Acronym octatuttip (alt.: octtut tuttric)
Name oct atop tuttip,
(oct,tut,tut)-trigonic
Circumradius sqrt(2) = 1.414214
Lace city
in approx. ASCII-art
     o3x3o     
               
x3x3o     x3x3o
Confer
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

ox oo3xx3ox&#x   → height = sqrt(3/8) = 0.612372
(oct || tuttip)

o. o.3o.3o.    | 6  * |  4  4  0  0  0 | 2 2  2  8  2  0 0 0 0 | 1  4 1 4 4 0 0 0 | 2 2 2 0
.o .o3.o3.o    | * 24 |  0  1  1  2  1 | 0 0  1  2  1  2 1 1 2 | 0  2 1 1 2 1 2 1 | 1 2 1 1
---------------+------+----------------+-----------------------+------------------+--------
.. .. x. ..    | 2  0 | 12  *  *  *  * | 1 1  0  1  0  0 0 0 0 | 1  1 0 2 2 0 0 0 | 1 1 2 0
oo oo3oo3oo&#x | 1  1 |  * 24  *  *  * | 0 0  1  2  1  0 0 0 0 | 0  2 1 1 2 0 0 0 | 1 2 1 0
.x .. .. ..    | 0  2 |  *  * 12  *  * | 0 0  1  0  0  2 1 0 0 | 0  2 1 0 0 1 2 0 | 1 2 0 1
.. .. .x ..    | 0  2 |  *  *  * 24  * | 0 0  0  1  0  1 0 1 1 | 0  1 0 1 1 1 1 1 | 1 1 1 1
.. .. .. .x    | 0  2 |  *  *  *  * 12 | 0 0  0  0  1  0 1 0 2 | 0  0 1 0 2 0 2 1 | 0 2 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.3o.    | 3  0 |  3  0  0  0  0 | * 4  *  *  *  * * * * | 1  0 0 0 2 0 0 0 | 0 1 2 0
ox .. .. ..&#x | 1  2 |  0  2  1  0  0 | * * 12  *  *  * * * * | 0  2 1 0 0 0 0 0 | 1 2 0 0
.. .. xx ..&#x | 2  2 |  1  2  0  1  0 | * *  * 24  *  * * * * | 0  1 0 1 1 0 0 0 | 1 1 1 0
.. .. .. ox&#x | 1  2 |  0  2  0  0  1 | * *  *  * 12  * * * * | 0  0 1 0 2 0 0 0 | 0 2 1 0
.x .. .x ..    | 0  4 |  0  0  2  2  0 | * *  *  *  * 12 * * * | 0  1 0 0 0 1 1 0 | 1 1 0 1
.x .. .. .x    | 0  4 |  0  0  2  0  2 | * *  *  *  *  * 6 * * | 0  0 1 0 0 0 2 0 | 0 2 0 1
.. .o3.x ..    | 0  3 |  0  0  0  3  0 | * *  *  *  *  * * 8 * | 0  0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.x    | 0  6 |  0  0  0  3  3 | * *  *  *  *  * * * 8 | 0  0 0 0 1 0 1 1 | 0 1 1 1
---------------+------+----------------+-----------------------+------------------+--------
.. o.3x.3o.     6  0 | 12  0  0  0  0 | 4 4  0  0  0  0 0 0 0 | 1  * * * * * * * | 0 0 2 0
ox .. xx ..&#x  2  4 |  1  4  2  2  0 | 0 0  2  2  0  1 0 0 0 | * 12 * * * * * * | 1 1 0 0
ox .. .. ox&#x  1  4 |  0  4  2  0  2 | 0 0  2  0  2  0 1 0 0 | *  * 6 * * * * * | 0 2 0 0
.. oo3xx ..&#x  3  3 |  3  3  0  3  0 | 1 0  0  3  0  0 0 1 0 | *  * * 8 * * * * | 1 0 1 0
.. .. xx3ox&#x  3  6 |  3  6  0  3  3 | 0 1  0  3  3  0 0 0 1 | *  * * * 8 * * * | 0 1 1 0
.x .o3.x ..     0  6 |  0  0  3  6  0 | 0 0  0  0  0  3 0 2 0 | *  * * * * 4 * * | 1 0 0 1
.x .. .x3.x     0 12 |  0  0  6  6  6 | 0 0  0  0  0  3 3 0 2 | *  * * * * * 4 * | 0 1 0 1
.. .o3.x3.x     0 12 |  0  0  0 12  6 | 0 0  0  0  0  0 0 4 4 | *  * * * * * * 2 | 0 0 1 1
---------------+------+----------------+-----------------------+------------------+--------
ox oo3xx ..&#x  3  6 |  3  6  3  6  0 | 1 0  3  6  0  3 0 2 0 | 0  3 0 2 0 1 0 0 | 4 * * *
ox .. xx3ox&#x  3 12 |  3 12  6  6  6 | 0 1  6  6  6  3 3 0 2 | 0  3 3 0 2 0 1 0 | * 4 * *
.. oo3xx3ox&#x  6 12 | 12 12  0 12  6 | 4 4  0 12  6  0 0 4 4 | 1  0 0 4 4 0 0 1 | * * 2 *
.x .o3.x3.x     0 24 |  0  0 12 24 12 | 0 0  0  0  0 12 6 8 8 | 0  0 0 0 0 4 4 2 | * * * 1

