Acronym zeep Name hecatonicosoctaexon prism,vertex figure of riv Circumradius sqrt(3)/2 = 0.866025 Coordinates (1/sqrt(2), 0, 0, 0, 0, 0, 0, 1/2)   & all permutations in all but last coord., all changes of sign Volume sqrt(2)/630 = 0.0022448 Confer general polytopal classes: segmentozetta

Incidence matrix according to Dynkin symbol

```x x3o3o3o3o3o4o

. . . . . . . . | 28 |  1  12 | 12  60 |  60  160 | 160  240 | 240 192 | 192  64 |  64 1
----------------+----+--------+--------+----------+----------+---------+---------+------
x . . . . . . . |  2 | 14   * ♦ 12   0 |  60    0 | 160    0 | 240   0 | 192   0 |  64 0
. x . . . . . . |  2 |  * 168 |  1  10 |  10   40 |  40   80 |  80  80 |  80  32 |  32 1
----------------+----+--------+--------+----------+----------+---------+---------+------
x x . . . . . . |  4 |  2   2 | 84   * ♦  10    0 |  40    0 |  80   0 |  80   0 |  32 0
. x3o . . . . . |  3 |  0   3 |  * 560 |   1    8 |   8   24 |  24  32 |  32  16 |  16 1
----------------+----+--------+--------+----------+----------+---------+---------+------
x x3o . . . . . ♦  6 |  3   6 |  3   2 | 280    * ♦   8    0 |  24   0 |  32   0 |  16 0
. x3o3o . . . . ♦  4 |  0   6 |  0   4 |   * 1120 |   1    6 |   6  12 |  12   8 |   8 1
----------------+----+--------+--------+----------+----------+---------+---------+------
x x3o3o . . . . ♦  8 |  4  12 |  6   8 |   4    2 | 560    * ♦   6   0 |  12   0 |   8 0
. x3o3o3o . . . ♦  5 |  0  10 |  0  10 |   0    5 |   * 1344 |   1   4 |   4   4 |   4 1
----------------+----+--------+--------+----------+----------+---------+---------+------
x x3o3o3o . . . ♦ 10 |  5  20 | 10  20 |  10   10 |   5    2 | 672   * |   4   0 |   4 0
. x3o3o3o3o . . ♦  6 |  0  15 |  0  20 |   0   15 |   0    6 |   * 896 |   1   2 |   2 1
----------------+----+--------+--------+----------+----------+---------+---------+------
x x3o3o3o3o . . ♦ 12 |  6  30 | 15  40 |  20   30 |  15   12 |   6   2 | 448   * |   2 0
. x3o3o3o3o3o . ♦  7 |  0  21 |  0  35 |   0   35 |   0   21 |   0   7 |   * 256 |   1 1
----------------+----+--------+--------+----------+----------+---------+---------+------
x x3o3o3o3o3o . ♦ 14 |  7  42 | 21  70 |  35   70 |  35   42 |  21  14 |   7   2 | 128 *
. x3o3o3o3o3o4o ♦ 14 |  0  84 |  0 280 |   0  560 |   0  672 |   0 448 |   0 128 |   * 2
```

```x o3o3o *c3o3o3o3x
. . . .    . . . . | 28 |  1  12 | 12  60 |  60  160 | 160  240 | 240 192 | 192  32  32 | 32 32 1
-------------------+----+--------+--------+----------+----------+---------+-------------+--------
x . . .    . . . . |  2 | 14   * ♦ 12   0 |  60    0 | 160    0 | 240   0 | 192   0   0 | 32 32 0
. . . .    . . . x |  2 |  * 168 |  1  10 |  10   40 |  40   80 |  80  80 |  80  16  16 | 16 16 1
-------------------+----+--------+--------+----------+----------+---------+-------------+--------
x . . .    . . . x |  4 |  2   2 | 84   * ♦  10    0 |  40    0 |  80   0 |  80   0   0 | 16 16 0
