Acronym rake
Name rectified chilliaicositetraxennon,
lattice B10 contact polytope (span of its small roots),
lattice D10 contact polytope (span of its roots)
Circumradius 1
Inradius
wrt. vee 		1/sqrt(2) = 0.707107
Inradius
wrt. reday 		1/sqrt(5) = 0.447214
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume 169/18900 = 0.0089418
Surface [5 sqrt(2)+502 sqrt(5)]/5760 = 0.199220
Dihedral angles
  • at rene between reday and reday:   arccos(-4/5) = 143.130102°
  • at ene between reday and vee:   arccos[-1/sqrt(10)] = 108.434949°
Face vector 180, 2880, 14400, 43680, 88704, 120960, 107520, 57600, 15360, 1044
Confer
general polytopal classes:
Wythoffian polyxenna  
analogs:
rectified orthoplex rOn  
External
links 		wikipedia  

Incidence matrix according to Dynkin symbol

o3x3o3o3o3o3o3o3o4o

. . . . . . . . . . | 180 ♦   32 |  16   224 |  112   896 |  448  2240 |  1120   3584 |  1792  3584 |  1792  2048 | 1024   512 |  256  2
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
. x . . . . . . . . |   2 | 2880 |   1    14 |   14    84 |   84   280 |   280    560 |   560   672 |   672   448 |  448   128 |  128  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x . . . . . . . . |   3 |    3 | 960     * ♦   14     0 |   84     0 |   280      0 |   560     0 |   672     0 |  448     0 |  128  0
. x3o . . . . . . . |   3 |    3 |   * 13440 |    1    12 |   12    60 |    60    160 |   160   240 |   240   192 |  192    64 |   64  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x3o . . . . . . . ♦   6 |   12 |   4     4 | 3360     * ♦   12     0 |    60      0 |   160     0 |   240     0 |  192     0 |   64  0
. x3o3o . . . . . . ♦   4 |    6 |   0     4 |    * 40320 |    1    10 |    10     40 |    40    80 |    80    80 |   80    32 |   32  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x3o3o . . . . . . ♦  10 |   30 |  10    20 |    5     5 | 8064     * ♦    10      0 |    40     0 |    80     0 |   80     0 |   32  0
. x3o3o3o . . . . . ♦   5 |   10 |   0    10 |    0     5 |    * 80640 |     1      8 |     8    24 |    24    32 |   32    16 |   16  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x3o3o3o . . . . . ♦  15 |   60 |  20    60 |   15    30 |    6     6 | 13440      * ♦     8     0 |    24     0 |   32     0 |   16  0
. x3o3o3o3o . . . . ♦   6 |   15 |   0    20 |    0    15 |    0     6 |     * 107520 |     1     6 |     6    12 |   12     8 |    8  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x3o3o3o3o . . . . ♦  21 |  105 |  35   140 |   35   105 |   21    42 |     7      7 | 15360     * ♦     6     0 |   12     0 |    8  0
. x3o3o3o3o3o . . . ♦   7 |   21 |   0    35 |    0    35 |    0    21 |     0      7 |     * 92160 |     1     4 |    4     4 |    4  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x3o3o3o3o3o . . . ♦  28 |  168 |  56   280 |   70   280 |   56   168 |    28     56 |     8     8 | 11520     * |    4     0 |    4  0
. x3o3o3o3o3o3o . . ♦   8 |   28 |   0    56 |    0    70 |    0    56 |     0     28 |     0     8 |     * 46080 |    1     2 |    2  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x3o3o3o3o3o3o . . ♦  36 |  252 |  84   504 |  126   630 |  126   504 |    84    252 |    36    72 |     9     9 | 5120     * |    2  0
. x3o3o3o3o3o3o3o . ♦   9 |   36 |   0    84 |    0   126 |    0   126 |     0     84 |     0    36 |     0     9 |    * 10240 |    1  1
--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------
o3x3o3o3o3o3o3o3o . ♦  45 |  360 | 120   840 |  210  1260 |  252  1260 |   210    840 |   120   360 |    45    90 |   10    10 | 1024  *
. x3o3o3o3o3o3o3o4o ♦  18 |  144 |   0   672 |    0  2016 |    0  4032 |     0   5376 |     0  4608 |     0  2304 |    0   512 |    * 20


