Acronym	riv
Name	rectified pentacosidodecayotton, lattice B9 contact polytope (span of its small roots), lattice D9 contact polytope (span of its roots), equatorial cross-section of vee-first rake
Circumradius	1
Inradius wrt. ek	1/sqrt(2) = 0.707107
Inradius wrt. rene	sqrt(2)/3 = 0.471405
Coordinates	(1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume	503 sqrt(2)/22680 = 0.031365
Surface	25/42 = 0.595238
Dihedral angles	at roc between rene and rene:   arccos(-7/9) = 141.057559° at oca between ek and rene:   arccos(-1/3) = 109.471221°
Face vector	144, 2016, 8736, 22176, 36288, 37632, 23040, 6912, 530
Confer	general polytopal classes: Wythoffian polyyotta   analogs: rectified orthoplex rOn
External links

Incidence matrix according to Dynkin symbol

o3x3o3o3o3o3o3o4o

. . . . . . . . . | 144 ♦   28 |  14  168 |   84   560 |  280  1120 |  560  1344 |  672   896 |  448  256 | 128  2
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
. x . . . . . . . |   2 | 2016 |   1   12 |   12    60 |   60   160 |  160   240 |  240   192 |  192   64 |  64  1
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
o3x . . . . . . . |   3 |    3 | 672    * ♦   12     0 |   60     0 |  160     0 |  240     0 |  192    0 |  64  0
. x3o . . . . . . |   3 |    3 |   * 8064 |    1    10 |   10    40 |   40    80 |   80    80 |   80   32 |  32  1
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
o3x3o . . . . . . ♦   6 |   12 |   4    4 | 2016     * ♦   10     0 |   40     0 |   80     0 |   80    0 |  32  0
. x3o3o . . . . . ♦   4 |    6 |   0    4 |    * 20160 |    1     8 |    8    24 |   24    32 |   32   16 |  16  1
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
o3x3o3o . . . . . ♦  10 |   30 |  10   20 |    5     5 | 4032     * ♦    8     0 |   24     0 |   32    0 |  16  0
. x3o3o3o . . . . ♦   5 |   10 |   0   10 |    0     5 |    * 32256 |    1     6 |    6    12 |   12    8 |   8  1
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
o3x3o3o3o . . . . ♦  15 |   60 |  20   60 |   15    30 |    6     6 | 5376     * ♦    6     0 |   12    0 |   8  0
. x3o3o3o3o . . . ♦   6 |   15 |   0   20 |    0    15 |    0     6 |    * 32256 |    1     4 |    4    4 |   4  1
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
o3x3o3o3o3o . . . ♦  21 |  105 |  35  140 |   35   105 |   21    42 |    7     7 | 4608     * |    4    0 |   4  0
. x3o3o3o3o3o . . ♦   7 |   21 |   0   35 |    0    35 |    0    21 |    0     7 |    * 18432 |    1    2 |   2  1
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
o3x3o3o3o3o3o . . ♦  28 |  168 |  56  280 |   70   280 |   56   168 |   28    56 |    8     8 | 2304    * |   2  0
. x3o3o3o3o3o3o . ♦   8 |   28 |   0   56 |    0    70 |    0    56 |    0    28 |    0     8 |    * 4608 |   1  1
------------------+-----+------+----------+------------+------------+------------+------------+-----------+-------
o3x3o3o3o3o3o3o . ♦  36 |  252 |  84  504 |  126   630 |  126   504 |   84   252 |   36    72 |    9    9 | 512  *
. x3o3o3o3o3o3o4o ♦  16 |  112 |   0  448 |    0  1120 |    0  1792 |    0  1792 |    0  1024 |    0  256 |   * 18

o3o3o *b3o3o3o3o3x3o

. . .    . . . . . . | 144 ♦   28 |  168  14 |   560   84 |  1120  280 |  1344  560 |   896  672 |  128  128  448 |  2  64  64
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
. . .    . . . . x . |   2 | 2016 |   12   1 |    60   12 |   160   60 |   240  160 |   192  240 |   32   32  192 |  1  32  32
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
. . .    . . . o3x . |   3 |    3 | 8064   * |    10    1 |    40   10 |    80   40 |    80   80 |   16   16   80 |  1  16  16
. . .    . . . . x3o |   3 |    3 |    * 672 ♦     0   12 |     0   60 |     0  160 |     0  240 |    0    0  192 |  0  32  32
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
. . .    . . o3o3x . ♦   4 |    6 |    4   0 | 20160    * |     8    1 |    24    8 |    32   24 |    8    8   32 |  1   8   8
. . .    . . . o3x3o ♦   6 |   12 |    4   4 |     * 2160 ♦     0   10 |     0   40 |     0   80 |    0    0   80 |  0  16  16
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
. . .    . o3o3o3x . ♦   5 |   10 |   10   0 |     5    0 | 32256    * |     6    1 |    12    6 |    4    4   12 |  1   4   4
. . .    . . o3o3x3o ♦  10 |   30 |   20  10 |     5    5 |     * 4032 ♦     0    8 |     0   24 |    0    0   32 |  0   8   8
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
. . .    o3o3o3o3x . ♦   6 |   15 |   20   0 |    15    0 |     6    0 | 32256    * |     4    1 |    2    2    4 |  1   2   2
. . .    . o3o3o3x3o ♦  15 |   60 |   60  20 |    30   15 |     6    6 |     * 5376 ♦     0    6 |    0    0   12 |  0   4   4
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
. o . *b3o3o3o3o3x . ♦   7 |   21 |   35   0 |    35    0 |    21    0 |     7    0 | 18432    * |    1    1    1 |  1   1   1
. . .    o3o3o3o3x3o ♦  21 |  105 |  140  35 |   105   35 |    42   21 |     7    7 |     * 4608 |    0    0    4 |  0   2   2
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
o3o . *b3o3o3o3o3x . ♦   8 |   28 |   56   0 |    70    0 |    56    0 |    28    0 |     8    0 | 2304    *    * |  1   1   0
. o3o *b3o3o3o3o3x . ♦   8 |   28 |   56   0 |    70    0 |    56    0 |    28    0 |     8    0 |    * 2304    * |  1   0   1
. o . *b3o3o3o3o3x3o ♦  28 |  168 |  280  56 |   280   70 |   168   56 |    56   28 |     8    8 |    *    * 2304 |  0   1   1
---------------------+-----+------+----------+------------+------------+------------+------------+----------------+-----------
o3o3o *b3o3o3o3o3x . ♦  16 |  112 |  448   0 |  1120    0 |  1792    0 |  1792    0 |  1024    0 |  128  128    0 | 18   *   *
o3o . *b3o3o3o3o3x3o ♦  36 |  252 |  504  84 |   630  126 |   504  126 |   252   84 |    72   36 |    9    0    9 |  * 256   *
. o3o *b3o3o3o3o3x3o ♦  36 |  252 |  504  84 |   630  126 |   504  126 |   252   84 |    72   36 |    0    9    9 |  *   * 256