Acronym ekip
Name diacosipentacontahexazetton prism,
vertex figure of rake
Circumradius sqrt(3)/2 = 0.866025
Coordinates (1/sqrt(2), 0, 0, 0, 0, 0, 0, 0, 1/2)   & all permutations in all but last coord., all changes of sign
Confer
general polytopal classes:
segmentoyotta  

Incidence matrix according to Dynkin symbol

x x3o3o3o3o3o3o4o

. . . . . . . . . | 32 |  1  14 |  14  84 |  84  280 |  280  560 |  560  672 |  672  448 |  448 128 | 128 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x . . . . . . . . |  2 | 16   *   14   0 |  84    0 |  280    0 |  560    0 |  672    0 |  448   0 | 128 0
. x . . . . . . . |  2 |  * 224 |   1  12 |  12   60 |   60  160 |  160  240 |  240  192 |  192  64 |  64 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x x . . . . . . . |  4 |  2   2 | 112   *   12    0 |   60    0 |  160    0 |  240    0 |  192   0 |  64 0
. x3o . . . . . . |  3 |  0   3 |   * 896 |   1   10 |   10   40 |   40   80 |   80   80 |   80  32 |  32 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x x3o . . . . . .   6 |  3   6 |   3   2 | 448    *    10    0 |   40    0 |   80    0 |   80   0 |  32 0
. x3o3o . . . . .   4 |  0   6 |   0   4 |   * 2240 |    1    8 |    8   24 |   24   32 |   32  16 |  16 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x x3o3o . . . . .   8 |  4  12 |   6   8 |   4    2 | 1120    *     8    0 |   24    0 |   32   0 |  16 0
. x3o3o3o . . . .   5 |  0  10 |   0  10 |   0    5 |    * 3584 |    1    6 |    6   12 |   12   8 |   8 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x x3o3o3o . . . .  10 |  5  20 |  10  20 |  10   10 |    5    2 | 1792    *     6    0 |   12   0 |   8 0
. x3o3o3o3o . . .   6 |  0  15 |   0  20 |   0   15 |    0    6 |    * 3584 |    1    4 |    4   4 |   4 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x x3o3o3o3o . . .  12 |  6  30 |  15  40 |  20   30 |   15   12 |    6    2 | 1792    * |    4   0 |   4 0
. x3o3o3o3o3o . .   7 |  0  21 |   0  35 |   0   35 |    0   21 |    0    7 |    * 2048 |    1   2 |   2 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x x3o3o3o3o3o . .  14 |  7  42 |  21  70 |  35   70 |   35   42 |   21   14 |    7    2 | 1024   * |   2 0
. x3o3o3o3o3o3o .   8 |  0  28 |   0  56 |   0   70 |    0   56 |    0   28 |    0    8 |    * 512 |   1 1
------------------+----+--------+---------+----------+-----------+-----------+-----------+----------+------
x x3o3o3o3o3o3o .  16 |  8  56 |  28 112 |  56  140 |   70  112 |   56   56 |   28   16 |    8   2 | 256 *
. x3o3o3o3o3o3o4o  16 |  0 112 |   0 448 |   0 1120 |    0 1792 |    0 1792 |    0 1024 |    0 256 |   * 2

