Acronym odinaq Name octa-diminished naq Circumradius sqrt(3)/2 = 0.866025 Lace hyper cityin approx. ASCII-art ``` N //|\ / / | \ / _O--+----_E - x3o3o *b3o3o (hin) /_- | | _- / E-----+--O / - o3o3x *b3o3o (alt. hin) \ | / / \|// N where: N = o3o3o *b3x (hex) E = x3o3o *b3o (gyro hex) O = o3o3x *b3o (alt. gyro hex) ``` Confer uniform relative: naq   general polytopal classes: scaliform

This scaliform polyexon is obtained from naq, when, in the same D4 × A1 × A1 × A1 symmetry representation, as given in the lace hyper city display above, the 8 vertices of the encasing cube of position subspace, there representing a single point in object subspace each, will be chopped off.

Alternatively it could be obtained as the tegum sum of 3 mutually gyrated and lacing orthogonal hexips. Those then show up in the lace hyper city display as the 3 diagonals (N-N, E-E, O-O) of the oct of position subspace.

Incidence matrix according to Dynkin symbol

```xoo oxo oox oxo3ooo3oox *e3xoo&#zx   → all heights = 0
(tegum sum of 3 mutually gyrated, lacings-orthogonal hexips)

o.. o.. o.. o..3o..3o.. *e3o..    & | 48 |  1   6  16 |  12  24   72  48 |  8  8  48  64  24   96  192 | 1  40  20 16  60  240  80  120 | 12  4 12  72  96  72  36  24 |  6  28 20 4
------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------
x.. ... ... ... ... ...    ...    & |  2 | 24   *   * |   0  16    0   0 |  0  8  24   0   0   48    0 | 0  16   0  0  48   96   0    0 |  4  0 12  48  32  24   0   0 |  6  16  4 0
... ... ... ... ... ...    x..    & |  2 |  * 144   * |   4   0    8   0 |  4  0   4  16   4    0   16 | 1   8   8  8   0   16  16   16 |  4  4  0   4  16   8  16   4 |  1   4  8 4
oo. oo. oo. oo.3oo.3oo. *e3oo.&#x & |  2 |  *   * 384 |   0   2    6   6 |  0  1   6   6   3   15   30 | 0   6   2  3  12   48  14   24 |  2  1  3  18  22  18  10   6 |  3   8  7 2
------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------
... ... ... ... o.. ... *e3x..    & |  3 |  0   3   0 | 192   *    *   * |  2  0   0   4   0    0    0 | 1   2   4  4   0    0   4    0 |  2  4  0   0   4   0   8   0 |  0   1  4 4
xo. ... ... ... ... ...    ...&#x & |  3 |  1   0   2 |   * 384    *   * |  0  1   3   0   0    6    0 | 0   3   0  0   9   18   0    0 |  1  0  3  12   8   6   0   0 |  3   5  2 0
... ... ... ox. ... ...    ...&#x & |  3 |  0   1   2 |   *   * 1152   * |  0  0   1   2   1    0    4 | 0   2   1  2   0    6   4    6 |  1  1  0   2   6   4   6   2 |  1   2  4 2
ooo ooo ooo ooo3ooo3ooo *e3ooo&#x   |  3 |  0   0   3 |   *   *    * 768 |  0  0   0   0   0    3    6 | 0   0   0  0   3   12   3    6 |  0  0  1   6   6   6   3   2 |  2   3  3 1
------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------
... ... ... o..3o.. ... *e3x..    & ♦  4 |  0   6   0 |   4   0    0   0 | 96  *   *   *   *    *    * | 1   0   2  2   0    0   0    0 |  1  4  0   0   0   0   4   0 |  0   0  2 4
xo. ox. ... ... ... ...    ...&#x & ♦  4 |  2   0   4 |   0   4    0   0 |  * 96   *   *   *    *    * ♦ 0   0   0  0   6    0   0    0 |  0  0  3   6   0   0   0   0 |  3   2  0 0
xo. ... ... ox. ... ...    ...&#x & ♦  4 |  1   1   4 |   0   2    2   0 |  *  * 576   *   *    *    * | 0   2   0  0   0    4   0    0 |  1  0  0   2   4   2   0   0 |  1   2  2 0
... ... ... ox.3oo. ...    ...&#x & ♦  4 |  0   3   3 |   1   0    3   0 |  *  *   * 768   *    *    * | 0   1   1  1   0    0   2    0 |  1  1  0   0   3   0   4   0 |  0   1  3 2
... ... ... ox. ... ...    xo.&#x & ♦  4 |  0   2   4 |   0   0    4   0 |  *  *   *   * 288    *    * | 0   0   0  2   0    0   0    4 |  0  1  0   0   0   2   4   2 |  1   0  2 2
xoo ... ... ... ... ...    ...&#x & ♦  4 |  1   0   5 |   0   2    0   2 |  *  *   *   *   * 1152    * | 0   0   0  0   2    4   0    0 |  0  0  1   4   2   2   0   0 |  2   2  1 0
... ... ... oxo ... ...    ...&#x & ♦  4 |  0   1   5 |   0   0    2   2 |  *  *   *   *   *    * 2304 | 0   0   0  0   0    2   1    2 |  0  0  0   1   2   2   2   1 |  1   1  2 1
