Acronym thexgyt (alt.: pex tedjak)
Name truncated-hexadecachoral gyrotrigonism,
partially expanded tridiminished icosiheptaheptacontidipeton,
partially expanded tridiminished 21,2
Circumradius sqrt(8/3) = 1.632993
Lace city
in approx. ASCII-art
     		where:
    E		E = o3x3x *b3o (thex)
X    		O = o3x3o *b3x
    O		X = x3x3o *b3o
Confer
related scaliform:
tedjak  
general polytopal classes:
segmentopeta   scaliform  

By means of a (partial) Stott contraction at the central node positions, applied simultanuously to all layers, this polypeton would reduce to tedjak, the tri-diminishing of the Gosset polytope jak.


Incidence matrix according to Dynkin symbol

xoo3xxx3oxo *b3oox&#x   → all pairwise heights = 1/sqrt(2) = 0.707107

o..3o..3o.. *b3o..    & | 144 |  1   4   4 |  4   4   6   8   4 |  4  1  12  2  4   8  4 | 1  4  6  8   5 | 2  5  1
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x.. ... ...    ...    & |   2 | 72   *   * |  4   0   4   0   0 |  4  0   8  2  0   4  0 | 1  4  4  4   4 | 2  4  1
... x.. ...    ...    & |   2 |  * 288   * |  1   2   0   2   0 |  2  1   4  0  2   0  1 | 1  2  4  3   0 | 2  3  0
oo.3oo.3oo. *b3oo.&#x & |   2 |  *   * 288 |  0   0   2   2   2 |  0  0   4  1  1   5  2 | 0  2  2  5   4 | 1  4  1
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x..3x.. ...    ...    & |   6 |  3   3   0 | 96   *   *   *   * |  2  0   2  0  0   0  0 | 1  2  2  1   0 | 2  2  0
... x..3o..    ...    & |   3 |  0   3   0 |  * 192   *   *   * |  1  1   1  0  1   0  0 | 1  1  3  1   0 | 2  2  0
xo. ... ...    ...&#x & |   3 |  1   0   2 |  *   * 288   *   * |  0  0   2  1  0   2  0 | 0  2  1  2   3 | 1  3  1
... xx. ...    ...&#x & |   4 |  0   2   2 |  *   *   * 288   * |  0  0   2  0  1   0  1 | 0  1  2  3   0 | 1  3  0
ooo3ooo3ooo *b3ooo&#x   |   3 |  0   0   3 |  *   *   *   * 192 |  0  0   0  0  0   3  1 | 0  0  0  3   3 | 0  3  1
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x..3x..3o..    ...    &   12 |  6  12   0 |  4   4   0   0   0 | 48  *   *  *  *   *  * | 1  1  1  0   0 | 2  1  0
... x..3o.. *b3o..    &    6 |  0  12   0 |  0   8   0   0   0 |  * 24   *  *  *   *  * | 1  0  2  0   0 | 2  1  0
xo.3xx. ...    ...&#x &    9 |  3   6   6 |  1   1   3   3   0 |  *  * 192  *  *   *  * | 0  1  1  1   0 | 1  2  0
xo. ... ox.    ...&#x &    4 |  2   0   4 |  0   0   4   0   0 |  *  *   * 72  *   *  * | 0  2  0  0   2 | 1  2  1
... xx. ... *b3oo.&#x &    6 |  0   6   3 |  0   2   0   3   0 |  *  *   *  * 96   *  * | 0  0  2  1   0 | 1  2  0
xoo ... ...    ...&#x &    4 |  1   0   5 |  0   0   2   0   2 |  *  *   *  *  * 288  * | 0  0  0  1   2 | 0  2  1
... xxx ...    ...&#x      6 |  0   3   6 |  0   0   0   3   2 |  *  *   *  *  *   * 96 | 0  0  0  3   0 | 0  3  0