x o3o3o *c3o3o3o3o3x

. . . .    . . . . . | 32 |  1  14 |  14  84 |  84  280 |  280  560 |  560  672 |  672  448 |  448  64  64 |  64  64 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x . . .    . . . . . |  2 | 16   *   14   0 |  84    0 |  280    0 |  560    0 |  672    0 |  448   0   0 |  64  64 0
. . . .    . . . . x |  2 |  * 224 |   1  12 |  12   60 |   60  160 |  160  240 |  240  192 |  192  32  32 |  32  32 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x . . .    . . . . x |  4 |  2   2 | 112   *   12    0 |   60    0 |  160    0 |  240    0 |  192   0   0 |  32  32 0
. . . .    . . . o3x |  3 |  0   3 |   * 896 |   1   10 |   10   40 |   40   80 |   80   80 |   80  16  16 |  16  16 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x . . .    . . . o3x   6 |  3   6 |   3   2 | 448    *    10    0 |   40    0 |   80    0 |   80   0   0 |  16  16 0
. . . .    . . o3o3x   4 |  0   6 |   0   4 |   * 2240 |    1    8 |    8   24 |   24   32 |   32   8   8 |   8   8 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x . . .    . . o3o3x   8 |  4  12 |   6   8 |   4    2 | 1120    *     8    0 |   24    0 |   32   0   0 |   8   8 0
. . . .    . o3o3o3x   5 |  0  10 |   0  10 |   0    5 |    * 3584 |    1    6 |    6   12 |   12   4   4 |   4   4 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x . . .    . o3o3o3x  10 |  5  20 |  10  20 |  10   10 |    5    2 | 1792    *     6    0 |   12   0   0 |   4   4 0
. . . .    o3o3o3o3x   6 |  0  15 |   0  20 |   0   15 |    0    6 |    * 3584 |    1    4 |    4   2   2 |   2   2 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x . . .    o3o3o3o3x  12 |  6  30 |  15  40 |  20   30 |   15   12 |    6    2 | 1792    * |    4   0   0 |   2   2 0
. . o . *c3o3o3o3o3x   7 |  0  21 |   0  35 |   0   35 |    0   21 |    0    7 |    * 2048 |    1   1   1 |   1   1 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x . o . *c3o3o3o3o3x  14 |  7  42 |  21  70 |  35   70 |   35   42 |   21   14 |    7    2 | 1024   *   * |   1   1 0
. o3o . *c3o3o3o3o3x   8 |  0  28 |   0  56 |   0   70 |    0   56 |    0   28 |    0    8 |    * 256   * |   1   0 1
. . o3o *c3o3o3o3o3x   8 |  0  28 |   0  56 |   0   70 |    0   56 |    0   28 |    0    8 |    *   * 256 |   0   1 1
---------------------+----+--------+---------+----------+-----------+-----------+-----------+--------------+----------
x o3o . *c3o3o3o3o3x  16 |  8  56 |  28 112 |  56  140 |   70  112 |   56   56 |   28   16 |    8   2   0 | 128   * *
x . o3o *c3o3o3o3o3x  16 |  8  56 |  28 112 |  56  140 |   70  112 |   56   56 |   28   16 |    8   0   2 |   * 128 *
. o3o3o *c3o3o3o3o3x  16 |  0 112 |   0 448 |   0 1120 |    0 1792 |    0 1792 |    0 1024 |    0 128 128 |   *   * 2

xx3oo3oo3oo3oo3oo3oo4oo&#x   → height = 1
(ek || ek)

