Acronym codify
Name tetracontaocta-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton,
tegum sum of 3 pairwise bigyrated hexadecachoron duoprisms
Circumradius 1
Lace hyper city
in approx. ASCII-art
                   
                   
                   
                   
                   
         N         
                   
                   
                   
                   
                   
                   
                   
    _E---------_O  
  O----------E  |  
  |  |       |  |  
  |  |       |  |  
  |  |       |  |  
  | _O-------|-_E  
  E----------O     
                   
                   
         N         
       /  \\       
     /  |  \ \     
   /    _ - N_ \   
 / _ - |    |  -_\ 
N _           _ - N
 \  -_|  _ +     / 
   \  N        /   
     \ \  |  /     
       \\  /       
         N         
                   
                   
    _O---------_E  
  E----------O  |  
  |  |       |  |  
  |  |       |  |  
  |  |       |  |  
  | _E-------|-_O  
  O----------E     
                   
                   
                   
                   
                   
                   
                   
         N         
                   
                   
                   
                   
                   
i.e. the vertex positions of an 1/q-ico

where:
N = o3o3o *b3x (hex)
E = x3o3o *b3o (gyro hex)
O = o3o3x *b3o (alt. gyro hex)
Confer
uniform relative:
fy   hocto   hexdip  
related segmentozetta:
hexal hesa  
general polytopal classes:
scaliform  

This polyzetton originated from a representation of fy within its D4 × D4 subsymmetry by Krieger in 2018. In fact it is obtained therefrom by eliminating the vertex subset of 2 mutually perpendicular vertex inscribed icoes. The remainder then happens to be a tegum sum of 3 pairwise bigyrated hexdips, which, as Klitzing pointed out, obviously will be a scaliform polyzetton.

The tegum sum of E-tethex and gyro-dual O-tethex, as being required in second and fourth layer of the above lace hyper city, clearly is nothing but a single hesa each.

It shall be pointed out that in the run of these investigations Krieger observed that the related figure of just 2 such pairwise bigyrated hexdips, so far being called gecdify (i.e. 64(=g)+48(=c)-diminished fy), just happens to be nothing else than hocto.


Incidence matrix according to Dynkin symbol

xoo3ooo3oxo *b3oox xoo3ooo3oxo *f3oox&&#zx   → all heights = 0
(tegum sum of 3 pairwise bigyrated hexdips)

