Acronym hede
Name demi-dekeract,
Gosset polytope 17,1
Circumradius sqrt(5)/2 = 1.118034
Coordinates (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all even permutations, all even changes of sign
Confer
general polytopal classes:
Coxeter-Elte-Gosset polytopes  

Incidence matrix according to Dynkin symbol

x3o3o *b3o3o3o3o3o3o3o

. . .    . . . . . . . | 512     45 |   360 |   120    840 |  210   1260 |  252   1260 |  210   840 | 120   360 |  45   90 | 10  10
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x . .    . . . . . . . |   2 | 11520     16 |     8     56 |   28    112 |   56    140 |   70   112 |  56    56 |  28   16 |  8   2
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o .    . . . . . . . |   3 |     3 | 61440 |     1      7 |    7     21 |   21     35 |   35    35 |  35    21 |  21    7 |  7   1
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o3o    . . . . . . .    4 |     6 |     4 | 15360      *     7      0 |   21      0 |   35     0 |  35     0 |  21    0 |  7   0
x3o . *b3o . . . . . .    4 |     6 |     4 |     * 107520 |    1      6 |    6     15 |   15    20 |  20    15 |  15    6 |  6   1
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o3o *b3o . . . . . .    8 |    24 |    32 |     8      8 | 7680      *     6      0 |   15     0 |  20     0 |  15    0 |  6   0
x3o . *b3o3o . . . . .    5 |    10 |    10 |     0      5 |    * 129024 |    1      5 |    5    10 |  10    10 |  10    5 |  5   1
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o3o *b3o3o . . . . .   16 |    80 |   160 |    40     80 |   10     16 | 8064      *     5     0 |  10     0 |  10    0 |  5   0
x3o . *b3o3o3o . . . .    6 |    15 |    20 |     0     15 |    0      6 |    * 107520 |    1     4 |   4     6 |   6    4 |  4   1
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o3o *b3o3o3o . . . .   32 |   240 |   640 |   160    480 |   60    192 |   12     32 | 3360     *    4     0 |   6    0 |  4   0
x3o . *b3o3o3o3o . . .    7 |    21 |    35 |     0     35 |    0     21 |    0      7 |    * 61440 |   1     3 |   3    3 |  3   1
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o3o *b3o3o3o3o . . .   64 |   672 |  2240 |   560   2240 |  280   1344 |   84    448 |   14    64 | 960     * |   3    0 |  3   0
x3o . *b3o3o3o3o3o . .    8 |    28 |    56 |     0     70 |    0     56 |    0     28 |    0     8 |   * 23040 |   1    2 |  2   1
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o3o *b3o3o3o3o3o . .  128 |  1792 |  7168 |  1792   8960 | 1120   7168 |  448   3584 |  112  1024 |  16   128 | 180    * |  2   0
x3o . *b3o3o3o3o3o3o .    9 |    36 |    84 |     0    126 |    0    126 |    0     84 |    0    36 |   0     9 |   * 5120 |  1   1
-----------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
x3o3o *b3o3o3o3o3o3o .  256 |  4608 | 21504 |  5376  32256 | 4032  32256 | 2016  21504 |  672  9216 | 144  2304 |  18  256 | 20   *
x3o . *b3o3o3o3o3o3o3o   10 |    45 |   120 |     0    210 |    0    252 |    0    210 |    0   120 |   0    45 |   0   10 |  * 512

o3o3o3o3o3o3o3o3o4s

demi( . . . . . . . . . . ) | 512     45 |   360 |   120    840 |  210   1260 |  252   1260 |  210   840 | 120   360 |  45   90 | 10  10
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . . . . . . . . o4s   |   2 | 11520     16 |     8     56 |   28    112 |   56    140 |   70   112 |  56    56 |  28   16 |  8   2
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
sefa( . . . . . . . o3o4s ) |   3 |     3 | 61440 |     1      7 |    7     21 |   21     35 |   35    35 |  35    21 |  21    7 |  7   1
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . . . . . . . o3o4s      4 |     6 |     4 | 15360      *     7      0 |   21      0 |   35     0 |  35     0 |  21    0 |  7   0
sefa( . . . . . . o3o3o4s )    4 |     6 |     4 |     * 107520 |    1      6 |    6     15 |   15    20 |  20    15 |  15    6 |  6   1
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . . . . . . o3o3o4s      8 |    24 |    32 |     8      8 | 7680      *     6      0 |   15     0 |  20     0 |  15    0 |  6   0
sefa( . . . . . o3o3o3o4s )    5 |    10 |    10 |     0      5 |    * 129024 |    1      5 |    5    10 |  10    10 |  10    5 |  5   1
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . . . . . o3o3o3o4s     16 |    80 |   160 |    40     80 |   10     16 | 8064      *     5     0 |  10     0 |  10    0 |  5   0
sefa( . . . . o3o3o3o3o4s )    6 |    15 |    20 |     0     15 |    0      6 |    * 107520 |    1     4 |   4     6 |   6    4 |  4   1
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . . . . o3o3o3o3o4s     32 |   240 |   640 |   160    480 |   60    192 |   12     32 | 3360     *    4     0 |   6    0 |  4   0
sefa( . . . o3o3o3o3o3o4s )    7 |    21 |    35 |     0     35 |    0     21 |    0      7 |    * 61440 |   1     3 |   3    3 |  3   1
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . . . o3o3o3o3o3o4s     64 |   672 |  2240 |   560   2240 |  280   1344 |   84    448 |   14    64 | 960     * |   3    0 |  3   0
sefa( . . o3o3o3o3o3o3o4s )    8 |    28 |    56 |     0     70 |    0     56 |    0     28 |    0     8 |   * 23040 |   1    2 |  2   1
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . . o3o3o3o3o3o3o4s    128 |  1792 |  7168 |  1792   8960 | 1120   7168 |  448   3584 |  112  1024 |  16   128 | 180    * |  2   0
sefa( . o3o3o3o3o3o3o3o4s )    9 |    36 |    84 |     0    126 |    0    126 |    0     84 |    0    36 |   0     9 |   * 5120 |  1   1
----------------------------+-----+-------+-------+--------------+-------------+-------------+------------+-----------+----------+-------
      . o3o3o3o3o3o3o3o4s    256 |  4608 | 21504 |  5376  32256 | 4032  32256 | 2016  21504 |  672  9216 | 144  2304 |  18  256 | 20   *
sefa( o3o3o3o3o3o3o3o3o4s )   10 |    45 |   120 |     0    210 |    0    252 |    0    210 |    0   120 |   0    45 |   0   10 |  * 512

starting figure: o3o3o3o3o3o3o3o3o4x

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