Acronym ritgyt
Name rectified-tesseractic gyrotrigonism
Circumradius sqrt(5/3) = 1.290994
Lace city
in approx. ASCII-art
     		where:
    E		E = x3o3x *b3o (rit)
X    		O = x3o3o *b3x
    O		X = o3o3x *b3x
Confer
general polytopal classes:
segmentopeta   scaliform  

By means of a (partial) Stott expansion at the central node positions, applied simultanuously to all layers, this polypeton would produce tahgyt.


Incidence matrix according to Dynkin symbol

xxo3ooo3xox *b3oxx&#x   → all pairwise heights = 1/sqrt(2) = 0.707107

o..3o..3o.. *b3o..    & | 96 |   6   6 |   6  3  12  18  3 |  3  2  6  18   8   6  15 | 1  8  6  2  7  12 | 2  5  3
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x.. ... ...    ...    & |  2 | 288   * |   2  1   2   2  0 |  2  1  2   5   2   1   2 | 1  5  2  1  2   3 | 2  3  1
oo.3oo.3oo. *b3oo.&#x & |  2 |   * 288 |   0  0   2   4  1 |  0  0  1   4   2   2   6 | 0  2  2  1  3   6 | 1  3  2
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x..3o.. ...    ...    & |  3 |   3   0 | 192  *   *   *  * |  1  1  1   0   1   0   0 | 1  3  0  1  1   0 | 2  2  0
x.. ... x..    ...    & |  4 |   4   0 |   * 72   *   *  * |  2  0  0   4   0   0   0 | 1  4  2  0  0   2 | 2  2  1
xx. ... ...    ...&#x & |  4 |   2   2 |   *  * 288   *  * |  0  0  1   2   0   0   1 | 0  2  1  0  1   2 | 1  2  1
... ... xo.    ...&#x & |  3 |   1   2 |   *  *   * 576  * |  0  0  0   1   1   1   1 | 0  1  1  1  1   2 | 1  2  1
ooo3ooo3ooo *b3ooo&#x   |  3 |   0   3 |   *  *   *   * 96 |  0  0  0   0   0   0   6 | 0  0  0  0  3   6 | 0  3  2
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x..3o..3x..    ...    &  12 |  24   0 |   8  6   0   0  0 | 24  *  *   *   *   *   * | 1  2  0  0  0   0 | 2  1  0
x..3o.. ... *b3o..    &   4 |   6   0 |   4  0   0   0  0 |  * 48  *   *   *   *   * | 1  1  0  1  0   0 | 2  1  0
xx.3oo. ...    ...&#x &   6 |   6   3 |   2  0   3   0  0 |  *  * 96   *   *   *   * | 0  2  0  0  1   0 | 1  2  0
xx. ... xo.    ...&#x &   6 |   5   4 |   0  1   2   2  0 |  *  *  * 288   *   *   * | 0  1  1  0  0   1 | 1  1  1
... oo.3xo.    ...&#x &   4 |   3   3 |   1  0   0   3  0 |  *  *  *   * 192   *   * | 0  1  0  1  1   0 | 1  2  0
... ... xo.    ox.&#x &   4 |   2   4 |   0  0   0   4  0 |  *  *  *   *   * 144   * | 0  0  1  1  0   1 | 1  1  1
xxo ... ...    ...&#x &   5 |   2   6 |   0  0   1   2  2 |  *  *  *   *   *   * 288 | 0  0  0  0  1   2 | 0  2  1
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x..3o..3x.. *b3o..    &  32 |  96   0 |  64 24   0   0  0 |  8 16  0   0   0   0   0 | 3  *  *  *  *   * | 2  0  0
xx.3oo.3xo.    ...&#x &  16 |  30  12 |  12  6  12  12  0 |  1  1  4   6   4   0   0 | * 48  *  *  *   * | 1  1  0
xx. ... xo.    ox.&#x &   8 |   8   8 |   0  2   4   8  0 |  0  0  0   4   0   2   0 | *  * 72  *  *   * | 1  0  1