o..3o..3o.. *b3o.. o..3o..3o.. *f3o..     & | 192 |   12   32 |   24   288  144 |  16   256   96   288  1152 |  2   64   80   480   480   720  1440 |  16  144  192  216  1152  144   864 |  112  24  240  224  336  36 |  16 12   88
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x.. ... ...    ... ... ... ...    ...     & |   2 | 1152    * |    4    16    0 |   4    32    8    24    48 |  1   16   16    64    48    48    96 |   8   28   32   48   128   12    72 |   24  12   52   32   40   6 |   4  7   20
oo.3oo.3oo. *b3oo. oo.3oo.3oo. *f3oo.&#x  & |   2 |    * 3072 |    0    12    9 |   0    12    6    18    90 |  0    6    4    36    42    72   144 |   2   12   18   30   132   18   108 |   12   6   42   30   48   9 |   2  6   18
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x..3o.. ...    ... ... ... ...    ...     & |   3 |    3    0 | 1536     *    * |   2     8    0     0     0 |  1    8    8    12    12     0     0 |   8   12    8   24    24    0     0 |   10  12   24    8    6   0 |   2  6    9
xo. ... ...    ... ... ... ...    ...&#x  & |   3 |    1    2 |    * 18432    * |   0     2    1     3     6 |  0    2    1     9     6     9    18 |   1    4    6    9    26    3    18 |    5   3   14    8   11   3 |   1  4    7
ooo3ooo3ooo *b3ooo ooo3ooo3ooo *f3ooo&#x    |   3 |    0    3 |    *     * 9216    0     0    0     0    12 |  0    0    0     0     6    12    24 |   0    0    0    6    24    4    24 |    0   2   12    6   12   4 |   0  4    6
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x..3o..3o..    ... ... ... ...    ...     &    4 |    6    0 |    4     0    0 | 768     *    *     *     * |  1    4    4     0     0     0     0 |   8    6    0   12     0    0     0 |    4  12   12    0    0   0 |   1  6    4
xo.3oo. ...    ... ... ... ...    ...&#x  &    4 |    3    3 |    1     3    0 |   * 12288    *     *     * |  0    1    1     3     3     0     0 |   1    3    3    6     9    0     0 |    4   3    9    4    3   0 |   1  3    5
xo. ... ox.    ... ... ... ...    ...&#x  &    4 |    2    4 |    0     4    0 |   *     * 4608     *     * |  0    2    0     0     0     6     0 |   1    0    0    6     0    3     6 |    0   3    6    0    2   3 |   0  4    2
xo. ... ...    ... ... ... ox.    ...&#x  &    4 |    2    4 |    0     4    0 |   *     *    * 13824     * |  0    0    0     4     0     0     4 |   0    2    4    0     8    0     4 |    4   0    4    4    4   1 |   1  2    4
xoo ... ...    ... ... ... ...    ...&#x  &    4 |    1    5 |    0     2    2 |   *     *    *     * 55296 |  0    0    0     0     1     2     4 |   0    0    0    2     6    1     6 |    0   1    5    2    4   2 |   0  3    3
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x..3o..3o.. *b3o.. ... ... ...    ...     &    8 |   24    0 |   32     0    0 |  16     0    0     0     0 | 48    *    *     *     *     *     *    8    0    0    0     0    0     0 |    0  12    0    0    0   0 |   0  6    0
xo.3oo.3ox.    ... ... ... ...    ...&#x  &    8 |   12   12 |    8    24    0 |   2     8    6     0     0 |  * 1536    *     *     *     *     * |   1    0    0    3     0    0     0 |    0   3    3    0    0   0 |   0  3    1
xo.3oo. ... *b3oo. ... ... ...    ...&#x  &    5 |    6    4 |    4     6    0 |   1     4    0     0     0 |  *    * 3072     *     *     *     * |   1    3    0    3     0    0     0 |    3   3    6    0    0   0 |   1  3    3
xo.3oo. ...    ... ... ... ox.    ...&#x  &    5 |    4    6 |    1     9    0 |   0     2    0     3     0 |  *    *    * 18432     *     *     * |   0    1    2    0     2    0     0 |    3   0    2    2    1   0 |   1  1    3
xoo3ooo ...    ... ... ... ...    ...&#x  &    5 |    3    7 |    1     6    3 |   0     2    0     0     3 |  *    *    *     * 18432     *     * |   0    0    0    2     4    0     0 |    0   1    4    2    2   0 |   0  2    3
xoo ... oxo    ... ... ... ...    ...&#x  &    5 |    2    8 |    0     6    4 |   0     0    1     0     4 |  *    *    *     *     * 27648     * |   0    0    0    1     0    1     2 |    0   1    2    0    1   2 |   0  3    1
