Acronym toa tutcup, toe || tutcup
Name toe atop tutcup
Circumradius sqrt(21/8) = 1.620185
Lace city
in approx. ASCII-art
    x3x3x    
             
             
             
             
o3x3x   x3x3o
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

xxo3xxx3oxx&#x   → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569
                   height(1,3) = sqrt(3/2) = 1.224745
(toe || tutcup)   → height(2,13) = 1/sqrt(2) = 0.707107

o..3o..3o..    | 12  *  * | 1  2  2  2  0  0  0  0  0 0 | 2 1  2  2  1  2  2  1  2 0 0 0  0  0  0 0 0 | 1 2 1 1 2 1 1  2  2  1 0 0 0 0 0 | 1 1 2 1 1 0
.o.3.o.3.o.    |  * 24  * | 0  0  1  0  1  1  1  1  0 0 | 0 0  1  1  1  0  0  0  1 1 1 1  1  1  1 0 0 | 0 1 1 1 0 0 0  1  1  1 1 1 1 1 0 | 1 0 1 1 1 1
..o3..o3..o    |  *  * 12 | 0  0  0  2  0  0  0  2  2 1 | 0 0  0  0  0  1  2  2  2 0 0 0  1  2  2 1 2 | 0 0 0 0 1 1 2  1  2  2 0 1 1 2 1 | 0 1 1 1 2 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
x.. ... ...    |  2  0  0 | 6  *  *  *  *  *  *  *  * * | 2 0  2  0  0  2  0  0  0 0 0 0  0  0  0 0 0 | 1 2 1 0 2 1 0  2  0  0 0 0 0 0 0 | 1 1 2 1 0 0
... x.. ...    |  2  0  0 | * 12  *  *  *  *  *  *  * * | 1 1  0  1  0  0  1  0  0 0 0 0  0  0  0 0 0 | 1 1 0 1 1 0 1  0  1  0 0 0 0 0 0 | 1 1 1 0 1 0
oo.3oo.3oo.&#x |  1  1  0 | *  * 24  *  *  *  *  *  * * | 0 0  1  1  1  0  0  0  1 0 0 0  0  0  0 0 0 | 0 1 1 1 0 0 0  1  1  1 0 0 0 0 0 | 1 0 1 1 1 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 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 1 1 0 0 0 0  1  0  0 1 1 1 0 0 | 1 0 1 1 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 1 0 1 0 0 0  0  1  0 1 1 0 1 0 | 1 0 1 0 1 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 1 1 0 0 0  0  0  1 1 0 1 1 0 | 1 0 0 1 1 1
.oo3.oo3.oo&#x |  0  1  1 | *  *  *  *  *  *  * 24  * * | 0 0  0  0  0  0  0  0  1 0 0 0  1  1  1 0 0 | 0 0 0 0 0 0 0  1  1  1 0 1 1 1 0 | 0 0 1 1 1 1
... ..x ...    |  0  0  2 | *  *  *  *  *  *  *  * 12 * | 0 0  0  0  0  0  1  0  0 0 0 0  0  1  0 1 1 | 0 0 0 0 1 0 1  0  1  0 0 1 0 1 1 | 0 1 1 0 1 1
... ... ..x    |  0  0  2 | *  *  *  *  *  *  *  *  * 6 | 0 0  0  0  0  0  0  2  0 0 0 0  0  0  2 0 2 | 0 0 0 0 0 1 2  0  0  2 0 0 1 2 1 | 0 1 0 1 2 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
x..3x.. ...    |  6  0  0 | 3  3  0  0  0  0  0  0  0 0 | 4 *  *  *  *  *  *  *  * * * *  *  *  * * * | 1 1 0 0 1 0 0  0  0  0 0 0 0 0 0 | 1 1 1 0 0 0
... x..3o..    |  3  0  0 | 0  3  0  0  0  0  0  0  0 0 | * 4  *  *  *  *  *  *  * * * *  *  *  * * * | 1 0 0 1 0 0 1  0  0  0 0 0 0 0 0 | 1 1 0 0 1 0
xx. ... ...&#x |  2  2  0 | 1  0  2  0  1  0  0  0  0 0 | * * 12  *  *  *  *  *  * * * *  *  *  * * * | 0 1 1 0 0 0 0  1  0  0 0 0 0 0 0 | 1 0 1 1 0 0
... xx. ...&#x |  2  2  0 | 0  1  2  0  0  1  0  0  0 0 | * *  * 12  *  *  *  *  * * * *  *  *  * * * | 0 1 0 1 0 0 0  0  1  0 0 0 0 0 0 | 1 0 1 0 1 0