ooo3xxx3oxx&#x   → height(1,2) = height(1,3) = sqrt(5/8) = 0.790569
                   height(2,3) = 1

o..3o..3o..    | 6  *  * |  4  2  2  0 0  0  0 0 | 2 2  4 1  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.    | * 12  * |  0  1  0  2 1  0  0 0 | 0 0  2 1  1  0 0 1 2  2 1 0 0 | 0 1 2  2 1 0 0 1 1 2 0 | 1 1 2 0 1
..o3..o3..o    | *  * 12 |  0  0  1  0 0  1  2 1 | 0 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  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 |  * 12  *  * *  *  * * | 0 0  2 1  1  0 0 0 0  0 0 0 0 | 0 1 2  2 1 0 0 0 0 0 0 | 1 1 2 0 0
o.o3o.o3o.o&#x | 1  0  1 |  *  * 12  * *  *  * * | 0 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 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  0 |  *  *  *  * 6  *  * * | 0 0  0 1  0  0 0 0 2  0 1 0 0 | 0 0 2  0 1 0 0 1 0 2 0 | 1 0 2 0 1
.oo3.oo3.oo&#x | 0  1  1 |  *  *  *  * * 12  * * | 0 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  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  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 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 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 0 | * * 12 *  *  * * * *  * * * * | 0 1 1  1 0 0 0 0 0 0 0 | 1 1 1 0 0
... ... ox.&#x | 1  2  0 |  0  2  0  0 1  0  0 0 | * *  * 6  *  * * * *  * * * * | 0 0 2  0 1 0 0 0 0 0 0 | 1 0 2 0 0
ooo3ooo3ooo&#x | 1  1  1 |  0  1  1  0 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  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  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 0 | * *  * *  *  * * 4 *  * * * * | 0 1 0  0 0 0 0 1 1 0 0 | 1 1 0 0 1
... .x.3.x.    | 0  6  0 |  0  0  0  3 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 0  2  1 0 | * *  * *  *  * * * * 12 * * * | 0 0 0  1 0 0 0 0 1 1 0 | 0 1 1 0 1
... ... .xx&#x | 0  2  2 |  0  0  0  0 1  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  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  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 0 | 4 4  0 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 0 | 1 0  3 0  0  0 0 1 0  0 0 0 0 | * 4 *  * * * * * * * * | 1 1 0 0 0
... xx.3ox.&#x  3  6  0 |  3  6  0  3 3  0  0 0 | 0 1  3 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 0  2  1 0 | 0 0  1 0  2  1 0 0 0  1 0 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0
... ... oxx&#x  1  2  2 |  0  2  2  0 1  2  0 1 | 0 0  0 1  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  0  3 0 | 1 0  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  0  3 3 | 0 1  0 0  0  3 3 0 0  0 0 0 1 | * * *  * * * 4 * * * * | 0 0 1 1 0
.o.3.x.3.x.     0 12  0 |  0  0  0 12 6  0  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 0  3  3 0 | 0 0  0 0  0  0 0 1 0  3 0 1 0 | * * *  * * * * * 4 * * | 0 1 0 0 1
... .xx3.xx&#x  0  6  6 |  0  0  0  3 3  6  3 3 | 0 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  0 12 6 | 0 0  0 0  0  0 0 0 0  0 0 4 4 | * * *  * * * * * * * 1 | 0 0 0 1 1
---------------+---------+-----------------------+-------------------------------+------------------------+----------
oo.3xx.3ox.&#x  6 12  0 | 12 12  0 12 6  0  0 0 | 4 4 12 6  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 0  3  3 0 | 1 0  3 0  3  3 0 1 0  3 0 1 0 | 0 1 0  3 0 1 0 0 1 0 0 | * 4 * * *
... xxx3oxx&#x  3  6  6 |  3  6  6  3 3  6  3 3 | 0 1  3 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  0 12 6 | 4 4  0 0  0 12 6 0 0  0 0 4 4 | 1 0 0  0 0 4 4 0 0 0 1 | * * * 1 *
.oo3.xx3.xx&#x  0 12 12 |  0  0  0 12 6 12 12 6 | 0 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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