o.3o.3o.3o.3o.3o.3o.4o.    | 16  * |  14  1   0 |  84  14   0 |  280  84    0 |  560  280    0 |  672  560    0 |  448  672    0 | 128  448   0 | 1 128 0
.o3.o3.o3.o3.o3.o3.o4.o    |  * 16 |   0  1  14 |   0  14  84 |    0  84  280 |    0  280  560 |    0  560  672 |    0  672  448 |   0  448 128 | 0 128 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x. .. .. .. .. .. .. ..    |  2  0 | 112  *   * |  12   1   0 |   60  12    0 |  160   60    0 |  240  160    0 |  192  240    0 |  64  192   0 | 1  64 0
oo3oo3oo3oo3oo3oo3oo4oo&#x |  1  1 |   * 16   *    0  14   0 |    0  84    0 |    0  280    0 |    0  560    0 |    0  672    0 |   0  448   0 | 0 128 0
.x .. .. .. .. .. .. ..    |  0  2 |   *  * 112 |   0   1  12 |    0  12   60 |    0   60  160 |    0  160  240 |    0  240  192 |   0  192  64 | 0  64 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x.3o. .. .. .. .. .. ..    |  3  0 |   3  0   0 | 448   *   * |   10   1    0 |   40   10    0 |   80   40    0 |   80   80    0 |  32   80   0 | 1  32 0
xx .. .. .. .. .. .. ..&#x |  2  2 |   1  2   1 |   * 112   *     0  12    0 |    0   60    0 |    0  160    0 |    0  240    0 |   0  192   0 | 0  64 0
.x3.o .. .. .. .. .. ..    |  0  3 |   0  0   3 |   *   * 448 |    0   1   10 |    0   10   40 |    0   40   80 |    0   80   80 |   0   80  32 | 0  32 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x.3o.3o. .. .. .. .. ..      4  0 |   6  0   0 |   4   0   0 | 1120   *    * |    8    1    0 |   24    8    0 |   32   24    0 |  16   32   0 | 1  16 0
xx3oo .. .. .. .. .. ..&#x   3  3 |   3  3   3 |   1   3   1 |    * 448    *     0   10    0 |    0   40    0 |    0   80    0 |   0   80   0 | 0  32 0
.x3.o3.o .. .. .. .. ..      0  4 |   0  0   6 |   0   0   4 |    *   * 1120 |    0    1    8 |    0    8   24 |    0   24   32 |   0   32  16 | 0  16 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x.3o.3o.3o. .. .. .. ..      5  0 |  10  0   0 |  10   0   0 |    5   0    0 | 1792    *    * |    6    1    0 |   12    6    0 |   8   12   0 | 1   8 0
xx3oo3oo .. .. .. .. ..&#x   4  4 |   6  4   6 |   4   6   4 |    1   4    1 |    * 1120    *     0    8    0 |    0   24    0 |   0   32   0 | 0  16 0
.x3.o3.o3.o .. .. .. ..      0  5 |   0  0  10 |   0   0  10 |    0   0    5 |    *    * 1792 |    0    1    6 |    0    6   12 |   0   12   8 | 0   8 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x.3o.3o.3o.3o. .. .. ..      6  0 |  15  0   0 |  20   0   0 |   15   0    0 |    6    0    0 | 1792    *    * |    4    1    0 |   4    4   0 | 1   4 0
xx3oo3oo3oo .. .. .. ..&#x   5  5 |  10  5  10 |  10  10  10 |    5  10    5 |    1    5    1 |    * 1792    *     0    6    0 |   0   12   0 | 0   8 0
.x3.o3.o3.o3.o .. .. ..      0  6 |   0  0  15 |   0   0  20 |    0   0   15 |    0    0    6 |    *    * 1792 |    0    1    4 |   0    4   4 | 0   4 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x.3o.3o.3o.3o.3o. .. ..      7  0 |  21  0   0 |  35   0   0 |   35   0    0 |   21    0    0 |    7    0    0 | 1024    *    * |   2    1   0 | 1   2 0
xx3oo3oo3oo3oo .. .. ..&#x   6  6 |  15  6  15 |  20  15  20 |   15  20   15 |    6   15    6 |    1    6    1 |    * 1792    * |   0    4   0 | 0   4 0
.x3.o3.o3.o3.o3.o .. ..      0  7 |   0  0  21 |   0   0  35 |    0   0   35 |    0    0   21 |    0    0    7 |    *    * 1024 |   0    1   2 | 0   2 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x.3o.3o.3o.3o.3o.3o. ..      8  0 |  28  0   0 |  56   0   0 |   70   0    0 |   56    0    0 |   28    0    0 |    8    0    0 | 256    *   * | 1   1 0
xx3oo3oo3oo3oo3oo .. ..&#x   7  7 |  21  7  21 |  35  21  35 |   35  35   35 |   21   35   21 |    7   21    7 |    1    7    1 |   * 1024   * | 0   2 0
.x3.o3.o3.o3.o3.o3.o ..      0  8 |   0  0  28 |   0   0  56 |    0   0   70 |    0    0   56 |    0    0   28 |    0    0    8 |   *    * 256 | 0   1 1
---------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+--------------+--------
x.3o.3o.3o.3o.3o.3o.4o.     16  0 | 112  0   0 | 448   0   0 | 1120   0    0 | 1792    0    0 | 1792    0    0 | 1024    0    0 | 256    0   0 | 1   * *
xx3oo3oo3oo3oo3oo3oo ..&#x   8  8 |  28  8  28 |  56  28  56 |   70  56   70 |   56   70   56 |   28   56   28 |    8   28    8 |   1    8   1 | * 256 *
.x3.o3.o3.o3.o3.o3.o4.o      0 16 |   0  0 112 |   0   0 448 |    0   0 1120 |    0    0 1792 |    0    0 1792 |    0    0 1024 |   0    0 256 | *   * 1