------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------
... ... ... o..3o..3o.. *e3x..    & ♦  8 |  0  24   0 |  32   0    0   0 | 16  0   0   0   0    0    0 | 6   *   *  *   *    *   *    * |  0  4  0   0   0   0   0   0 |  0   0  0 4
xo. ... ... ox.3oo. ...    ...&#x & ♦  5 |  1   3   6 |   1   3    6   0 |  0  0   3   2   0    0    0 | * 384   *  *   *    *   *    * |  1  0  0   0   2   0   0   0 |  0   1  2 0
... ... ... ox.3oo.3oo.    ...&#x & ♦  5 |  0   6   4 |   4   0    6   0 |  1  0   0   4   0    0    0 | *   * 192  *   *    *   *    * |  1  1  0   0   0   0   2   0 |  0   0  2 2
... ... ... ox.3oo. ... *e3xo.&#x & ♦  8 |  0  12  12 |   8   0   24   0 |  2  0   0   8   6    0    0 | *   *   * 96   *    *   *    * |  0  1  0   0   0   0   2   0 |  0   0  1 2
xoo oxo ... ... ... ...    ...&#x & ♦  5 |  2   0   8 |   0   6    0   4 |  0  1   0   0   0    4    0 | *   *   *  * 576    *   *    * |  0  0  1   2   0   0   0   0 |  2   1  0 0
xoo ... ... oxo ... ...    ...&#x & ♦  5 |  1   1   8 |   0   3    3   4 |  0  0   1   0   0    2    2 | *   *   *  *   * 2304   *    * |  0  0  0   1   1   1   0   0 |  1   1  1 0
... ... ... oxo3ooo ...    ...&#x & ♦  5 |  0   3   7 |   1   0    6   3 |  0  0   0   2   0    0    3 | *   *   *  *   *    * 768    * |  0  0  0   0   2   0   2   0 |  0   1  2 1
... ... ... oxo ... oox    ...&#x & ♦  5 |  0   2   8 |   0   0    6   4 |  0  0   0   0   1    0    4 | *   *   *  *   *    *   * 1152 |  0  0  0   0   0   1   1   1 |  1   0  1 1
------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------
xo. ... ... ox.3oo.3oo.    ...&#x & ♦  6 |  1   6   8 |   4   4   12   0 |  1  0   6   8   0    0    0 | 0   4   2  0   0    0   0    0 | 96  *  *   *   *   *   *   * |  0   0  2 0
... ... ... ox.3oo.3oo. *e3xo.&#x & ♦ 16 |  0  48  32 |  64   0   96   0 | 32  0   0  64  24    0    0 | 2   0  16  8   0    0   0    0 |  * 12  *   *   *   *   *   * |  0   0  0 2
xoo oxo oox ... ... ...    ...&#x   ♦  6 |  3   0  12 |   0  12    0   8 |  0  3   0   0   0   12    0 | 0   0   0  0   6    0   0    0 |  *  * 96   *   *   *   *   * |  2   0  0 0
xoo oxo ... ... ... oox    ...&#x & ♦  6 |  2   1  12 |   0   8    4   8 |  0  1   2   0   0    8    4 | 0   0   0  0   2    4   0    0 |  *  *  * 576   *   *   *   * |  1   1  0 0
xoo ... ... oxo3ooo ...    ...&#x & ♦  6 |  1   3  11 |   1   4    9   6 |  0  0   3   3   0    3    6 | 0   1   0  0   0    3   2    0 |  *  *  *   * 768   *   *   * |  0   1  1 0
xoo ... ... oxo ... oox    ...&#x & ♦  6 |  1   2  12 |   0   4    8   8 |  0  0   2   0   1    4    8 | 0   0   0  0   0    4   0    2 |  *  *  *   *   * 576   *   * |  1   0  1 0
... ... ... oxo3ooo3oox    ...&#x & ♦  9 |  0  12  20 |   8   0   36  12 |  2  0   0  16   6    0   24 | 0   0   2  1   0    0   8    6 |  *  *  *   *   *   * 192   * |  0   0  1 1
... ... ... oxo ... oox    xoo&#x   ♦  6 |  0   3  12 |   0   0   12   8 |  0  0   0   0   3    0   12 | 0   0   0  0   0    0   0    6 |  *  *  *   *   *   *   * 192 |  1   0  0 1
------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------
xoo oxo oox xoo ... oxo    oox&#zx  ♦ 12 |  6   6  48 |   0  48   48  64 |  0 12  24   0  12   96   96 | 0   0   0  0  48   96   0   48 |  0  0  8  24   0  24   0   8 | 24   *  * *
xoo oxo ... ... ooo3oox    ...&#x & ♦  7 |  2   3  16 |   1  10   12  12 |  0  1   6   4   0   12   12 | 0   2   0  0   3   12   4    0 |  0  0  0   3   4   0   0   0 |  * 192  * *
xoo ... ... oxo3ooo3oox    ...&#x & ♦ 10 |  1  12  28 |   8   8   48  24 |  2  0  12  24   6   12   48 | 0   8   4  1   0   24  16   12 |  2  0  0   0   8   6   2   0 |  *   * 96 *
... ... ... oxo3ooo3oox *e3xoo&#x   ♦ 24 |  0  72  96 |  96   0  288  96 | 48  0   0 192  72    0  288 | 3   0  48 24   0    0  96  144 |  0  3  0   0   0   0  24  24 |  *   *  * 8
```

```o(xo)o o(ox)o o(xo)o3o(oo)o3o(ox)o *d3x(oo)x&#xt   → both heights = 1/2
(hex || tegum sum of 2 relatively and mutually gyrated, lacings-orthogonal hexips || hex)

...
```