Acronym tutatope
Name tut atop tope,
tut-first cap of pattix
Circumradius sqrt(41/12) = 1.848423
Lace city
in approx. ASCII-art
    x3x3o    
             
             
x3x3x   x3x3x
Confer
uniform relative:
pattix  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

ox ox3xx3xx&#x   → height = sqrt(3/8) = 0.612372
(tut || tope)

o. o.3o.3o.    | 12  * |  2 1  4  0  0  0  0 | 1 2  2  2  4  4  0  0  0 0  0 0 | 1  1  2  2 2  2 4 0 0 0 0 | 1 1 2 2 0
.o .o3.o3.o    |  * 48 |  0 0  1  1  1  1  1 | 0 0  1  1  1  1  1  1  1 1  1 1 | 0  1  1  1 1  1 1 1 1 1 1 | 1 1 1 1 1
---------------+-------+---------------------+---------------------------------+---------------------------+----------
.. .. x. ..    |  2  0 | 12 *  *  *  *  *  * | 1 1  0  0  2  0  0  0  0 0  0 0 | 1  0  1  0 2  0 2 0 0 0 0 | 1 0 1 2 0
.. .. .. x.    |  2  0 |  * 6  *  *  *  *  * | 0 2  0  0  0  4  0  0  0 0  0 0 | 1  0  0  2 0  2 4 0 0 0 0 | 0 1 2 2 0
oo oo3oo3oo&#x |  1  1 |  * * 48  *  *  *  * | 0 0  1  1  1  1  0  0  0 0  0 0 | 0  1  1  1 1  1 1 0 0 0 0 | 1 1 1 1 0
.x .. .. ..    |  0  2 |  * *  * 24  *  *  * | 0 0  1  0  0  0  1  1  1 0  0 0 | 0  1  1  1 0  0 0 1 1 1 0 | 1 1 1 0 1
.. .x .. ..    |  0  2 |  * *  *  * 24  *  * | 0 0  0  1  0  0  1  0  0 1  1 0 | 0  1  0  0 1  1 0 1 1 0 1 | 1 1 0 1 1
.. .. .x ..    |  0  2 |  * *  *  *  * 24  * | 0 0  0  0  1  0  0  1  0 1  0 1 | 0  0  1  0 1  0 1 1 0 1 1 | 1 0 1 1 1
.. .. .. .x    |  0  2 |  * *  *  *  *  * 24 | 0 0  0  0  0  1  0  0  1 0  1 1 | 0  0  0  1 0  1 1 0 1 1 1 | 0 1 1 1 1
---------------+-------+---------------------+---------------------------------+---------------------------+----------
.. o.3x. ..    |  3  0 |  3 0  0  0  0  0  0 | 4 *  *  *  *  *  *  *  * *  * * | 1  0  0  0 2  0 0 0 0 0 0 | 1 0 0 2 0
.. .. x.3x.    |  6  0 |  3 3  0  0  0  0  0 | * 4  *  *  *  *  *  *  * *  * * | 1  0  0  0 0  0 2 0 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x |  1  2 |  0 0  2  1  0  0  0 | * * 24  *  *  *  *  *  * *  * * | 0  1  1  1 0  0 0 0 0 0 0 | 1 1 1 0 0
.. ox .. ..&#x |  1  2 |  0 0  2  0  1  0  0 | * *  * 24  *  *  *  *  * *  * * | 0  1  0  0 1  1 0 0 0 0 0 | 1 1 0 1 0
.. .. xx ..&#x |  2  2 |  1 0  2  0  0  1  0 | * *  *  * 24  *  *  *  * *  * * | 0  0  1  0 1  0 1 0 0 0 0 | 1 0 1 1 0
.. .. .. xx&#x |  2  2 |  0 1  2  0  0  0  1 | * *  *  *  * 24  *  *  * *  * * | 0  0  0  1 0  1 1 0 0 0 0 | 0 1 1 1 0
.x .x .. ..    |  0  4 |  0 0  0  2  2  0  0 | * *  *  *  *  * 12  *  * *  * * | 0  1  0  0 0  0 0 1 1 0 0 | 1 1 0 0 1
.x .. .x ..    |  0  4 |  0 0  0  2  0  2  0 | * *  *  *  *  *  * 12  * *  * * | 0  0  1  0 0  0 0 1 0 1 0 | 1 0 1 0 1
.x .. .. .x    |  0  4 |  0 0  0  2  0  0  2 | * *  *  *  *  *  *  * 12 *  * * | 0  0  0  1 0  0 0 0 1 1 0 | 0 1 1 0 1
.. .x3.x ..    |  0  6 |  0 0  0  0  3  3  0 | * *  *  *  *  *  *  *  * 8  * * | 0  0  0  0 1  0 0 1 0 0 1 | 1 0 0 1 0
.. .x .. .x    |  0  4 |  0 0  0  0  2  0  2 | * *  *  *  *  *  *  *  * * 12 * | 0  0  0  0 0  1 0 0 1 0 1 | 0 1 0 1 1
