *    * 1260 |   0   0    0   4   1 |   0   0   6   4 |  0  4  6 |  1  4
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
o3o3o3o3x . . . .    6 |   15 |   20    0 |   15    0    0 |    6    0    0    0 | 210   *    *   *   *    4   0   0   0 |  6  0  0 |  4  0
. o3o3o3x3o . . .   15 |   60 |   60   20 |   30   15    0 |    6    6    0    0 |   * 840    *   *   * |   1   3   0   0 |  3  3  0 |  3  1
. . o3o3x3o3o . .   20 |   90 |   60   60 |   15   30   15 |    0    6    6    0 |   *   * 1260   *   * |   0   2   2   0 |  1  4  1 |  2  2
. . . o3x3o3o3o .   15 |   60 |   20   60 |    0   15   30 |    0    0    6    6 |   *   *    * 840   * |   0   0   3   1 |  0  3  3 |  1  3
. . . . x3o3o3o3o    6 |   15 |    0   20 |    0    0   15 |    0    0    0    6 |   *   *    *   * 210    0   0   0   4 |  0  0  6 |  0  4
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
o3o3o3o3x3o . . .   21 |  105 |  140   35 |  105   35    0 |   42   21    0    0 |   7   7    0   0   0 | 120   *   *   * |  3  0  0 |  3  0
. o3o3o3x3o3o . .   35 |  210 |  210  140 |  105  105   35 |   21   42   21    0 |   0   7    7   0   0 |   * 360   *   * |  1  2  0 |  2  1
. . o3o3x3o3o3o .   35 |  210 |  140  210 |   35  105  105 |    0   21   42   21 |   0   0    7   7   0 |   *   * 360   * |  0  2  1 |  1  2
. . . o3x3o3o3o3o   21 |  105 |   35  140 |    0   35  105 |    0    0   21   42 |   0   0    0   7   7 |   *   *   * 120 |  0  0  3 |  0  3
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
o3o3o3o3x3o3o . .   56 |  420 |  560  280 |  420  280   70 |  168  168   56    0 |  28  56   28   0   0 |   8   8   0   0 | 45  *  * |  2  0
. o3o3o3x3o3o3o .   70 |  560 |  560  560 |  280  420  280 |   56  168  168   56 |   0  28   56  28   0 |   0   8   8   0 |  * 90  * |  1  1
. . o3o3x3o3o3o3o   56 |  420 |  280  560 |   70  280  420 |    0   56  168  168 |   0   0   28  56  28 |   0   0   8   8 |  *  * 45 |  0  2
------------------+-----+------+-----------+----------------+---------------------+----------------------+-----------------+----------+------
o3o3o3o3x3o3o3o .  126 | 1260 | 1680 1260 | 1260 1260  630 |  504  756  504  126 |  84 252  252  84   0 |  36  72  36   0 |  9  9  0 | 10  *
. o3o3o3x3o3o3o3o  126 | 1260 | 1260 1680 |  630 1260 1260 |  126  504  756  504 |   0  84  252 252  84 |   0  36  72  36 |  0  9  9 |  * 10
or
. . . . . . . . .    | 252    25 |  100 |  100  100 |   50  200 |  10  100  100 |  20 100 | 20 25 | 10
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
. . . . x . . . .    |   2 | 3150 |    8 |   12   16 |    8   48 |   2   32   36 |   8  48 | 12 16 |  8
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
. . . o3x . . . .  & |   3 |    3 | 8400 |    3    4 |    3   18 |   1   16   18 |   5  30 |  9 12 |  7
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
. . o3o3x . . . .  &    4 |    6 |    4 | 6300    * |    2    4 |   1    8    6 |   4  16 |  7  8 |  6
. . . o3x3o . . .       6 |   12 |    8 |    * 4200 |    0    6 |   0    6    9 |   2  18 |  6  9 |  6
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
. o3o3o3x . . . .  &    5 |   10 |   10 |    5    0 | 2520    * |   1    4    0 |   4   6 |  6  4 |  5
. . o3o3x3o . . .  &   10 |   30 |   30 |    5    5 |    * 5040 |   0    2    3 |   1   9 |  4  6 |  5
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
o3o3o3o3x . . . .  &    6 |   15 |   20 |   15    0 |    6    0 | 420    *    *    4   0 |  6  0 |  4
. o3o3o3x3o . . .  &   15 |   60 |   80 |   30   15 |    6    6 |   * 1680    * |   1   3 |  3  3 |  4
. . o3o3x3o3o . .      20 |   90 |  120 |   30   30 |    0   12 |   *    * 1260 |   0   4 |  2  4 |  4
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
o3o3o3o3x3o . . .  &   21 |  105 |  175 |  105   35 |   42   21 |   7    7    0 | 240   * |  3  0 |  3
. o3o3o3x3o3o . .  &   35 |  210 |  350 |  140  105 |   21   63 |   0    7    7 |   * 720 |  1  2 |  3
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
o3o3o3o3x3o3o . .  &   56 |  420 |  840 |  490  280 |  168  224 |  28   56   28 |   8   8 | 90  * |  2
. o3o3o3x3o3o3o .      70 |  560 | 1120 |  560  420 |  112  336 |   0   56   56 |   0  16 |  * 90 |  2
---------------------+-----+------+------+-----------+-----------+---------------+---------+-------+---
o3o3o3o3x3o3o3o .  &  126 | 1260 | 2940 | 1890 1260 |  630 1260 |  84  336  252 |  36 108 |  9  9 | 20

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