Acronym henne
Name demi-enneract,
Gosset polytope 16,1
Circumradius sqrt(9/8) = 1.060660
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))   & all even permutations, all even changes of sign
Confer
general polytopal classes:
segmentoyotta   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  

Incidence matrix according to Dynkin symbol

x3o3o *b3o3o3o3o3o3o

. . .    . . . . . . | 256    36 |   252 |   84   504 |  126   630 |  126   504 |  84  252 |  36   72 |  9   9
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x . .    . . . . . . |   2 | 4608     14 |    7    42 |   21    70 |   35    70 |  35   42 |  21   14 |  7   2
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x3o .    . . . . . . |   3 |    3 | 21504 |    1     6 |    6    15 |   15    20 |  20   15 |  15    6 |  6   1
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x3o3o    . . . . . .    4 |    6 |     4 | 5376     *     6     0 |   15     0 |  20    0 |  15    0 |  6   0
x3o . *b3o . . . . .    4 |    6 |     4 |    * 32256 |    1     5 |    5    10 |  10   10 |  10    5 |  5   1
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x3o3o *b3o . . . . .    8 |   24 |    32 |    8     8 | 4032     *     5     0 |  10    0 |  10    0 |  5   0
x3o . *b3o3o . . . .    5 |   10 |    10 |    0     5 |    * 32256 |    1     4 |   4    6 |   6    4 |  4   1
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x3o3o *b3o3o . . . .   16 |   80 |   160 |   40    80 |   10    16 | 2016     *    4    0 |   6    0 |  4   0
x3o . *b3o3o3o . . .    6 |   15 |    20 |    0    15 |    0     6 |    * 21504 |   1    3 |   3    3 |  3   1
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x3o3o *b3o3o3o . . .   32 |  240 |   640 |  160   480 |   60   192 |   12    32 | 672    * |   3    0 |  3   0
x3o . *b3o3o3o3o . .    7 |   21 |    35 |    0    35 |    0    21 |    0     7 |   * 9216 |   1    2 |  2   1
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x3o3o *b3o3o3o3o . .   64 |  672 |  2240 |  560  2240 |  280  1344 |   84   448 |  14   64 | 144    * |  2   0
x3o . *b3o3o3o3o3o .    8 |   28 |    56 |    0    70 |    0    56 |    0    28 |   0    8 |   * 2304 |  1   1
---------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
x3o3o *b3o3o3o3o3o .  128 | 1792 |  7168 | 1792  8960 | 1120  7168 |  448  3584 | 112 1024 |  16  128 | 18   *
x3o . *b3o3o3o3o3o3o    9 |   36 |    84 |    0   126 |    0   126 |    0    84 |   0   36 |   0    9 |  * 256

o3o3o3o3o3o3o3o4s

demi( . . . . . . . . . ) | 256    36 |   252 |   84   504 |  126   630 |  126   504 |  84  252 |  36   72 |  9   9 
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
      . . . . . . . o4s   |   2 | 4608     14 |    7    42 |   21    70 |   35    70 |  35   42 |  21   14 |  7   2
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
sefa( . . . . . . o3o4s ) |   3 |    3 | 21504 |    1     6 |    6    15 |   15    20 |  20   15 |  15    6 |  6   1
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
      . . . . . . o3o4s      4 |    6 |     4 | 5376     *     6     0 |   15     0 |  20    0 |  15    0 |  6   0
sefa( . . . . . o3o3o4s )    4 |    6 |     4 |    * 32256 |    1     5 |    5    10 |  10   10 |  10    5 |  5   1
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
      . . . . . o3o3o4s      8 |   24 |    32 |    8     8 | 4032     *     5     0 |  10    0 |  10    0 |  5   0
sefa( . . . . o3o3o3o4s )    5 |   10 |    10 |    0     5 |    * 32256 |    1     4 |   4    6 |   6    4 |  4   1
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
      . . . . o3o3o3o4s     16 |   80 |   160 |   40    80 |   10    16 | 2016     *    4    0 |   6    0 |  4   0
sefa( . . . o3o3o3o3o4s )    6 |   15 |    20 |    0    15 |    0     6 |    * 21504 |   1    3 |   3    3 |  3   1
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
      . . . o3o3o3o3o4s     32 |  240 |   640 |  160   480 |   60   192 |   12    32 | 672    * |   3    0 |  3   0
sefa( . . o3o3o3o3o3o4s )    7 |   21 |    35 |    0    35 |    0    21 |    0     7 |   * 9216 |   1    2 |  2   1
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
      . . o3o3o3o3o3o4s     64 |  672 |  2240 |  560  2240 |  280  1344 |   84   448 |  14   64 | 144    * |  2   0
sefa( . o3o3o3o3o3o3o4s )    8 |   28 |    56 |    0    70 |    0    56 |    0    28 |   0    8 |   * 2304 |  1   1
--------------------------+-----+------+-------+------------+------------+------------+----------+----------+-------
      . o3o3o3o3o3o3o4s    128 | 1792 |  7168 | 1792  8960 | 1120  7168 |  448  3584 | 112 1024 |  16  128 | 18   *
sefa( o3o3o3o3o3o3o3o4s )    9 |   36 |    84 |    0   126 |    0   126 |    0    84 |   0   36 |   0    9 |  * 256