oo3oo3oo *b3oo3oo3oo3oo3xx&#x   → height = 1
(ek || ek)

o.3o.3o. *b3o.3o.3o.3o.3o.    | 16  * |  14  1   0 |  84  14   0 |  280  84    0 |  560  280    0 |  672  560    0 |  448  672    0 |  64  64  448   0   0 | 1  64  64 0
.o3.o3.o *b3.o3.o3.o3.o3.o    |  * 16 |   0  1  14 |   0  14  84 |    0  84  280 |    0  280  560 |    0  560  672 |    0  672  448 |   0   0  448  64  64 | 0  64  64 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
.. .. ..    .. .. .. .. x.    |  2  0 | 112  *   * |  12   1   0 |   60  12    0 |  160   60    0 |  240  160    0 |  192  240    0 |  32  32  192   0   0 | 1  32  32 0
oo3oo3oo *b3oo3oo3oo3oo3oo&#x |  1  1 |   * 16   *    0  14   0 |    0  84    0 |    0  280    0 |    0  560    0 |    0  672    0 |   0   0  448   0   0 | 0  64  64 0
.. .. ..    .. .. .. .. .x    |  0  2 |   *  * 112 |   0   1  12 |    0  12   60 |    0   60  160 |    0  160  240 |    0  240  192 |   0   0  192  32  32 | 0  32  32 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
.. .. ..    .. .. .. o.3x.    |  3  0 |   3  0   0 | 448   *   * |   10   1    0 |   40   10    0 |   80   40    0 |   80   80    0 |  16  16   80   0   0 | 1  16  16 0
.. .. ..    .. .. .. .. xx&#x |  2  2 |   1  2   1 |   * 112   *     0  12    0 |    0   60    0 |    0  160    0 |    0  240    0 |   0   0  192   0   0 | 0  32  32 0
.. .. ..    .. .. .. .o3.x    |  0  3 |   0  0   3 |   *   * 448 |    0   1   10 |    0   10   40 |    0   40   80 |    0   80   80 |   0   0   80  16  16 | 0  16  16 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
.. .. ..    .. .. o.3o.3x.      4  0 |   6  0   0 |   4   0   0 | 1120   *    * |    8    1    0 |   24    8    0 |   32   24    0 |   8   8   32   0   0 | 1   8   8 0
.. .. ..    .. .. .. oo3xx&#x   3  3 |   3  3   3 |   1   3   1 |    * 448    *     0   10    0 |    0   40    0 |    0   80    0 |   0   0   80   0   0 | 0  16  16 0
.. .. ..    .. .. .o3.o3.x      0  4 |   0  0   6 |   0   0   4 |    *   * 1120 |    0    1    8 |    0    8   24 |    0   24   32 |   0   0   32   8   8 | 0   8   8 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
.. .. ..    .. o.3o.3o.3x.      5  0 |  10  0   0 |  10   0   0 |    5   0    0 | 1792    *    * |    6    1    0 |   12    6    0 |   4   4   12   0   0 | 1   4   4 0
.. .. ..    .. .. oo3oo3xx&#x   4  4 |   6  4   6 |   4   6   4 |    1   4    1 |    * 1120    *     0    8    0 |    0   24    0 |   0   0   32   0   0 | 0   8   8 0
.. .. ..    .. .o3.o3.o3.x      0  5 |   0  0  10 |   0   0  10 |    0   0    5 |    *    * 1792 |    0    1    6 |    0    6   12 |   0   0   12   4   4 | 0   4   4 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
.. .. ..    o.3o.3o.3o.3x.      6  0 |  15  0   0 |  20   0   0 |   15   0    0 |    6    0    0 | 1792    *    * |    4    1    0 |   2   2    4   0   0 | 1   2   2 0
