Acronym opeatut (alt.: octoct tuttric)
Name ope atop tut,
(oct,oct,tut)-trigonic
Circumradius sqrt(17/12) = 1.190238
Lace city
in approx. ASCII-art
o3x3o     o3x3o
               
     x3x3o     
Confer
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

ox oo3xx3xo&#x   → height = sqrt(3/8) = 0.612372
(tut || ope)

o. o.3o.3o.    | 12  * |  2 1  2 0  0 | 1 2  1  4  2  0 0 0 | 1  2 1 2 4 0 0 0 | 1 2 2 0
.o .o3.o3.o    |  * 12 |  0 0  2 1  4 | 0 0  2  4  1  4 2 2 | 0  4 1 2 2 2 2 1 | 2 2 1 1
---------------+-------+--------------+---------------------+------------------+--------
.. .. x. ..    |  2  0 | 12 *  * *  * | 1 1  0  2  0  0 0 0 | 1  1 0 2 2 0 0 0 | 1 1 2 0
.. .. .. x.    |  2  0 |  * 6  * *  * | 0 2  0  0  2  0 0 0 | 1  0 1 0 4 0 0 0 | 0 2 2 0
oo oo3oo3oo&#x |  1  1 |  * * 24 *  * | 0 0  1  2  1  0 0 0 | 0  2 1 1 2 0 0 0 | 1 2 1 0
.x .. .. ..    |  0  2 |  * *  * 6  * | 0 0  2  0  0  4 0 0 | 0  4 1 0 0 2 2 0 | 2 2 0 1
.. .. .x ..    |  0  2 |  * *  * * 24 | 0 0  0  1  0  1 1 1 | 0  1 0 1 1 1 1 1 | 1 1 1 1
---------------+-------+--------------+---------------------+------------------+--------
.. o.3x. ..    |  3  0 |  3 0  0 0  0 | 4 *  *  *  *  * * * | 1  0 0 2 0 0 0 0 | 1 0 2 0
.. .. x.3x.    |  6  0 |  3 3  0 0  0 | * 4  *  *  *  * * * | 1  0 0 0 2 0 0 0 | 0 1 2 0
ox .. .. ..&#x |  1  2 |  0 0  2 1  0 | * * 12  *  *  * * * | 0  2 1 0 0 0 0 0 | 1 2 0 0
.. .. xx ..&#x |  2  2 |  1 0  2 0  1 | * *  * 24  *  * * * | 0  1 0 1 1 0 0 0 | 1 1 1 0
.. .. .. xo&#x |  2  1 |  0 1  2 0  0 | * *  *  * 12  * * * | 0  0 1 0 2 0 0 0 | 0 2 1 0
.x .. .x ..    |  0  4 |  0 0  0 2  2 | * *  *  *  * 12 * * | 0  1 0 0 0 1 1 0 | 1 1 0 1
.. .o3.x ..    |  0  3 |  0 0  0 0  3 | * *  *  *  *  * 8 * | 0  0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.o    |  0  3 |  0 0  0 0  3 | * *  *  *  *  * * 8 | 0  0 0 0 1 0 1 1 | 0 1 1 1
---------------+-------+--------------+---------------------+------------------+--------
.. o.3x.3x.     12  0 | 12 6  0 0  0 | 4 4  0  0  0  0 0 0 | 1  * * * * * * * | 0 0 2 0
ox .. xx ..&#x   2  4 |  1 0  4 2  2 | 0 0  2  2  0  1 0 0 | * 12 * * * * * * | 1 1 0 0
ox .. .. xo&#x   2  2 |  0 1  4 1  0 | 0 0  2  0  2  0 0 0 | *  * 6 * * * * * | 0 2 0 0
.. oo3xx ..&#x   3  3 |  3 0  3 0  3 | 1 0  0  3  0  0 1 0 | *  * * 8 * * * * | 1 0 1 0
.. .. xx3xo&#x   6  3 |  3 3  6 0  3 | 0 1  0  3  3  0 0 1 | *  * * * 8 * * * | 0 1 1 0
.x .o3.x ..      0  6 |  0 0  0 3  6 | 0 0  0  0  0  3 2 0 | *  * * * * 4 * * | 1 0 0 1
.x .. .x3.o      0  6 |  0 0  0 3  6 | 0 0  0  0  0  3 0 2 | *  * * * * * 4 * | 0 1 0 1
.. .o3.x3.o      0  6 |  0 0  0 0 12 | 0 0  0  0  0  0 4 4 | *  * * * * * * 2 | 0 0 1 1
---------------+-------+--------------+---------------------+------------------+--------
ox oo3xx ..&#x   3  6 |  3 0  6 3  6 | 1 0  3  6  0  3 2 0 | 0  3 0 2 0 1 0 0 | 4 * * *
ox .. xx3xo&#x   6  6 |  3 3 12 3  6 | 0 1  6  6  6  3 0 2 | 0  3 3 0 2 0 1 0 | * 4 * *
.. oo3xx3xo&#x  12  6 | 12 6 12 0 12 | 4 4  0 12  6  0 4 4 | 1  0 0 4 4 0 0 1 | * * 2 *
.x .o3.x3.o      0 12 |  0 0  0 6 24 | 0 0  0  0  0 12 8 8 | 0  0 0 0 0 4 4 2 | * * * 1