.. .. .x3.x    |  0  6 |  0 0  0  0  0  3  3 | * *  *  *  *  *  *  *  * *  * 8 | 0  0  0  0 0  0 1 0 0 1 1 | 0 0 1 1 1
---------------+-------+---------------------+---------------------------------+---------------------------+----------
.. o.3x.3x.     12  0 | 12 6  0  0  0  0  0 | 4 4  0  0  0  0  0  0  0 0  0 0 | 1  *  *  * *  * * * * * * | 0 0 0 2 0
ox ox .. ..&#x   1  4 |  0 0  4  2  2  0  0 | 0 0  2  2  0  0  1  0  0 0  0 0 | * 12  *  * *  * * * * * * | 1 1 0 0 0
ox .. xx ..&#x   2  4 |  1 0  4  2  0  2  0 | 0 0  2  0  2  0  0  1  0 0  0 0 | *  * 12  * *  * * * * * * | 1 0 1 0 0
ox .. .. xx&#x   2  4 |  0 1  4  2  0  0  2 | 0 0  2  0  0  2  0  0  1 0  0 0 | *  *  * 12 *  * * * * * * | 0 1 1 0 0
.. ox3xx ..&#x   3  6 |  3 0  6  0  3  3  0 | 1 0  0  3  3  0  0  0  0 1  0 0 | *  *  *  * 8  * * * * * * | 1 0 0 1 0
.. ox .. xx&#x   2  4 |  0 1  4  0  2  0  2 | 0 0  0  2  0  2  0  0  0 0  1 0 | *  *  *  * * 12 * * * * * | 0 1 0 1 0
.. .. xx3xx&#x   6  6 |  3 3  6  0  0  3  3 | 0 1  0  0  3  3  0  0  0 0  0 1 | *  *  *  * *  * 8 * * * * | 0 0 1 1 0
.x .x3.x ..      0 12 |  0 0  0  6  6  6  0 | 0 0  0  0  0  0  3  3  0 2  0 0 | *  *  *  * *  * * 4 * * * | 1 0 0 0 1
.x .x .. .x      0  8 |  0 0  0  4  4  0  4 | 0 0  0  0  0  0  2  0  2 0  2 0 | *  *  *  * *  * * * 6 * * | 0 1 0 0 1
.x .. .x3.x      0 12 |  0 0  0  6  0  6  6 | 0 0  0  0  0  0  0  3  3 0  0 2 | *  *  *  * *  * * * * 4 * | 0 0 1 0 1
.. .x3.x3.x      0 24 |  0 0  0  0 12 12 12 | 0 0  0  0  0  0  0  0  0 4  6 4 | *  *  *  * *  * * * * * 2 | 0 0 0 1 1
---------------+-------+---------------------+---------------------------------+---------------------------+----------
ox ox3xx ..&#x   3 12 |  3 0 12  6  6  6  0 | 1 0  6  6  6  0  3  3  0 2  0 0 | 0  3  3  0 2  0 0 1 0 0 0 | 4 * * * *
ox ox .. xx&#x   2  8 |  0 1  8  4  4  0  4 | 0 0  4  4  0  4  2  0  2 0  2 0 | 0  2  0  2 0  2 0 0 1 0 0 | * 6 * * *
ox .. xx3xx&#x   6 12 |  3 3 12  6  0  6  6 | 0 1  6  0  6  6  0  3  3 0  0 2 | 0  0  3  3 0  0 2 0 0 1 0 | * * 4 * *
.. ox3xx3xx&#x  12 24 | 12 6 24  0 12 12 12 | 4 4  0 12 12 12  0  0  0 4  6 4 | 1  0  0  0 4  6 4 0 0 0 1 | * * * 2 *
.x .x3.x3.x      0 48 |  0 0  0 24 24 24 24 | 0 0  0  0  0  0 12 12 12 8 12 8 | 0  0  0  0 0  0 0 4 6 4 2 | * * * * 1

oxx3xxx3xxx&#x   → height(1,2) = height(1,3) = sqrt(5/8) = 0.790569
                   height(2,3) = 1
                   height(1,23) = sqrt(3/8) = 0.612372

o..3o..3o..    | 12  *  * |  2 1  2  2  0  0  0  0  0  0  0 | 1 2  1  2  2  2  1  2  2 0 0 0  0  0  0 0 0 0 | 1 1 1 2  1  2  2 1 1 2 0 0 0 0 0 | 1 1 1 2 1 0
.o.3.o.3.o.    |  * 24  * |  0 0  1  0  1  1  1  1  0  0  0 | 0 0  1  1  1  1  0  0  0 1 1 1  1  1  1 0 0 0 | 0 1 1 1  1  1  1 0 0 0 1 1 1 1 0 | 1 1 1 1 0 1
..o3..o3..o    |  *  * 24 |  0 0  0  1  0  0  0  1  1  1  1 | 0 0  0  0  0  1  1  1  1 0 0 0  1  1  1 1 1 1 | 0 0 0 0  1  1  1 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
---------------+----------+---------------------------------+-----------------------------------------------+----------------------------------+------------