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x..3x..3o.. *b3o..    &   48 | 24  96   0 | 32  64   0   0   0 | 16  8   0  0  0   0  0 | 3  *  *  *   * | 2  0  0
xo.3xx.3ox.    ...&#x &   24 | 12  24  24 |  8   8  24  12   0 |  2  0   8  6  0   0  0 | * 24  *  *   * | 1  1  0
xo.3xx. ... *b3oo.&#x &   18 |  6  24  12 |  4  12   6  12   0 |  1  1   4  0  4   0  0 | *  * 48  *   * | 1  1  0
xoo3xxx ...    ...&#x &   12 |  3   9  15 |  1   2   6   9   6 |  0  0   2  0  1   3  3 | *  *  * 96   * | 0  2  0
xoo ... oxo    ...&#x &    5 |  2   0   8 |  0   0   6   0   4 |  0  0   0  1  0   4  0 | *  *  *  * 144 | 0  1  1
------------------------+-----+------------+--------------------+------------------------+----------------+--------
xo.3xx.3ox. *b3oo.&#x &   96 | 48 192  96 | 64 128  96  96   0 | 32 16  64 24 32   0  0 | 2  8 16  0   0 | 3  *  *
xoo3xxx3oxo    ...&#x &   30 | 12  36  48 |  8  16  36  36  24 |  2  1  16  6  8  24 12 | 0  1  2  8   6 | * 24  *
xoo ... oxo    oox&#x      6 |  3   0  12 |  0   0  12   0   8 |  0  0   0  3  0  12  0 | 0  0  0  0   6 | *  * 24

x..3x..3o.. *b3o.. || .oo3.xx3.xo *b3.ox&#x   → height = sqrt(3/8) = 0.612372
( thex || gyro (thex || gyro thex) )

o..3o..3o.. *b3o..      | 48  * |  1  4   4   0  0  0 |  4  4  4   8  2   4  0  0  0  0  0 |  4 1  8  2  4  4  4  4   4  0  0  0  0  0  0 | 1  4  4  2  4  4  4  1 0  0 0 | 2  4  1 1 0
.o.3.o.3.o. *b3.o.    & |  * 96 |  0  0   2   4  1  2 |  0  0  1   4  2   4  2  4  4  4  3 |  0 0  2  1  4  2  2  4   6  2  1  2  2  6  1 | 0  2  1  2  2  3  6  2 1  3 2 | 1  3  1 2 1
------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------
x.. ... ...    ...      |  2  0 | 24  *   *   *  *  * |  4  0  4   0  0   0  0  0  0  0  0 |  4 0  8  2  0  0  4  0   0  0  0  0  0  0  0 | 1  4  4  0  4  4  0  0 0  0 0 | 2  4  1 0 0
... x.. ...    ...      |  2  0 |  * 96   *   *  *  * |  1  2  0   2  0   0  0  0  0  0  0 |  2 1  2  0  2  2  0  1   0  0  0  0  0  0  0 | 1  2  2  2  1  0  2  0 0  0 0 | 2  2  0 1 0
oo.3oo.3oo. *b3oo.&#x & |  1  1 |  *  * 192   *  *  * |  0  0  1   2  1   2  0  0  0  0  0 |  0 0  2  1  2  1  2  2   3  0  0  0  0  0  0 | 0  2  1  1  2  3  3  1 0  0 0 | 1  3  1 1 0
... .x. ...    ...    & |  0  2 |  *  *   * 192  *  * |  0  0  0   1  0   0  1  1  1  1  0 |  0 0  1  0  1  1  0  1   0  1  1  1  1  2  0 | 0  1  1  1  1  0  2  0 1  2 1 | 1  2  0 1 1
... ... .x.    ...    & |  0  2 |  *  *   *   * 48  * |  0  0  0   0  2   0  0  4  0  0  2 |  0 0  0  1  4  0  0  0   4  2  0  2  0  4  1 | 0  2  0  2  0  2  4  2 1  2 2 | 1  2  1 2 1
.oo3.oo3.oo *b3.oo&#x   |  0  2 |  *  *   *   *  * 96 |  0  0  0   0  0   2  0  0  0  2  2 |  0 0  0  0  0  0  1  2   4  0  0  0  1  4  1 | 0  0  0  0  1  2  4  2 0  2 2 | 0  2  1 2 1