ooo3xxx3oox&#x   → height(1,2) = 1
                   height(1,3) = height(2,3) = sqrt(5/8) = 0.790569

o..3o..3o..    | 6 *  * |  4 1  2  0  0  0 0 | 2 2  4  2  4 1 0 0  0 0 0 0 | 1 2 2  4 1 2 2 0 0 0 0 | 1 2 2 1 0
.o.3.o.3.o.    | * 6  * |  0 1  0  4  2  0 0 | 0 0  4  2  0 0 2 2  4 1 0 0 | 0 2 2  4 1 0 0 1 2 2 0 | 1 2 2 0 1
..o3..o3..o    | * * 12 |  0 0  1  0  1  2 1 | 0 0  0  1  2 1 0 0  2 1 1 2 | 0 0 0  2 1 1 2 0 1 2 1 | 0 1 2 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
... x.. ...    | 2 0  0 | 12 *  *  *  *  * * | 1 1  1  0  1 0 0 0  0 0 0 0 | 1 1 1  1 0 1 1 0 0 0 0 | 1 1 1 1 0
oo.3oo.3oo.&#x | 1 1  0 |  * 6  *  *  *  * * | 0 0  4  2  0 0 0 0  0 0 0 0 | 0 2 2  4 1 0 0 0 0 0 0 | 1 2 2 0 0
o.o3o.o3o.o&#x | 1 0  1 |  * * 12  *  *  * * | 0 0  0  1  2 1 0 0  0 0 0 0 | 0 0 0  2 1 1 2 0 0 0 0 | 0 1 2 1 0
... .x. ...    | 0 2  0 |  * *  * 12  *  * * | 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
.oo3.oo3.oo&#x | 0 1  1 |  * *  *  * 12  * * | 0 0  0  1  0 0 0 0  2 1 0 0 | 0 0 0  2 1 0 0 0 1 2 0 | 0 1 2 0 1
... ..x ...    | 0 0  2 |  * *  *  *  * 12 * | 0 0  0  0  1 0 0 0  1 0 1 1 | 0 0 0  1 0 1 1 0 1 1 1 | 0 1 1 1 1
... ... ..x    | 0 0  2 |  * *  *  *  *  * 6 | 0 0  0  0  0 1 0 0  0 1 0 2 | 0 0 0  0 1 0 2 0 0 2 1 | 0 0 2 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
o..3x.. ...    | 3 0  0 |  3 0  0  0  0  0 0 | 4 *  *  *  * * * *  * * * * | 1 1 0  0 0 1 0 0 0 0 0 | 1 1 0 1 0
... x..3o..    | 3 0  0 |  3 0  0  0  0  0 0 | * 4  *  *  * * * *  * * * * | 1 0 1  0 0 0 1 0 0 0 0 | 1 0 1 1 0
... xx. ...&#x | 2 2  0 |  1 2  0  1  0  0 0 | * * 12  *  * * * *  * * * * | 0 1 1  1 0 0 0 0 0 0 0 | 1 1 1 0 0
ooo3ooo3ooo&#x | 1 1  1 |  0 1  1  0  1  0 0 | * *  * 12  * * * *  * * * * | 0 0 0  2 1 0 0 0 0 0 0 | 0 1 2 0 0
... x.x ...&#x | 2 0  2 |  1 0  2  0  0  1 0 | * *  *  * 12 * * *  * * * * | 0 0 0  1 0 1 1 0 0 0 0 | 0 1 1 1 0
... ... o.x&#x | 1 0  2 |  0 0  2  0  0  0 1 | * *  *  *  * 6 * *  * * * * | 0 0 0  0 1 0 2 0 0 0 0 | 0 0 2 1 0
.o.3.x. ...    | 0 3  0 |  0 0  0  3  0  0 0 | * *  *  *  * * 4 *  * * * * | 0 1 0  0 0 0 0 1 1 0 0 | 1 1 0 0 1
... .x.3.o.    | 0 3  0 |  0 0  0  3  0  0 0 | * *  *  *  * * * 4  * * * * | 0 0 1  0 0 0 0 1 0 1 0 | 1 0 1 0 1
... .xx ...&#x | 0 2  2 |  0 0  0  1  2  1 0 | * *  *  *  * * * * 12 * * * | 0 0 0  1 0 0 0 0 1 1 0 | 0 1 1 0 1