... x.. ...    |  2  0  0 | 12 *  *  *  *  *  *  *  *  *  * | 1 1  0  1  0  0  0  1  0 0 0 0  0  0  0 0 0 0 | 1 1 0 1  0  1  0 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0
... ... x..    |  2  0  0 |  * 6  *  *  *  *  *  *  *  *  * | 0 2  0  0  2  0  0  0  2 0 0 0  0  0  0 0 0 0 | 1 0 1 2  0  0  2 0 1 2 0 0 0 0 0 | 1 0 1 2 1 0
oo.3oo.3oo.&#x |  1  1  0 |  * * 24  *  *  *  *  *  *  *  * | 0 0  1  1  1  1  0  0  0 0 0 0  0  0  0 0 0 0 | 0 1 1 1  1  1  1 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0
o.o3o.o3o.o&#x |  1  0  1 |  * *  * 24  *  *  *  *  *  *  * | 0 0  0  0  0  1  1  1  1 0 0 0  0  0  0 0 0 0 | 0 0 0 0  1  1  1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x. ... ...    |  0  2  0 |  * *  *  * 12  *  *  *  *  *  * | 0 0  1  0  0  0  0  0  0 1 1 0  1  0  0 0 0 0 | 0 1 1 0  1  0  0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
... .x. ...    |  0  2  0 |  * *  *  *  * 12  *  *  *  *  * | 0 0  0  1  0  0  0  0  0 1 0 1  0  1  0 0 0 0 | 0 1 0 1  0  1  0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
... ... .x.    |  0  2  0 |  * *  *  *  *  * 12  *  *  *  * | 0 0  0  0  1  0  0  0  0 0 1 1  0  0  1 0 0 0 | 0 0 1 1  0  0  1 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo3.oo3.oo&#x |  0  1  1 |  * *  *  *  *  *  * 24  *  *  * | 0 0  0  0  0  1  0  0  0 0 0 0  1  1  1 0 0 0 | 0 0 0 0  1  1  1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    |  0  0  2 |  * *  *  *  *  *  *  * 12  *  * | 0 0  0  0  0  0  1  0  0 0 0 0  1  0  0 1 1 0 | 0 0 0 0  1  0  0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
... ..x ...    |  0  0  2 |  * *  *  *  *  *  *  *  * 12  * | 0 0  0  0  0  0  0  1  0 0 0 0  0  1  0 1 0 1 | 0 0 0 0  0  1  0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
... ... ..x    |  0  0  2 |  * *  *  *  *  *  *  *  *  * 12 | 0 0  0  0  0  0  0  0  1 0 0 0  0  0  1 0 1 1 | 0 0 0 0  0  0  1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------+----------+---------------------------------+-----------------------------------------------+----------------------------------+------------
o..3x.. ...    |  3  0  0 |  3 0  0  0  0  0  0  0  0  0  0 | 4 *  *  *  *  *  *  *  * * * *  *  *  * * * * | 1 1 0 0  0  0  0 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
... x..3x..    |  6  0  0 |  3 3  0  0  0  0  0  0  0  0  0 | * 4  *  *  *  *  *  *  * * * *  *  *  * * * * | 1 0 0 1  0  0  0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
ox. ... ...&#x |  1  2  0 |  0 0  2  0  1  0  0  0  0  0  0 | * * 12  *  *  *  *  *  * * * *  *  *  * * * * | 0 1 1 0  1  0  0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... xx. ...&#x |  2  2  0 |  1 0  2  0  0  1  0  0  0  0  0 | * *  * 12  *  *  *  *  * * * *  *  *  * * * * | 0 1 0 1  0  1  0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... ... xx.