... oo.3xo. *b3ox.&#x &   8 |  12  12 |   8  0   0  24  0 |  0  2  0   0   8   6   0 | *  *  * 24  *   * | 1  1  0
xxo3ooo ...    ...&#x &   7 |   6   9 |   2  0   3   6  3 |  0  0  1   0   2   0   3 | *  *  *  * 96   * | 0  2  0
xxo ... xox    ...&#x &   8 |   6  12 |   0  1   4   8  4 |  0  0  0   2   0   1   4 | *  *  *  *  * 144 | 0  1  1
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
xx.3oo.3xo. *b3ox.&#x &  64 | 192  96 | 128 48  96 192  0 | 16 32 32  96  64  48   0 | 2 16 24  8  0   0 | 3  *  *
xxo3ooo3xox    ...&#x &  20 |  36  36 |  16  6  24  48 12 |  1  2  8  12  16   6  24 | 0  2  0  1  8   6 | * 24  *
xxo ... xox    oxx&#x    12 |  12  24 |   0  3  12  24  8 |  0  0  0  12   0   6  12 | 0  0  3  0  0   6 | *  * 24

x..3o..3x.. *b3o.. || .xo3.oo3.ox *b3.xx&#x   → height = sqrt(3/8) = 0.612372
( rit || gyro (rit || gyro rit) )

o..3o..3o.. *b3o..      | 32  * |  6   6  0  0  0 |  6  3  12  12   6  3  0  0  0   0  0 | 3  2  6 12  6  6  2  6  12  3  0  0  0  0  0  0  0 | 1  6  2  6  2  6  6  6  1 0 0  0  0 | 2 3  2  3 0
.o.3.o.3.o. *b3.o.    & |  * 64 |  0   3  3  3  3 |  0  0   6   3   6  3  3  3  3   9  6 | 0  0  3  3  6  1  3  3   9  6  1  3  1  4  3  9  3 | 0  1  3  3  1  4  3  9  3 1 1  3  4 | 1 1  4  3 1
------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------
x.. ... ...    ...    & |  2  0 | 96   *  *  *  * |  2  1   2   2   0  0  0  0  0   0  0 | 2  1  2  4  1  2  0  1   2  0  0  0  0  0  0  0  0 | 1  4  1  2  1  2  2  1  0 0 0  0  0 | 2 2  1  1 0
oo.3oo.3oo. *b3oo.&#x & |  1  1 |  * 192  *  *  * |  0  0   2   2   2  1  0  0  0   0  0 | 0  0  1  2  2  1  1  2   4  2  0  0  0  0  0  0  0 | 0  1  1  2  1  2  2  4  1 0 0  0  0 | 1 1  2  2 0
.x. ... ...    ...    & |  0  2 |  *   * 96  *  * |  0  0   2   0   0  0  2  1  0   2  0 | 0  0  2  1  2  0  0  0   2  0  1  2  0  2  1  2  0 | 0  1  2  1  0  2  1  2  0 1 1  1  2 | 1 1  2  1 1
... ... ...    .x.    & |  0  2 |  *   *  * 96  * |  0  0   0   0   2  0  0  1  2   0  2 | 0  0  0  0  2  0  2  1   0  2  0  2  1  0  0  3  2 | 0  0  2  1  1  0  0  3  2 1 0  1  3 | 1 0  3  1 1
.oo3.oo3.oo *b3.oo&#x   |  0  2 |  *   *  *  * 96 |  0  0   0   0   0  1  0  0  0   4  2 | 0  0  0  0  0  0  0  0   4  2  0  0  0  2  2  4  1 | 0  0  0  0  0  2  2  4  1 0 1  2  2 | 0 1  2  2 1
------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------
x..3o.. ...    ...    & |  3  0 |  3   0  0  0  0 | 64  *   *   *   *  *  *  *  *   *  * | 1  1  1  0  0  1  0  0   0  0  0  0  0  0  0  0  0 | 1  2  1  0  1  1  0  0  0 0 0  0  0 | 2 1  1  0 0
x.. ... x..    ...      |  4  0 |  4   0  0  0  0 |  * 24   *   *   *  *  *  *  *   *  * | 2  0  0  4  0  0  0  0   0  0  0  0  0  0  0  0  0 | 1  4  0  2  0  0  2  0  0 0 0  0  0 | 2 2  0  1 0
xx. ... ...    ...&#x & |  2  2 |  1   2  1  0  0 |  *  * 192   *   *  *  *  *  *   *  * | 0  0  1  1  1  0  0  0   1  0  0  0  0  0  0  0  0 | 0  1  1  1  0  1  1  1  0 0 0  0  0 | 1 1  1  1 0