... ... .ox&#x | 0 1  2 |  0 0  0  0  2  0 1 | * *  *  *  * * * *  * 6 * * | 0 0 0  0 1 0 0 0 0 2 0 | 0 0 2 0 1
..o3..x ...    | 0 0  3 |  0 0  0  0  0  3 0 | * *  *  *  * * * *  * * 4 * | 0 0 0  0 0 1 0 0 1 0 1 | 0 1 0 1 1
... ..x3..x    | 0 0  6 |  0 0  0  0  0  3 3 | * *  *  *  * * * *  * * * 4 | 0 0 0  0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
o..3x..3o..     6 0  0 | 12 0  0  0  0  0 0 | 4 4  0  0  0 0 0 0  0 0 0 0 | 1 * *  * * * * * * * * | 1 0 0 1 0
oo.3xx. ...&#x  3 3  0 |  3 3  0  3  0  0 0 | 1 0  3  0  0 0 1 0  0 0 0 0 | * 4 *  * * * * * * * * | 1 1 0 0 0
... xx.3oo.&#x  3 3  0 |  3 3  0  3  0  0 0 | 0 1  3  0  0 0 0 1  0 0 0 0 | * * 4  * * * * * * * * | 1 0 1 0 0
... xxx ...&#x  2 2  2 |  1 2  2  1  2  1 0 | 0 0  1  2  1 0 0 0  1 0 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0
... ... oox&#x  1 1  2 |  0 1  2  0  2  0 1 | 0 0  0  2  0 1 0 0  0 1 0 0 | * * *  * 6 * * * * * * | 0 0 2 0 0
o.o3x.x ...&#x  3 0  3 |  3 0  3  0  0  3 0 | 1 0  0  0  3 0 0 0  0 0 1 0 | * * *  * * 4 * * * * * | 0 1 0 1 0
... x.x3o.x&#x  3 0  6 |  3 0  6  0  0  3 3 | 0 1  0  0  3 3 0 0  0 0 0 1 | * * *  * * * 4 * * * * | 0 0 1 1 0
.o.3.x.3.o.     0 6  0 |  0 0  0 12  0  0 0 | 0 0  0  0  0 0 4 4  0 0 0 0 | * * *  * * * * 1 * * * | 1 0 0 0 1
.oo3.xx ...&#x  0 3  3 |  0 0  0  3  3  3 0 | 0 0  0  0  0 0 1 0  3 0 1 0 | * * *  * * * * * 4 * * | 0 1 0 0 1
... .xx3.ox&#x  0 3  6 |  0 0  0  3  6  3 3 | 0 0  0  0  0 0 0 1  3 3 0 1 | * * *  * * * * * * 4 * | 0 0 1 0 1
..o3..x3..x     0 0 12 |  0 0  0  0  0 12 6 | 0 0  0  0  0 0 0 0  0 0 4 4 | * * *  * * * * * * * 1 | 0 0 0 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
oo.3xx.3oo.&#x  6 6  0 | 12 6  0 12  0  0 0 | 4 4 12  0  0 0 4 4  0 0 0 0 | 1 4 4  0 0 0 0 1 0 0 0 | 1 * * * *
ooo3xxx ...&#x  3 3  3 |  3 3  3  3  3  3 0 | 1 0  3  3  3 0 1 0  3 0 1 0 | 0 1 0  3 0 1 0 0 1 0 0 | * 4 * * *
... xxx3oox&#x  3 3  6 |  3 3  6  3  6  3 3 | 0 1  3  6  3 3 0 1  3 3 0 1 | 0 0 1  3 3 0 1 0 0 1 0 | * * 4 * *
o.o3x.x3o.x&#x  6 0 12 | 12 0 12  0  0 12 6 | 4 4  0  0 12 6 0 0  0 0 4 4 | 1 0 0  0 0 4 4 0 0 0 1 | * * * 1 *
.oo3.xx3.ox&#x  0 6 12 |  0 0  0 12 12 12 6 | 0 0  0  0  0 0 4 4 12 6 4 4 | 0 0 0  0 0 0 0 1 4 4 1 | * * * * 1

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