. . . .    . . o3x |  3 |  0   3 |  * 560 |   1    8 |   8   24 |  24  32 |  32   8   8 |  8  8 1
-------------------+----+--------+--------+----------+----------+---------+-------------+--------
x . . .    . . o3x ♦  6 |  3   6 |  3   2 | 280    * ♦   8    0 |  24   0 |  32   0   0 |  8  8 0
. . . .    . o3o3x ♦  4 |  0   6 |  0   4 |   * 1120 |   1    6 |   6  12 |  12   4   4 |  4  4 1
-------------------+----+--------+--------+----------+----------+---------+-------------+--------
x . . .    . o3o3x ♦  8 |  4  12 |  6   8 |   4    2 | 560    * ♦   6   0 |  12   0   0 |  4  4 0
. . . .    o3o3o3x ♦  5 |  0  10 |  0  10 |   0    5 |   * 1344 |   1   4 |   4   2   2 |  2  2 1
-------------------+----+--------+--------+----------+----------+---------+-------------+--------
x . . .    o3o3o3x ♦ 10 |  5  20 | 10  20 |  10   10 |   5    2 | 672   * |   4   0   0 |  2  2 0
. . o . *c3o3o3o3x ♦  6 |  0  15 |  0  20 |   0   15 |   0    6 |   * 896 |   1   1   1 |  1  1 1
-------------------+----+--------+--------+----------+----------+---------+-------------+--------
x . o . *c3o3o3o3x ♦ 12 |  6  30 | 15  40 |  20   30 |  15   12 |   6   2 | 448   *   * |  1  1 0
. o3o . *c3o3o3o3x ♦  7 |  0  21 |  0  35 |   0   35 |   0   21 |   0   7 |   * 128   * |  1  0 1
. . o3o *c3o3o3o3x ♦  7 |  0  21 |  0  35 |   0   35 |   0   21 |   0   7 |   *   * 128 |  0  1 1
-------------------+----+--------+--------+----------+----------+---------+-------------+--------
x o3o . *c3o3o3o3x ♦ 14 |  7  42 | 21  70 |  35   70 |  35   42 |  21  14 |   7   2   0 | 64  * *
x . o3o *c3o3o3o3x ♦ 14 |  7  42 | 21  70 |  35   70 |  35   42 |  21  14 |   7   0   2 |  * 64 *
. o3o3o *c3o3o3o3x ♦ 14 |  0  84 |  0 280 |   0  560 |   0  672 |   0 448 |   0  64  64 |  *  * 2
```

```xx3oo3oo3oo3oo3oo4oo&#x   → height = 1
(zee || zee)

o.3o.3o.3o.3o.3o.4o.    | 14  * | 12  1  0 |  60 12   0 | 160  60   0 | 240 160   0 | 192 240   0 |  64 192   0 | 1  64 0
.o3.o3.o3.o3.o3.o4.o    |  * 14 |  0  1 12 |   0 12  60 |   0  60 160 |   0 160 240 |   0 240 192 |   0 192  64 | 0  64 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x. .. .. .. .. .. ..    |  2  0 | 84  *  * |  10  1   0 |  40  10   0 |  80  40   0 |  80  80   0 |  32  80   0 | 1  32 0
oo3oo3oo3oo3oo3oo4oo&#x |  1  1 |  * 14  * ♦   0 12   0 |   0  60   0 |   0 160   0 |   0 240   0 |   0 192   0 | 0  64 0
.x .. .. .. .. .. ..    |  0  2 |  *  * 84 |   0  1  10 |   0  10  40 |   0  40  80 |   0  80  80 |   0  80  32 | 0  32 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o. .. .. .. .. ..    |  3  0 |  3  0  0 | 280  *   * |   8   1   0 |  24   8   0 |  32  24   0 |  16  32   0 | 1  16 0
xx .. .. .. .. .. ..&#x |  2  2 |  1  2  1 |   * 84   * ♦   0  10   0 |   0  40   0 |   0  80   0 |   0  80   0 | 0  32 0