o3o3o *b3o3o3o3o3o3x3o

. . .    . . . . . . . | 180 ♦   32 |   224  16 |   896  112 |  2240  448 |   3584  1120 |  3584  1792 |  2048  1792 |  256  256 1024 |  2 128 128
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
. . .    . . . . . x . |   2 | 2880 |    14   1 |    84   14 |   280   84 |    560   280 |   672   560 |   448   672 |   64   64  448 |  1  64  64
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
. . .    . . . . o3x . |   3 |    3 | 13440   * |    12    1 |    60   12 |    160    60 |   240   160 |   192   240 |   32   32  192 |  1  32  32
. . .    . . . . . x3o |   3 |    3 |     * 960 ♦     0   14 |     0   84 |      0   280 |     0   560 |     0   672 |    0    0  448 |  0  64  64
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
. . .    . . . o3o3x . ♦   4 |    6 |     4   0 | 40320    * |    10    1 |     40    10 |    80    40 |    80    80 |   16   16   80 |  1  16  16
. . .    . . . . o3x3o ♦   6 |   12 |     4   4 |     * 3360 ♦     0   12 |      0    60 |     0   160 |     0   240 |    0    0  192 |  0  32  32
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
. . .    . . o3o3o3x . ♦   5 |   10 |    10   0 |     5    0 | 80640    * |      8     1 |    24     8 |    32    24 |    8    8   32 |  1   8   8
. . .    . . . o3o3x3o ♦  10 |   30 |    20  10 |     5    5 |     * 8064 ♦      0    10 |     0    40 |     0    80 |    0    0   80 |  0  16  16
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
. . .    . o3o3o3o3x . ♦   6 |   15 |    20   0 |    15    0 |     6    0 | 107520     * |     6     1 |    12     6 |    4    4   12 |  1   4   4
. . .    . . o3o3o3x3o ♦  15 |   60 |    60  20 |    30   15 |     6    6 |      * 13440 ♦     0     8 |     0    24 |    0    0   32 |  0   8   8
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
. . .    o3o3o3o3o3x . ♦   7 |   21 |    35   0 |    35    0 |    21    0 |      7     0 | 92160     * |     4     1 |    2    2    4 |  1   2   2
. . .    . o3o3o3o3x3o ♦  21 |  105 |   140  35 |   105   35 |    42   21 |      7     7 |     * 15360 ♦     0     6 |    0    0   12 |  0   4   4
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
. o . *b3o3o3o3o3o3x . ♦   8 |   28 |    56   0 |    70    0 |    56    0 |     28     0 |     8     0 | 46080     * |    1    1    1 |  1   1   1
. . .    o3o3o3o3o3x3o ♦  28 |  168 |   280  56 |   280   70 |   168   56 |     56    28 |     8     8 |     * 11520 |    0    0    4 |  0   2   2
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
o3o . *b3o3o3o3o3o3x . ♦   9 |   36 |    84   0 |   126    0 |   126    0 |     84     0 |    36     0 |     9     0 | 5120    *    * |  1   1   0
. o3o *b3o3o3o3o3o3x . ♦   9 |   36 |    84   0 |   126    0 |   126    0 |     84     0 |    36     0 |     9     0 |    * 5120    * |  1   0   1
. o . *b3o3o3o3o3o3x3o ♦  36 |  252 |   504  84 |   630  126 |   504  126 |    252    84 |    72    36 |     9     9 |    *    * 5120 |  0   1   1
-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------
o3o3o *b3o3o3o3o3o3x . ♦  18 |  144 |   672   0 |  2016    0 |  4032    0 |   5376     0 |  4608     0 |  2304     0 |  256  256    0 | 20   *   *
o3o . *b3o3o3o3o3o3x3o ♦  45 |  360 |   840 120 |  1260  210 |  1260  252 |    840   210 |   360   120 |    90    45 |   10    0   10 |  * 512   *
. o3o *b3o3o3o3o3o3x3o ♦  45 |  360 |   840 120 |  1260  210 |  1260  252 |    840   210 |   360   120 |    90    45 |    0   10   10 |  *   * 512

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