xoo ... ...    ... ... ... oxo    ...&#x  &    5 |    2    8 |    0     6    4 |   0     0    0     1     4 |  *    *    *     *     *     * 55296 |   0    0    0    0     2    0     2 |    0   0    2    1    2   1 |   0  2    2
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
xo.3oo.3ox. *b3oo. ... ... ...    ...&#x  &   16 |   48   32 |   64    96    0 |  32    64   24     0     0 |  2    8   16     0     0     0     0 | 192    *    *    *     *    *     * |    0   3    0    0    0   0 |   0  3    0
xo.3oo. ... *b3oo. ... ... ox.    ...&#x  &    6 |    7    8 |    4    16    0 |   1     8    0     6     0 |  0    0    2     4     0     0     0 |   * 4608    *    *     *    *     * |    2   0    2    0    0   0 |   1  1    2
xo.3oo. ...    ... ... oo.3ox.    ...&#x  &    6 |    6    9 |    2    18    0 |   0     6    0     9     0 |  0    0    0     6     0     0     0 |   *    * 6144    *     *    *     * |    2   0    0    1    0   0 |   1  0    2
xoo3ooo3oxo    ... ... ... ...    ...&#x  &    9 |   12   20 |    8    36   12 |   2    16    6     0    24 |  0    1    2     0     8     6     0 |   *    *    * 4608     *    *     * |    0   1    2    0    0   0 |   0  2    1
xoo3ooo ...    ... ... ... oxo    ...&#x  &    6 |    4   11 |    1    13    6 |   0     3    0     3     9 |  0    0    0     1     2     0     3 |   *    *    *    * 36864    *     * |    0   0    1    1    1   0 |   0  1    2
xoo ... oxo    oox ... ... ...    ...&#x  &    6 |    3   12 |    0    12    8 |   0     0    3     0    12 |  0    0    0     0     0     6     0 |   *    *    *    *     * 4608     * |    0   1    0    0    0   2 |   0  3    0
xoo ... oxo    ... ... ... ...    oox&#x  &    6 |    3   12 |    0    12    8 |   0     0    1     2    12 |  0    0    0     0     0     2     4 |   *    *    *    *     *    * 27648 |    0   0    1    0    1   1 |   0  2    1
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
xo.3oo. ... *b3oo. ... oo.3ox.    ...&#x  &    7 |    9   12 |    5    30    0 |   1    16    0    18     0 |  0    0    3    18     0     0     0 |   0    3    4    0     0    0     0 | 3072   *    *    *    *   * |   1  0    1
xoo3ooo3oxo *b3oox ... ... ...    ...&#x  &   24 |   72   96 |   96   288   96 |  48   192   72     0   288 |  3   24   48     0    96   144     0 |   3    0    0   24     0   24     0 |    * 192    *    *    *   * |   0  2    0
xoo3ooo3oxo    ... ... ... ...    oox&#x  &   10 |   13   28 |    8    56   24 |   2    24    6    12    60 |  0    1    4     8    16    12    24 |   0    2    0    2     8    0     6 |    *   * 4608    *    *   * |   0  1    1
xoo3ooo ...    ... ... ooo3oxo    ...&#x  &    7 |    6   15 |    2    24    9 |   0     8    0     9    18 |  0    0    0     6     6     0     9 |   0    0    1    0     6    0     0 |    *   *    * 6144    *   * |   0  0    2
xoo3ooo ...    ... ... ... oxo    oox&#x  &    7 |    5   16 |    1    22   12 |   0     4    1     6    24 |  0    0    0     2     4     3    12 |   0    0    0    0     4    0     3 |    *   *    *    * 9216   * |   0  1    1
xoo ... oxo    oox xoo ... oxo    oox&#zx     12 |   12   48 |    0    96   64 |   0     0   24    24   192 |  0    0    0     0     0    96    96 |   0    0    0    0     0   16    48 |    *   *    *    *    * 576 |   0  2    0
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
xo.3oo. ... *b3oo. ... oo.3ox. *f3oo.&#x  &    8 |   12   16 |    8    48    0 |   2    32    0    36     0 |  0    0    8    48     0     0     0 |   0   12   16    0     0    0     0 |    8   0    0    0    0   0 | 384  *    *
xoo3ooo3oxo *b3oox xoo ... oxo    oox&#zx &   48 |  168  384 |  192  1536  768 |  96   768  384   576  3456 |  6   96  192   384   768  1728  2304 |  12   96    0  192   768  288  1152 |    0   8   96    0  192  24 |   * 48    *
xoo3ooo3oxo    ... ... ooo ... *f3oox&#x  &   11 |   15   36 |    9    84   36 |   2    40    6    36   108 |  0    1    6    36    36    18    72 |   0    6    8    3    48    0    18 |    2   0    3    8    6   0 |   *  * 1536

o(xo)o(xo)o3o(oo)x(oo)o3o(ox)o(ox)o o(xo)o(ox)o3o(oo)o(oo)o3o(ox)o(xo)o *e3x(oo)x(oo)x&#xt   → all heights = 1/sqrt(8) = 0.353553
(hex || pseudo gyro hesa || pseudo octhex || pseudo alt. gyro hesa || hex)

...

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