------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------
x..3x.. ...    ...      |  6  0 |  3  3   0   0  0  0 | 32  *  *   *  *   *  *  *  *  *  * |  2 0  2  0  0  0  0  0   0  0  0  0  0  0  0 | 1  2  2  0  1  0  0  0 0  0 0 | 2  2  0 0 0
... x..3o..    ...    & |  3  0 |  0  3   0   0  0  0 |  * 64  *   *  *   *  *  *  *  *  * |  1 1  0  0  1  1  0  0   0  0  0  0  0  0  0 | 1  1  1  2  0  0  1  0 0  0 0 | 2  1  0 1 0
xo. ... ...    ...&#x & |  2  1 |  1  0   2   0  0  0 |  *  * 96   *  *   *  *  *  *  *  * |  0 0  2  1  0  0  2  0   0  0  0  0  0  0  0 | 0  2  1  0  2  3  0  0 0  0 0 | 1  3  1 0 0
... xx. ...    ...&#x & |  2  2 |  0  1   2   1  0  0 |  *  *  * 192  *   *  *  *  *  *  * |  0 0  1  0  1  1  0  1   0  0  0  0  0  0  0 | 0  1  1  1  1  0  2  0 0  0 0 | 1  2  0 1 0
... ... ox.    ...&#x & |  1  2 |  0  0   2   0  1  0 |  *  *  *   * 96   *  *  *  *  *  * |  0 0  0  1  2  0  0  0   2  0  0  0  0  0  0 | 0  2  0  1  0  2  2  1 0  0 0 | 1  2  1 1 0
ooo3ooo3ooo *b3ooo&#x   |  1  2 |  0  0   2   0  0  1 |  *  *  *   *  * 192  *  *  *  *  * |  0 0  0  0  0  0  1  1   2  0  0  0  0  0  0 | 0  0  0  0  1  2  2  1 0  0 0 | 0  2  1 1 0
.o.3.x. ...    ...    & |  0  3 |  0  0   0   3  0  0 |  *  *  *   *  *   * 64  *  *  *  * |  0 0  1  0  0  0  0  0   0  1  1  0  1  0  0 | 0  1  1  0  1  0  0  0 1  2 0 | 1  2  0 0 1
... .x.3.x.    ...    & |  0  6 |  0  0   0   3  3  0 |  *  *  *   *  *   *  * 64  *  *  * |  0 0  0  0  1  0  0  0   0  1  0  1  0  1  0 | 0  1  0  1  0  0  1  0 1  1 1 | 1  1  0 1 1
... .x. ... *b3.o.    & |  0  3 |  0  0   0   3  0  0 |  *  *  *   *  *   *  *  * 64  *  * |  0 0  0  0  0  1  0  0   0  0  1  1  0  1  0 | 0  0  1  1  0  0  1  0 1  1 1 | 1  1  0 1 1
... .xx ...    ...&#x   |  0  4 |  0  0   0   2  0  2 |  *  *  *   *  *   *  *  *  * 96  * |  0 0  0  0  0  0  0  1   0  0  0  0  1  2  0 | 0  0  0  0  1  0  2  0 0  2 1 | 0  2  0 1 1
... ... .xo    ...&#x & |  0  3 |  0  0   0   0  1  2 |  *  *  *   *  *   *  *  *  *  * 96 |  0 0  0  0  0  0  0  0   2  0  0  0  0  2  1 | 0  0  0  0  0  1  2  2 0  1 2 | 0  1  1 2 1
------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------
x..3x..3o..    ...    &  12  0 |  6 12   0   0  0  0 |  4  4  0   0  0   0  0  0  0  0  0 | 16 *  *  *  *  *  *  *   *  *  *  *  *  *  * | 1  1  1  0  0  0  0  0 0  0 0 | 2  1  0 0 0
... x..3o.. *b3o..        6  0 |  0 12   0   0  0  0 |  0  8  0   0  0   0  0  0  0  0  0 |  * 8  *  *  *  *  *  *   *  *  *  *  *  *  * | 1  0  0  2  0  0  0  0 0  0 0 | 2  0  0 1 0