.x3.o .. .. .. .. ..    |  0  3 |  0  0  3 |   *  * 280 |   0   1   8 |   0   8  24 |   0  24  32 |   0  32  16 | 0  16 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o. .. .. .. ..    ♦  4  0 |  6  0  0 |   4  0   0 | 560   *   * |   6   1   0 |  12   6   0 |   8  12   0 | 1   8 0
xx3oo .. .. .. .. ..&#x ♦  3  3 |  3  3  3 |   1  3   1 |   * 280   * ♦   0   8   0 |   0  24   0 |   0  32   0 | 0  16 0
.x3.o3.o .. .. .. ..    ♦  0  4 |  0  0  6 |   0  0   4 |   *   * 560 |   0   1   6 |   0   6  12 |   0  12   8 | 0   8 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o. .. .. ..    ♦  5  0 | 10  0  0 |  10  0   0 |   5   0   0 | 672   *   * |   4   1   0 |   4   4   0 | 1   4 0
xx3oo3oo .. .. .. ..&#x ♦  4  4 |  6  4  6 |   4  6   4 |   1   4   1 |   * 560   * ♦   0   6   0 |   0  12   0 | 0   8 0
.x3.o3.o3.o .. .. ..    ♦  0  5 |  0  0 10 |   0  0  10 |   0   0   5 |   *   * 672 |   0   1   4 |   0   4   4 | 0   4 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o.3o. .. ..    ♦  6  0 | 15  0  0 |  20  0   0 |  15   0   0 |   6   0   0 | 448   *   * |   2   1   0 | 1   2 0
xx3oo3oo3oo .. .. ..&#x ♦  5  5 | 10  5 10 |  10 10  10 |   5  10   5 |   1   5   1 |   * 672   * |   0   4   0 | 0   4 0
.x3.o3.o3.o3.o .. ..    ♦  0  6 |  0  0 15 |   0  0  20 |   0   0  15 |   0   0   6 |   *   * 448 |   0   1   2 | 0   2 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o.3o.3o. ..    ♦  7  0 | 21  0  0 |  35  0   0 |  35   0   0 |  21   0   0 |   7   0   0 | 128   *   * | 1   1 0
xx3oo3oo3oo3oo .. ..&#x ♦  6  6 | 15  6 15 |  20 15  20 |  15  20  15 |   6  15   6 |   1   6   1 |   * 448   * | 0   2 0
.x3.o3.o3.o3.o3.o ..    ♦  0  7 |  0  0 21 |   0  0  35 |   0   0  35 |   0   0  21 |   0   0   7 |   *   * 128 | 0   1 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o.3o.3o.4o.    ♦ 14  0 | 84  0  0 | 280  0   0 | 560   0   0 | 672   0   0 | 448   0   0 | 128   0   0 | 1   * *
xx3oo3oo3oo3oo3oo ..&#x ♦  7  7 | 21  7 21 |  35 21  35 |  35  35  35 |  21  35  21 |   7  21   7 |   1   7   1 | * 128 *
.x3.o3.o3.o3.o3.o4.o    ♦  0 14 |  0  0 84 |   0  0 280 |   0   0 560 |   0   0 672 |   0   0 448 |   0   0 128 | *   * 1
```

```oo3oo3oo *b3oo3oo3oo3xx&#x   → height = 1
(zee || zee)

o.3o.3o. *b3o.3o.3o.3o.    | 14  * | 12  1  0 |  60 12   0 | 160  60   0 | 240 160   0 | 192 240   0 | 32 32 192  0  0 | 1 32 32 0
.o3.o3.o *b3.o3.o3.o3.o    |  * 14 |  0  1 12 |   0 12  60 |   0  60 160 |   0 160 240 |   0 240 192 |  0  0 192 32 32 | 0 32 32 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. ..    .. .. .. x.    |  2  0 | 84  *  * |  10  1   0 |  40  10   0 |  80  40   0 |  80  80   0 | 16 16  80  0  0 | 1 16 16 0
oo3oo3oo *b3oo3oo3oo3oo&#x |  1  1 |  * 14  * ♦   0 12   0 |   0  60   0 |   0 160   0 |   0 240   0 |  0  0 192  0  0 | 0 32 32 0
.. .. ..    .. .. .. .x    |  0  2 |  *  * 84 |   0  1  10 |   0  10  40 |   0  40  80 |   0  80  80 |  0  0  80 16 16 | 0 16 16 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. ..    .. .. o.3x.    |  3  0 |  3  0  0 | 280  *   * |   8   1   0 |  24   8   0 |  32  24   0 |  8  8  32  0  0 | 1  8  8 0