&#x |  2  2  0 |  0 1  2  0  0  0  1  0  0  0  0 | * *  *  * 12  *  *  *  * * * *  *  *  * * * * | 0 0 1 1  0  0  1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo3ooo3ooo&#x |  1  1  1 |  0 0  1  1  0  0  0  1  0  0  0 | * *  *  *  * 24  *  *  * * * *  *  *  * * * * | 0 0 0 0  1  1  1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x |  1  0  2 |  0 0  0  2  0  0  0  0  1  0  0 | * *  *  *  *  * 12  *  * * * *  *  *  * * * * | 0 0 0 0  1  0  0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... x.x ...&#x |  2  0  2 |  1 0  0  2  0  0  0  0  0  1  0 | * *  *  *  *  *  * 12  * * * *  *  *  * * * * | 0 0 0 0  0  1  0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.x&#x |  2  0  2 |  0 1  0  2  0  0  0  0  0  0  1 | * *  *  *  *  *  *  * 12 * * *  *  *  * * * * | 0 0 0 0  0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x.3.x. ...    |  0  6  0 |  0 0  0  0  3  3  0  0  0  0  0 | * *  *  *  *  *  *  *  * 4 * *  *  *  * * * * | 0 1 0 0  0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.x. ... .x.    |  0  4  0 |  0 0  0  0  2  0  2  0  0  0  0 | * *  *  *  *  *  *  *  * * 6 *  *  *  * * * * | 0 0 1 0  0  0  0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .x.3.x.    |  0  6  0 |  0 0  0  0  0  3  3  0  0  0  0 | * *  *  *  *  *  *  *  * * * 4  *  *  * * * * | 0 0 0 1  0  0  0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x |  0  2  2 |  0 0  0  0  1  0  0  2  1  0  0 | * *  *  *  *  *  *  *  * * * * 12  *  * * * * | 0 0 0 0  1  0  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .xx ...&#x |  0  2  2 |  0 0  0  0  0  1  0  2  0  1  0 | * *  *  *  *  *  *  *  * * * *  * 12  * * * * | 0 0 0 0  0  1  0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xx&#x |  0  2  2 |  0 0  0  0  0  0  1  2  0  0  1 | * *  *  *  *  *  *  *  * * * *  *  * 12 * * * | 0 0 0 0  0  0  1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x3..x ...    |  0  0  6 |  0 0  0  0  0  0  0  0  3  3  0 | * *  *  *  *  *  *  *  * * * *  *  *  * 4 * * | 0 0 0 0  0  0  0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
..x ... ..x    |  0  0  4 |  0 0  0  0  0  0  0  0  2  0  2 | * *  *  *  *  *  *  *  * * * *  *  *  * * 6 * | 0 0 0 0  0  0  0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..x3..x    |  0  0  6 |  0 0  0  0  0  0  0  0  0  3  3 | * *  *  *  *  *  *  *  * * * *  *  *  * * * 4 | 0 0 0 0  0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+----------+---------------------------------+-----------------------------------------------+----------------------------------+------------
o..3x..3x..     12  0  0 | 12 6  0  0  0  0  0  0  0  0  0 | 4 4  0  0  0  0  0  0  0 0 0 0  0  0  0 0 0 0 | 1 * * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
ox.3xx. ...&#x   3  6  0 |  3 0  6  0  3  3  0  0  0  0  0 | 1 0  3  3  0  0  0  0  0 1 0 0  0  0  0 0 0 0 | * 4 * *  *  *  * * * * * * * * * | 1 1 0 0 0 0
ox. ... xx.&#x   2  4  0 |  0 1  4  0  2  0  2  0  0  0  0 | 0 0  2  0  2  0  0  0  0 0 1 0  0  0  0 0 0 0 | * * 6 *  *  *  * * * * * * * * * | 1 0 1 0 0 0