... ... xo.    ...&#x & |  2  1 |  1   2  0  0  0 |  *  *   * 192   *  *  *  *  *   *  * | 0  0  0  1  0  1  0  1   1  0  0  0  0  0  0  0  0 | 0  1  0  1  1  1  1  1  0 0 0  0  0 | 1 1  1  1 0
... ... ...    ox.&#x & |  1  2 |  0   2  0  1  0 |  *  *   *   * 192  *  *  *  *   *  * | 0  0  0  0  1  0  1  1   0  1  0  0  0  0  0  0  0 | 0  0  1  1  1  0  0  2  1 0 0  0  0 | 1 0  2  1 0
ooo3ooo3ooo *b3ooo&#x   |  1  2 |  0   2  0  0  1 |  *  *   *   *   * 96  *  *  *   *  * | 0  0  0  0  0  0  0  0   4  2  0  0  0  0  0  0  0 | 0  0  0  0  0  2  2  4  1 0 0  0  0 | 0 1  2  2 0
.x.3.o. ...    ...    & |  0  3 |  0   0  3  0  0 |  *  *   *   *   *  * 64  *  *   *  * | 0  0  1  0  0  0  0  0   0  0  1  1  0  1  0  0  0 | 0  1  1  0  0  1  0  0  0 1 1  0  1 | 1 1  1  0 1
.x. ... ...    .x.    & |  0  4 |  0   0  2  2  0 |  *  *   *   *   *  *  * 48  *   *  * | 0  0  0  0  2  0  0  0   0  0  0  2  0  0  0  2  0 | 0  0  2  1  0  0  0  2  0 1 0  1  2 | 1 0  2  1 1
... .o. ... *b3.x.    & |  0  3 |  0   0  0  3  0 |  *  *   *   *   *  *  *  * 64   *  * | 0  0  0  0  0  0  1  0   0  0  0  1  1  0  0  0  1 | 0  0  1  0  1  0  0  0  1 1 0  0  2 | 1 0  2  0 1
.xo ... ...    ...&#x & |  0  3 |  0   0  1  0  2 |  *  *   *   *   *  *  *  *  * 192  * | 0  0  0  0  0  0  0  0   1  0  0  0  0  1  1  1  0 | 0  0  0  0  0  1  1  1  0 0 1  1  1 | 0 1  1  1 1
... ... ...    .xx      |  0  4 |  0   0  0  2  2 |  *  *   *   *   *  *  *  *  *   * 96 | 0  0  0  0  0  0  0  0   0  1  0  0  0  0  0  2  1 | 0  0  0  0  0  0  0  2  1 0 0  1  2 | 0 0  2  1 1
------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------
x..3o..3x..    ...       12  0 | 24   0  0  0  0 |  8  6   0   0   0  0  0  0  0   0  0 | 8  *  *  *  *  *  *  *   *  *  *  *  *  *  *  *  * | 1  2  0  0  0  0  0  0  0 0 0  0  0 | 2 1  0  0 0
x..3o.. ... *b3o..    &   4  0 |  6   0  0  0  0 |  4  0   0   0   0  0  0  0  0   0  0 | * 16  *  *  *  *  *  *   *  *  *  *  *  *  *  *  * | 1  0  1  0  1  0  0  0  0 0 0  0  0 | 2 0  1  0 0
xx.3oo. ...    ...&#x &   3  3 |  3   3  3  0  0 |  1  0   3   0   0  0  1  0  0   0  0 | *  * 64  *  *  *  *  *   *  *  *  *  *  *  *  *  * | 0  1  1  0  0  1  0  0  0 0 0  0  0 | 1 1  1  0 0
xx. ... xo.    ...&#x &   4  2 |  4   4  1  0  0 |  0  1   2   2   0  0  0  0  0   0  0 | *  *  * 96  *  *  *  *   *  *  *  *  *  *  *  *  * | 0  1  0  1  0  0  1  0  0 0 0  0  0 | 1 1  0  1 0
xx. ... ...    ox.&#x &   2  4 |  1   4  2  2  0 |  0  0   2   0   2  0  0  1  0   0  0 | *  *  *  * 96  *  *  *   *  *  *  *  *  *  *  *  * | 0  0  1  1  0  0  0  1  0 0 0  0  0 | 1 0  1  1 0
... oo.3xo.    ...&#x &   3  1 |  3   3  0  0  0 |  1  0   0   3   0  0  0  0  0   0  0 | *  *  *  *  * 64  *  *   *  *  *  *  *  *  *  *  * | 0  1  0  0  1  1  0  0  0 0 0  0  0 | 1 1  1  0 0