xo.3xx. ...    ...&#x &   6  3 |  3  3   6   3  0  0 |  1  0  3   3  0   0  1  0  0  0  0 |  * * 64  *  *  *  *  *   *  *  *  *  *  *  * | 0  1  1  0  1  0  0  0 0  0 0 | 1  2  0 0 0
xo. ... ox.    ...&#x &   2  2 |  1  0   4   0  1  0 |  0  0  2   0  2   0  0  0  0  0  0 |  * *  * 48  *  *  *  *   *  *  *  *  *  *  * | 0  2  0  0  0  2  0  0 0  0 0 | 1  2  1 0 0
... xx.3ox.    ...&#x &   3  6 |  0  3   6   3  3  0 |  0  1  0   3  3   0  0  1  0  0  0 |  * *  *  * 64  *  *  *   *  *  *  *  *  *  * | 0  1  0  1  0  0  1  0 0  0 0 | 1  1  0 1 0
... xx. ... *b3oo.&#x &   3  3 |  0  3   3   3  0  0 |  0  1  0   3  0   0  0  0  1  0  0 |  * *  *  *  * 64  *  *   *  *  *  *  *  *  * | 0  0  1  1  0  0  1  0 0  0 0 | 1  1  0 1 0
xoo ... ...    ...&#x     2  2 |  1  0   4   0  0  1 |  0  0  2   0  0   2  0  0  0  0  0 |  * *  *  *  *  * 96  *   *  *  *  *  *  *  * | 0  0  0  0  1  2  0  0 0  0 0 | 0  2  1 0 0
... xxx ...    ...&#x     2  4 |  0  1   4   2  0  2 |  0  0  0   2  0   2  0  0  0  1  0 |  * *  *  *  *  *  * 96   *  *  *  *  *  *  * | 0  0  0  0  1  0  2  0 0  0 0 | 0  2  0 1 0
... ... oxo    ...&#x &   1  3 |  0  0   3   0  1  2 |  0  0  0   0  1   2  0  0  0  0  1 |  * *  *  *  *  *  *  * 192  *  *  *  *  *  * | 0  0  0  0  0  1  1  1 0  0 0 | 0  1  1 1 0
.o.3.x.3.x.    ...    &   0 12 |  0  0   0  12  6  0 |  0  0  0   0  0   0  4  4  0  0  0 |  * *  *  *  *  *  *  *   * 16  *  *  *  *  * | 0  1  0  0  0  0  0  0 1  1 0 | 1  1  0 0 1
.o.3.x. ... *b3.o.    &   0  6 |  0  0   0  12  0  0 |  0  0  0   0  0   0  4  0  4  0  0 |  * *  *  *  *  *  *  *   *  * 16  *  *  *  * | 0  0  1  0  0  0  0  0 1  1 0 | 1  1  0 0 1
... .x.3.x. *b3.o.    &   0 12 |  0  0   0  12  6  0 |  0  0  0   0  0   0  0  4  4  0  0 |  * *  *  *  *  *  *  *   *  *  * 16  *  *  * | 0  0  0  1  0  0  0  0 1  0 1 | 1  0  0 1 1
.oo3.xx ...    ...&#x     0  6 |  0  0   0   6  0  3 |  0  0  0   0  0   0  2  0  0  3  0 |  * *  *  *  *  *  *  *   *  *  *  * 32  *  * | 0  0  0  0  1  0  0  0 0  2 0 | 0  2  0 0 1
... .xx3.xo    ...&#x &   0  9 |  0  0   0   6  3  6 |  0  0  0   0  0   0  0  1  1  3  3 |  * *  *  *  *  *  *  *   *  *  *  *  * 64  * | 0  0  0  0  0  0  1  0 0  1 1 | 0  1  0 1 1
... ... .xo    .ox&#x     0  4 |  0  0   0   0  2  4 |  0  0  0   0  0   0  0  0  0  0  4 |  * *  *  *  *  *  *  *   *  *  *  *  *  * 24 | 0  0  0  0  0  0  0  2 0  0 2 | 0  0  1 2 1
------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------
x..3x..3o.. *b3o..       48  0 | 24 96   0   0  0  0 | 32 64  0   0  0   0  0  0  0  0  0 | 16 8  0  0  0  0  0  0   0  0  0  0  0  0  0 | 1  *  *  *  *  *  *  * *  * * | 2  0  0 0 0
xo.3xx.3ox.    ...&#x &  12 12 |  6 12  24  12  6  0 |  4  4 12  12 12   0  4  4  0  0  0 |  1 0  4  6  4  0  0  0   0  1  0  0  0  0  0 | * 16  *  *  *  *  *  * *  * * | 1  1  0 0 0