... xx.3xx.&#x   6  6  0 |  3 3  6  0  0  3  3  0  0  0  0 | 0 1  0  3  3  0  0  0  0 0 0 1  0  0  0 0 0 0 | * * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x   1  2  2 |  0 0  2  2  1  0  0  2  1  0  0 | 0 0  1  0  0  2  1  0  0 0 0 0  1  0  0 0 0 0 | * * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... xxx ...&#x   2  2  2 |  1 0  2  2  0  1  0  2  0  1  0 | 0 0  0  1  0  2  0  1  0 0 0 0  0  1  0 0 0 0 | * * * *  * 12  * * * * * * * * * | 0 1 0 1 0 0
... ... xxx&#x   2  2  2 |  0 1  2  2  0  0  1  2  0  0  1 | 0 0  0  0  1  2  0  0  1 0 0 0  0  0  1 0 0 0 | * * * *  *  * 12 * * * * * * * * | 0 0 1 1 0 0
o.x3x.x ...&#x   3  0  6 |  3 0  0  6  0  0  0  0  3  3  0 | 1 0  0  0  0  0  3  3  0 0 0 0  0  0  0 1 0 0 | * * * *  *  *  * 4 * * * * * * * | 0 1 0 0 1 0
o.x ... x.x&#x   2  0  4 |  0 1  0  4  0  0  0  0  2  0  2 | 0 0  0  0  0  0  2  0  2 0 0 0  0  0  0 0 1 0 | * * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... x.x3x.x&#x   6  0  6 |  3 3  0  6  0  0  0  0  0  3  3 | 0 1  0  0  0  0  0  3  3 0 0 0  0  0  0 0 0 1 | * * * *  *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.x.3.x.3.x.      0 24  0 |  0 0  0  0 12 12 12  0  0  0  0 | 0 0  0  0  0  0  0  0  0 4 6 4  0  0  0 0 0 0 | * * * *  *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.xx3.xx ...&#x   0  6  6 |  0 0  0  0  3  3  0  6  3  3  0 | 0 0  0  0  0  0  0  0  0 1 0 0  3  3  0 1 0 0 | * * * *  *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.xx ... .xx&#x   0  4  4 |  0 0  0  0  2  0  2  4  2  0  2 | 0 0  0  0  0  0  0  0  0 0 1 0  2  0  2 0 1 0 | * * * *  *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .xx3.xx&#x   0  6  6 |  0 0  0  0  0  3  3  6  0  3  3 | 0 0  0  0  0  0  0  0  0 0 0 1  0  3  3 0 0 1 | * * * *  *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..x3..x      0  0 24 |  0 0  0  0  0  0  0  0 12 12 12 | 0 0  0  0  0  0  0  0  0 0 0 0  0  0  0 4 6 4 | * * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+----------+---------------------------------+-----------------------------------------------+----------------------------------+------------
ox.3xx.3xx.&#x  12 24  0 | 12 6 24  0 12 12 12  0  0  0  0 | 4 4 12 12 12  0  0  0  0 4 6 4  0  0  0 0 0 0 | 1 4 6 4  0  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
oxx3xxx ...&#x   3  6  6 |  3 0  6  6  3  3  0  6  3  3  0 | 1 0  3  3  0  6  3  3  0 1 0 0  3  3  0 1 0 0 | 0 1 0 0  3  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
oxx ... xxx&#x   2  4  4 |  0 1  4  4  2  0  2  4  2  0  2 | 0 0  2  0  2  4  2  0  2 0 1 0  2  0  2 0 1 0 | 0 0 1 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... xxx3xxx&#x   6  6  6 |  3 3  6  6  0  3  3  6  0  3  3 | 0 1  0  3  3  6  0  3  3 0 0 1  0  3  3 0 0 1 | 0 0 0 1  0  3  3 0 0 1 0 0 0 1 0 | * * * 4 * *
o.x3x.x3x.x&#x  12  0 24 | 12 6  0 24  0  0  0  0 12 12 12 | 4 4  0  0  0  0 12 12 12 0 0 0  0  0  0 4 6 4 | 1 0 0 0  0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.xx3.xx3.xx&#x   0 24 24 |  0 0  0  0 12 12 12 24 12 12 12 | 0 0  0  0  0  0  0  0  0 4 6 4 12 12 12 4 6 4 | 0 0 0 0  0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1

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