... oo. ... *b3ox.&#x &   1  3 |  0   3  0  3  0 |  0  0   0   0   3  0  0  0  1   0  0 | *  *  *  *  *  * 64  *   *  *  *  *  *  *  *  *  * | 0  0  1  0  1  0  0  0  1 0 0  0  0 | 1 0  2  0 0
... ... xo.    ox.&#x &   2  2 |  1   4  0  1  0 |  0  0   0   2   2  0  0  0  0   0  0 | *  *  *  *  *  *  * 96   *  *  *  *  *  *  *  *  * | 0  0  0  1  1  0  0  1  0 0 0  0  0 | 1 0  1  1 0
xxo ... ...    ...&#x &   2  3 |  1   4  1  0  2 |  0  0   1   1   0  2  0  0  0   1  0 | *  *  *  *  *  *  *  * 192  *  *  *  *  *  *  *  * | 0  0  0  0  0  1  1  1  0 0 0  0  0 | 0 1  1  1 0
... ... ...    oxx&#x     1  4 |  0   4  0  2  2 |  0  0   0   0   2  2  0  0  0   0  1 | *  *  *  *  *  *  *  *   * 96  *  *  *  *  *  *  * | 0  0  0  0  0  0  0  2  1 0 0  0  0 | 0 0  2  1 0
.x.3.o.3.o.    ...    &   0  4 |  0   0  6  0  0 |  0  0   0   0   0  0  4  0  0   0  0 | *  *  *  *  *  *  *  *   *  * 16  *  *  *  *  *  * | 0  1  0  0  0  0  0  0  0 1 1  0  0 | 1 1  0  0 1
.x.3.o. ... *b3.x.    &   0 12 |  0   0 12 12  0 |  0  0   0   0   0  0  4  6  4   0  0 | *  *  *  *  *  *  *  *   *  *  * 16  *  *  *  *  * | 0  0  1  0  0  0  0  0  0 1 0  0  1 | 1 0  1  0 1
... .o.3.o. *b3.x.    &   0  4 |  0   0  0  6  0 |  0  0   0   0   0  0  0  0  4   0  0 | *  *  *  *  *  *  *  *   *  *  *  * 16  *  *  *  * | 0  0  0  0  1  0  0  0  0 1 0  0  1 | 1 0  1  0 1
.xo3.oo ...    ...&#x &   0  4 |  0   0  3  0  3 |  0  0   0   0   0  0  1  0  0   3  0 | *  *  *  *  *  *  *  *   *  *  *  *  * 64  *  *  * | 0  0  0  0  0  1  0  0  0 0 1  0  1 | 0 1  1  0 1
.xo ... .ox    ...&#x     0  4 |  0   0  2  0  4 |  0  0   0   0   0  0  0  0  0   4  0 | *  *  *  *  *  *  *  *   *  *  *  *  *  * 48  *  * | 0  0  0  0  0  0  1  0  0 0 1  1  0 | 0 1  0  1 1
.xo ... ...    .xx&#x &   0  6 |  0   0  2  3  4 |  0  0   0   0   0  0  0  1  0   2  2 | *  *  *  *  *  *  *  *   *  *  *  *  *  *  * 96  * | 0  0  0  0  0  0  0  1  0 0 0  1  1 | 0 0  1  1 1
... .oo ... *b3.xx&#x     0  6 |  0   0  0  6  3 |  0  0   0   0   0  0  0  0  2   0  3 | *  *  *  *  *  *  *  *   *  *  *  *  *  *  *  * 32 | 0  0  0  0  0  0  0  0  1 0 0  0  2 | 0 0  2  0 1
------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------
x..3o..3x.. *b3o..       32  0 | 96   0  0  0  0 | 64 24   0   0   0  0  0  0  0   0  0 | 8 16  0  0  0  0  0  0   0  0  0  0  0  0  0  0  0 | 1  *  *  *  *  *  *  *  * * *  *  * | 2 0  0  0 0
xx.3oo.3xo.    ...&#x &  12  4 | 24  12  6  0  0 |  8  6  12  12   0  0  4  0  0   0  0 | 1  0  4  6  0  4  0  0   0  0  1  0  0  0  0  0  0 | * 16  *  *  *  *  *  *  * * *  *  * | 1 1  0  0 0
xx.3oo. ... *b3ox.&#x &   4 12 |  6  12 12 12  0 |  4  0  12   0  12  0  4  6  4   0  0 | 0  1  4  0  6  0  4  0   0  0  0  1  0  0  0  0  0 | *  * 16  *  *  *  *  *  * * *  *  * | 1 0  1  0 0
xx. ... xo.    ox.&#x &   4  4 |  4   8  2  2  0 |  0  1   4   4   4  0  0  1  0   0  0 | 0  0  0  2  2  0  0  2   0  0  0  0  0  0  0  0  0 | *  *  * 48  *  *  *  *  * * *  *  * | 1 0  0  1 0