.. .. ..    .. .. .. xx&#x |  2  2 |  1  2  1 |   * 84   * ♦   0  10   0 |   0  40   0 |   0  80   0 |  0  0  80  0  0 | 0 16 16 0
.. .. ..    .. .. .o3.x    |  0  3 |  0  0  3 |   *  * 280 |   0   1   8 |   0   8  24 |   0  24  32 |  0  0  32  8  8 | 0  8  8 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. ..    .. o.3o.3x.    ♦  4  0 |  6  0  0 |   4  0   0 | 560   *   * |   6   1   0 |  12   6   0 |  4  4  12  0  0 | 1  4  4 0
.. .. ..    .. .. oo3xx&#x ♦  3  3 |  3  3  3 |   1  3   1 |   * 280   * ♦   0   8   0 |   0  24   0 |  0  0  32  0  0 | 0  8  8 0
.. .. ..    .. .o3.o3.x    ♦  0  4 |  0  0  6 |   0  0   4 |   *   * 560 |   0   1   6 |   0   6  12 |  0  0  12  4  4 | 0  4  4 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. ..    o.3o.3o.3x.    ♦  5  0 | 10  0  0 |  10  0   0 |   5   0   0 | 672   *   * |   4   1   0 |  2  2   4  0  0 | 1  2  2 0
.. .. ..    .. oo3oo3xx&#x ♦  4  4 |  6  4  6 |   4  6   4 |   1   4   1 |   * 560   * ♦   0   6   0 |  0  0  12  0  0 | 0  4  4 0
.. .. ..    .o3.o3.o3.x    ♦  0  5 |  0  0 10 |   0  0  10 |   0   0   5 |   *   * 672 |   0   1   4 |  0  0   4  2  2 | 0  2  2 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. o. .. *b3o.3o.3o.3x.    ♦  6  0 | 15  0  0 |  20  0   0 |  15   0   0 |   6   0   0 | 448   *   * |  1  1   1  0  0 | 1  1  1 0
.. .. ..    oo3oo3oo3xx&#x ♦  5  5 | 10  5 10 |  10 10  10 |   5  10   5 |   1   5   1 |   * 672   * |  0  0   4  0  0 | 0  2  2 0
.. .o .. *b3.o3.o3.o3.x    ♦  0  6 |  0  0 15 |   0  0  20 |   0   0  15 |   0   0   6 |   *   * 448 |  0  0   1  1  1 | 0  1  1 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
o.3o. .. *b3o.3o.3o.3x.    ♦  7  0 | 21  0  0 |  35  0   0 |  35   0   0 |  21   0   0 |   7   0   0 | 64  *   *  *  * | 1  1  0 0
.. o.3o. *b3o.3o.3o.3x.    ♦  7  0 | 21  0  0 |  35  0   0 |  35   0   0 |  21   0   0 |   7   0   0 |  * 64   *  *  * | 1  0  1 0
.. oo .. *b3oo3oo3oo3xx&#x ♦  6  6 | 15  6 15 |  20 15  20 |  15  20  15 |   6  15   6 |   1   6   1 |  *  * 448  *  * | 0  1  1 0
.o3.o .. *b3.o3.o3.o3.x    ♦  0  7 |  0  0 21 |   0  0  35 |   0   0  35 |   0   0  21 |   0   0   7 |  *  *   * 64  * | 0  1  0 1
.. .o3.o *b3.o3.o3.o3.x    ♦  0  7 |  0  0 21 |   0  0  35 |   0   0  35 |   0   0  21 |   0   0   7 |  *  *   *  * 64 | 0  0  1 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
o.3o.3o. *b3o.3o.3o.3x.    ♦ 14  0 | 84  0  0 | 280  0   0 | 560   0   0 | 672   0   0 | 448   0   0 | 64 64   0  0  0 | 1  *  * *
oo3oo .. *b3oo3oo3oo3xx&#x ♦  7  7 | 21  7 21 |  35 21  35 |  35  35  35 |  21  35  21 |   7  21   7 |  1  0   7  1  0 | * 64  * *
.. oo3oo *b3oo3oo3oo3xx&#x ♦  7  7 | 21  7 21 |  35 21  35 |  35  35  35 |  21  35  21 |   7  21   7 |  0  1   7  0  1 | *  * 64 *
.o3.o3.o *b3.o3.o3.o3.x    ♦  0 14 |  0  0 84 |   0  0 280 |   0   0 560 |   0   0 672 |   0   0 448 |  0  0   0 64 64 | *  *  * 1
```