starting figure: o3o3o3o3o3o3o3o4x

xo3oo3ox *b3oo3oo3oo3oo3oo&#x   → height = 1/sqrt(2) = 0.707107
(hocto || alternate hocto)

o.3o.3o. *b3o.3o.3o.3o.3o.    & | 256    28    8 |   168   84 |   56   280   224   28 |   70   280   56   350 |  56  168   70   336 |  28   56  56  196 |  8   8  28   64 | 1  8   9
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x. .. ..    .. .. .. .. ..    & |   2 | 3584    *     12    2 |    6    30    12    1 |   15    40    6    30 |  20   30   15    40 |  15   12  20   30 |  6   2  15   12 | 1  6   2
oo3oo3oo *b3oo3oo3oo3oo3oo&#x   |   2 |    * 1024      0   14 |    0     0    42    7 |    0     0   21    70 |   0    0   35    70 |   0    0  35   42 |  0   0  21   14 | 0  7   2
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x.3o. ..    .. .. .. .. ..    & |   3 |    3    0 | 14336    * |    1     5     1    0 |    5    10    1     5 |  10   10    5    10 |  10    5  10   10 |  5   1  10    5 | 1  5   1
xo .. ..    .. .. .. .. ..&#x & |   3 |    1    2 |     * 7168 |    0     0     6    1 |    0     0    6    15 |   0    0   15    20 |   0    0  20   15 |  0   0  15    6 | 0  6   1
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x.3o.3o.    .. .. .. .. ..    &    4 |    6    0 |     4    0 | 3584     *     *    *     5     0    1     0 |  10    0    5     0 |  10    0  10    0 |  5   0  10    0 | 1  5   0
x.3o. .. *b3o. .. .. .. ..    &    4 |    6    0 |     4    0 |    * 17920     *    * |    1     4    0     1 |   4    6    1     4 |   6    4   4    6 |  4   1   6    4 | 1  4   1
xo3oo ..    .. .. .. .. ..&#x &    4 |    3    3 |     1    3 |    *     * 14336    * |    0     0    1     5 |   0    0    5    10 |   0    0  10   10 |  0   0  10    5 | 0  5   1
xo .. ox    .. .. .. .. ..&#x      4 |    2    4 |     0    4 |    *     *     * 1792     0     0    6     0 |   0    0   15     0 |   0    0  20    0 |  0   0  15    0 | 0  6   0
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x.3o.3o. *b3o. .. .. .. ..    &    8 |   24    0 |    32    0 |    8     8     0    0 | 2240     *    *     *    4    0    1     0 |   6    0   4    0 |  4   0   6    0 | 1  4   0
x.3o. .. *b3o.3o. .. .. ..    &    5 |   10    0 |    10    0 |    0     5     0    0 |    * 14336    *     * |   1    3    0     1 |   3    3   1    3 |  3   1   3    3 | 1  3   1
xo3oo3ox    .. .. .. .. ..&#x      8 |   12   12 |     8   24 |    2     0     8    6 |    *     * 1792     *    0    0    5     0 |   0    0  10    0 |  0   0  10    0 | 0  5   0
xo3oo .. *b3oo .. .. .. ..&#x &    5 |    6    4 |     4    6 |    0     1     4    0 |    *     *    * 17920 |   0    0    1     4 |   0    0   4    6 |  0   0   6    4 | 0  4   1
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x.3o.3o. *b3o.3o. .. .. ..    &   16 |   80    0 |   160    0 |   40    80     0    0 |   10    16    0     0 | 896    *    *     *    3    0   1    0 |  3   0   3    0 | 1  3   0