.. .. ..    .. oo3oo3oo3xx&#x   5  5 |  10  5  10 |  10  10  10 |    5  10    5 |    1    5    1 |    * 1792    *     0    6    0 |   0   0   12   0   0 | 0   4   4 0
.. .. ..    .o3.o3.o3.o3.x      0  6 |   0  0  15 |   0   0  20 |    0   0   15 |    0    0    6 |    *    * 1792 |    0    1    4 |   0   0    4   2   2 | 0   2   2 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
.. o. .. *b3o.3o.3o.3o.3x.      7  0 |  21  0   0 |  35   0   0 |   35   0    0 |   21    0    0 |    7    0    0 | 1024    *    * |   1   1    1   0   0 | 1   1   1 0
.. .. ..    oo3oo3oo3oo3xx&#x   6  6 |  15  6  15 |  20  15  20 |   15  20   15 |    6   15    6 |    1    6    1 |    * 1792    * |   0   0    4   0   0 | 0   2   2 0
.. .o .. *b3.o3.o3.o3.o3.x      0  7 |   0  0  21 |   0   0  35 |    0   0   35 |    0    0   21 |    0    0    7 |    *    * 1024 |   0   0    1   1   1 | 0   1   1 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
o.3o. .. *b3o.3o.3o.3o.3x.      8  0 |  28  0   0 |  56   0   0 |   70   0    0 |   56    0    0 |   28    0    0 |    8    0    0 | 128   *    *   *   * | 1   1   0 0
.. o.3o. *b3o.3o.3o.3o.3x.      8  0 |  28  0   0 |  56   0   0 |   70   0    0 |   56    0    0 |   28    0    0 |    8    0    0 |   * 128    *   *   * | 1   0   1 0
.. oo .. *b3oo3oo3oo3oo3xx&#x   7  7 |  21  7  21 |  35  21  35 |   35  35   35 |   21   35   21 |    7   21    7 |    1    7    1 |   *   * 1024   *   * | 0   1   1 0
.o3.o .. *b3.o3.o3.o3.o3.x      0  8 |   0  0  28 |   0   0  56 |    0   0   70 |    0    0   56 |    0    0   28 |    0    0    8 |   *   *    * 128   * | 0   1   0 1
.. .o3.o *b3.o3.o3.o3.o3.x      0  8 |   0  0  28 |   0   0  56 |    0   0   70 |    0    0   56 |    0    0   28 |    0    0    8 |   *   *    *   * 128 | 0   0   1 1
------------------------------+-------+------------+-------------+---------------+----------------+----------------+----------------+----------------------+------------
o.3o.3o. *b3o.3o.3o.3o.3x.     16  0 | 112  0   0 | 448   0   0 | 1120   0    0 | 1792    0    0 | 1792    0    0 | 1024    0    0 | 128 128    0   0   0 | 1   *   * *
oo3oo .. *b3oo3oo3oo3oo3xx&#x   8  8 |  28  8  28 |  56  28  56 |   70  56   70 |   56   70   56 |   28   56   28 |    8   28    8 |   1   0    8   1   0 | * 128   * *
.. oo3oo *b3oo3oo3oo3oo3xx&#x   8  8 |  28  8  28 |  56  28  56 |   70  56   70 |   56   70   56 |   28   56   28 |    8   28    8 |   0   1    8   0   1 | *   * 128 *
.o3.o3.o *b3.o3.o3.o3.o3.x      0 16 |   0  0 112 |   0   0 448 |    0   0 1120 |    0    0 1792 |    0    0 1792 |    0    0 1024 |   0   0    0 128 128 | *   *   * 1

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