... oo.3xo. *b3ox.&#x &   4  4 |  6  12  0  6  0 |  4  0   0  12  12  0  0  0  4   0  0 | 0  1  0  0  0  4  4  6   0  0  0  0  1  0  0  0  0 | *  *  *  * 16  *  *  *  * * *  *  * | 1 0  1  0 0
xxo3ooo ...    ...&#x &   3  4 |  3   6  3  0  3 |  1  0   3   3   0  3  1  0  0   3  0 | 0  0  1  0  0  1  0  0   3  0  0  0  0  1  0  0  0 | *  *  *  *  * 64  *  *  * * *  *  * | 0 1  1  0 0
xxo ... xox    ...&#x     4  4 |  4   8  2  0  4 |  0  1   4   4   0  4  0  0  0   4  0 | 0  0  0  2  0  0  0  0   4  0  0  0  0  0  1  0  0 | *  *  *  *  *  * 48  *  * * *  *  * | 0 1  0  1 0
xxo ... ...    oxx&#x &   2  6 |  1   8  2  3  4 |  0  0   2   2   4  4  0  1  0   2  2 | 0  0  0  0  1  0  0  1   2  2  0  0  0  0  0  1  0 | *  *  *  *  *  *  * 96  * * *  *  * | 0 0  1  1 0
... ooo ... *b3oxx&#x     1  6 |  0   6  0  6  3 |  0  0   0   0   6  3  0  0  2   0  3 | 0  0  0  0  0  0  2  0   0  3  0  0  0  0  0  0  1 | *  *  *  *  *  *  *  * 32 * *  *  * | 0 0  2  0 0
.x.3.o.3.o. *b3.x.    &   0 32 |  0   0 48 48  0 |  0  0   0   0   0  0 32 24 32   0  0 | 0  0  0  0  0  0  0  0   0  0  8  8  8  0  0  0  0 | *  *  *  *  *  *  *  *  * 2 *  *  * | 1 0  0  0 1
.xo3.oo3.ox    ...&#x     0  8 |  0   0 12  0 12 |  0  0   0   0   0  0  8  0  0  24  0 | 0  0  0  0  0  0  0  0   0  0  2  0  0  8  6  0  0 | *  *  *  *  *  *  *  *  * * 8  *  * | 0 1  0  0 1
.xo ... .ox    .xx&#x     0  8 |  0   0  4  4  8 |  0  0   0   0   0  0  0  2  0   8  4 | 0  0  0  0  0  0  0  0   0  0  0  0  0  0  2  4  0 | *  *  *  *  *  *  *  *  * * * 24  * | 0 0  0  1 1
... .oo3.ox *b3.xx&#x &   0 16 |  0   0 12 18 12 |  0  0   0   0   0  0  4  6  8  12 12 | 0  0  0  0  0  0  0  0   0  0  0  1  1  4  0  6  4 | *  *  *  *  *  *  *  *  * * *  * 16 | 0 0  1  0 1
------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------
xx.3oo.3xo. *b3ox.&#x &  32 32 | 96  96 48 48  0 | 64 24  96  96  96  0 32 24 32   0  0 | 8 16 32 48 48 32 32 48   0  0  8  8  8  0  0  0  0 | 1  8  8 24  8  0  0  0  0 1 0  0  0 | 2 *  *  * *
xxo3ooo3xox    ...&#x    12  8 | 24  24 12  0 12 |  8  6  24  24   0 12  8  0  0  24  0 | 1  0  8 12  0  8  0  0  24  0  2  0  0  8  6  0  0 | 0  2  0  0  0  8  6  0  0 0 1  0  0 | * 8  *  * *
xxo3ooo ... *b3oxx&#x &   4 16 |  6  24 12 18 12 |  4  0  12  12  24 12  4  6  8  12 12 | 0  1  4  0  6  4  8  6  12 12  0  1  1  4  0  6  4 | 0  0  1  0  1  4  0  6  4 0 0  0  1 | * * 16  * *
xxo ... xox    oxx&#x     4  8 |  4  16  4  4  8 |  0  1   8   8   8  8  0  2  0   8  4 | 0  0  0  4  4  0  0  4   8  4  0  0  0  0  2  4  0 | 0  0  0  2  0  0  2  4  0 0 0  1  0 | * *  * 24 *
.xo3.oo3.ox *b3.xx&#x     0 64 |  0   0 96 96 96 |  0  0   0   0   0  0 64 48 64 192 96 | 0  0  0  0  0  0  0  0   0  0 16 16 16 64 45 96 32 | 0  0  0  0  0  0  0  0  0 2 8 24 16 | * *  *  * 1

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