xo.3xx. ... *b3oo.&#x &  12  6 |  6 12  12  12  0  0 |  4  4  6  12  0   0  4  0  4  0  0 |  1 0  4  0  0  4  0  0   0  0  1  0  0  0  0 | *  * 16  *  *  *  *  * *  * * | 1  1  0 0 0
... xx.3ox. *b3oo.&#x &   6 12 |  0 12  12  12  6  0 |  0  8  0  12  6   0  0  4  4  0  0 |  0 1  0  0  4  4  0  0   0  0  0  1  0  0  0 | *  *  * 16  *  *  *  * *  * * | 1  0  0 1 0
xoo3xxx ...    ...&#x     6  6 |  3  3  12   6  0  3 |  1  0  6   6  0   6  2  0  0  3  0 |  0 0  2  0  0  0  3  3   0  0  0  0  1  0  0 | *  *  *  * 32  *  *  * *  * * | 0  2  0 0 0
xoo ... oxo    ...&#x &   2  3 |  1  0   6   0  1  2 |  0  0  3   0  2   4  0  0  0  0  1 |  0 0  0  1  0  0  2  0   2  0  0  0  0  0  0 | *  *  *  *  * 96  *  * *  * * | 0  1  1 0 0
... xxx3oxo    ...&#x &   3  9 |  0  3   9   6  3  6 |  0  1  0   6  3   6  0  1  1  3  3 |  0 0  0  0  1  1  0  3   3  0  0  0  0  1  0 | *  *  *  *  *  * 64  * *  * * | 0  1  0 1 0
... ... oxo    oox&#x     1  4 |  0  0   4   0  2  4 |  0  0  0   0  2   4  0  0  0  0  4 |  0 0  0  0  0  0  0  0   4  0  0  0  0  0  1 | *  *  *  *  *  *  * 48 *  * * | 0  0  1 1 0
.o.3.x.3.x. *b3.o.    &   0 48 |  0  0   0  96 24  0 |  0  0  0   0  0   0 32 32 32  0  0 |  0 0  0  0  0  0  0  0   0  8  8  8  0  0  0 | *  *  *  *  *  *  *  * 2  * * | 1  0  0 0 1
.oo3.xx3.xo    ...&#x &   0 18 |  0  0   0  24  6 12 |  0  0  0   0  0   0  8  4  4 12  6 |  0 0  0  0  0  0  0  0   0  1  1  0  4  4  0 | *  *  *  *  *  *  *  * * 16 * | 0  1  0 0 1
... .xx3.xo *b3.ox&#x     0 24 |  0  0   0  24 12 24 |  0  0  0   0  0   0  0  8  8 12 24 |  0 0  0  0  0  0  0  0   0  0  0  2  0  8  6 | *  *  *  *  *  *  *  * *  * 8 | 0  0  0 1 1
------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------
xo.3xx.3ox. *b3oo.&#x &  48 48 | 24 96  96  96 24  0 | 32 64 48  96 48   0 32 32 32  0  0 | 16 8 32 24 32 32  0  0   0  8  8  8  0  0  0 | 1  8  8  8  0  0  0  0 1  0 0 | 2  *  * * *
xoo3xxx3oxo    ...&#x &  12 18 |  6 12  36  24  6 12 |  4  4 18  24 12  24  8  4  4 12  6 |  1 0  8  6  4  4 12 12  12  1  1  0  4  4  0 | 0  1  1  0  4  6  4  0 0  1 0 | * 16  * * *
xoo ... oxo    oox&#x     2  4 |  1  0   8   0  2  4 |  0  0  4   0  4   8  0  0  0  0  4 |  0 0  0  2  0  0  4  0   8  0  0  0  0  0  1 | 0  0  0  0  0  4  0  2 0  0 0 | *  * 24 * *
... xxx3oxo *b3oox&#x     6 24 |  0 12  24  24 12 24 |  0  8  0  24 12  24  0  8  8 12 24 |  0 1  0  0  8  8  0 12  24  0  0  2  0  8  6 | 0  0  0  2  0  0  8  6 0  0 1 | *  *  * 8 *
.oo3.xx3.xo *b3.ox&#x     0 96 |  0  0   0 192 48 96 |  0  0  0   0  0   0 64 64 64 96 96 |  0 0  0  0  0  0  0  0   0 16 16 16 32 64 24 | 0  0  0  0  0  0  0  0 2 16 8 | *  *  * * 1

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