x.3o. .. *b3o.3o.3o. .. ..    &    6 |   15    0 |    20    0 |    0    15     0    0 |    0     6    0     0 |   * 7168    *     * |   1    2   0    1 |  2   1   1    2 | 1  2   1
xo3oo3ox *b3oo .. .. .. ..&#x     16 |   48   32 |    64   96 |   16    16    64   24 |    2     0    8    16 |   *    * 1120     *    0    0   4    0 |  0   0   6    0 | 0  4   0
xo3oo .. *b3oo3oo .. .. ..&#x &    6 |   10    5 |    10   10 |    0     5    10    0 |    0     1    0     5 |   *    *    * 14336 |   0    0   1    3 |  0   0   3    3 | 0  3   1
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x.3o.3o. *b3o.3o.3o. .. ..    &   32 |  240    0 |   640    0 |  160   480     0    0 |   60   192    0     0 |  12   32    0     0 | 224    *   *    * |  2   0   1    0 | 1  2   0
x.3o. .. *b3o.3o.3o.3o. ..    &    7 |   21    0 |    35    0 |    0    35     0    0 |    0    21    0     0 |   0    7    0     0 |   * 2048   *    * |  1   1   0    1 | 1  1   1
xo3oo3ox *b3oo3oo .. .. ..&#x     32 |  160   80 |   320  320 |   80   160   320   80 |   20    32   40   160 |   2    0   10    32 |   *    * 448    * |  0   0   3    0 | 0  3   0
xo3oo .. *b3oo3oo3oo .. ..&#x &    7 |   15    6 |    20   15 |    0    15    20    0 |    0     6    0    15 |   0    1    0     6 |   *    *   * 7168 |  0   0   1    2 | 0  2   1
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x.3o.3o. *b3o.3o.3o.3o. ..    &   64 |  672    0 |  2240    0 |  560  2240     0    0 |  280  1344    0     0 |  84  448    0     0 |  14   64   0    0 | 32   *   *    * | 1  1   0
x.3o. .. *b3o.3o.3o.3o.3o.    &    8 |   28    0 |    56    0 |    0    70     0    0 |    0    56    0     0 |   0   28    0     0 |   0    8   0    0 |  * 256   *    * | 1  0   1
xo3oo3ox *b3oo3oo3oo .. ..&#x     64 |  480  192 |  1280  960 |  320   960  1280  240 |  120   384  160   960 |  24   64   60   384 |   2    0  12   64 |  *   * 112    * | 0  2   0
xo3oo .. *b3oo3oo3oo3oo ..&#x &    8 |   21    7 |    35   21 |    0    35    35    0 |    0    21    0    35 |   0    7    0    21 |   0    1   0    7 |  *   *   * 2048 | 0  1   1
--------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+---------
x.3o.3o. *b3o.3o.3o.3o.3o.    &  128 | 1792    0 |  7168    0 | 1792  8960     0    0 | 1120  7168    0     0 | 448 3584    0     0 | 112 1024   0    0 | 16 128   0    0 | 2  *   *
xo3oo3ox *b3oo3oo3oo3oo ..&#x    128 | 1344  448 |  4480 2688 | 1120  4480  4480  672 |  560  2688  560  4480 | 168  896  280  2688 |  28  128  84  896 |  2   0  14  128 | * 16   *
xo3oo .. *b3oo3oo3oo3oo3oo&#x &    9 |   28    8 |    56   28 |    0    70    56    0 |    0    56    0    70 |   0   28    0    56 |   0    8   0   28 |  0   1   0    8 | *  * 256

ooooo3oxooo3ooooo3ooxoo3ooooo3oooxo3ooooo3oooox&#xt   → all heights = sqrt(2)/3 = 0.471405
(pt || pseudo rene || pseudo trene || pseudo inv. brene || dual ene)

... 

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