... ... ox.&#x |  1  2  0 | 0  0  2  0  0  0  1  0  0 0 | * *  *  * 12  *  *  *  * * * *  *  *  * * * | 0 0 1 1 0 0 0  0  0  1 0 0 0 0 0 | 1 0 0 1 1 0
x.o ... ...&#x |  2  0  1 | 1  0  0  2  0  0  0  0  0 0 | * *  *  *  * 12  *  *  * * * *  *  *  * * * | 0 0 0 0 1 1 0  1  0  0 0 0 0 0 0 | 0 1 1 1 0 0
... x.x ...&#x |  2  0  2 | 0  1  0  2  0  0  0  0  1 0 | * *  *  *  *  * 12  *  * * * *  *  *  * * * | 0 0 0 0 1 0 1  0  1  0 0 0 0 0 0 | 0 1 1 0 1 0
... ... o.x&#x |  1  0  2 | 0  0  0  2  0  0  0  0  0 1 | * *  *  *  *  *  * 12  * * * *  *  *  * * * | 0 0 0 0 0 1 1  0  0  1 0 0 0 0 0 | 0 1 0 1 1 0
ooo3ooo3ooo&#x |  1  1  1 | 0  0  1  1  0  0  0  1  0 0 | * *  *  *  *  *  *  * 24 * * *  *  *  * * * | 0 0 0 0 0 0 0  1  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 | * *  *  *  *  *  *  *  * 4 * *  *  *  * * * | 0 1 0 0 0 0 0  0  0  0 1 1 0 0 0 | 1 0 1 0 0 1
.x. ... .x.    |  0  4  0 | 0  0  0  0  2  0  2  0  0 0 | * *  *  *  *  *  *  *  * * 6 *  *  *  * * * | 0 0 1 0 0 0 0  0  0  0 1 0 1 0 0 | 1 0 0 1 0 1
... .x.3.x.    |  0  6  0 | 0  0  0  0  0  3  3  0  0 0 | * *  *  *  *  *  *  *  * * * 4  *  *  * * * | 0 0 0 1 0 0 0  0  0  0 1 0 0 1 0 | 1 0 0 0 1 1
.xo ... ...&#x |  0  2  1 | 0  0  0  0  1  0  0  2  0 0 | * *  *  *  *  *  *  *  * * * * 12  *  * * * | 0 0 0 0 0 0 0  1  0  0 0 1 1 0 0 | 0 0 1 1 0 1
... .xx ...&#x |  0  2  2 | 0  0  0  0  0  1  0  2  1 0 | * *  *  *  *  *  *  *  * * * *  * 12  * * * | 0 0 0 0 0 0 0  0  1  0 0 1 0 1 0 | 0 0 1 0 1 1
... ... .xx&#x |  0  2  2 | 0  0  0  0  0  0  1  2  0 1 | * *  *  *  *  *  *  *  * * * *  *  * 12 * * | 0 0 0 0 0 0 0  0  0  1 0 0 1 1 0 | 0 0 0 1 1 1
..o3..x ...    |  0  0  3 | 0  0  0  0  0  0  0  0  3 0 | * *  *  *  *  *  *  *  * * * *  *  *  * 4 * | 0 0 0 0 1 0 0  0  0  0 0 1 0 0 1 | 0 1 1 0 0 1
... ..x3..x    |  0  0  6 | 0  0  0  0  0  0  0  0  3 3 | * *  *  *  *  *  *  *  * * * *  *  *  * * 4 | 0 0 0 0 0 0 1  0  0  0 0 0 0 1 1 | 0 1 0 0 1 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
x..3x..3o..     12  0  0 | 6 12  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 | 1 * * * * * *  *  *  * * * * * * | 1 1 0 0 0 0
xx.3xx. ...&#x   6  6  0 | 3  3  6  0  3  3  0  0  0 0 | 1 0  3  3  0  0  0  0  0 1 0 0  0  0  0 0 0 | * 4 * * * * *  *  *  * * * * * * | 1 0 1 0 0 0
xx. ... ox.&#x   2  4  0 | 1  0  4  0  2  0  2  0  0 0 | 0 0  2  0  2  0  0  0  0 0 1 0  0  0  0 0 0 | * * 6 * * * *  *  *  * * * * * * | 1 0 0 1 0 0
... xx.3ox.&#x   3  6  0 | 0  3  6  0  0  3  3  0  0 0 | 0 1  0  3  3  0  0  0  0 0 0 1  0  0  0 0 0 | * * * 4 * * *  *  *  * * * * * * | 1 0 0 0 1 0
x.o3x.x ...&#x   6  0  3 | 3  3  0  6  0  0  0  0  3 0 | 1 0  0  0  0  3  3  0  0 0 0 0  0  0  0 1 0 | * * * * 4 * *  *  *  * * * * * * | 0 1 1 0 0 0
x.o ... o.x&#x   2  0  2 | 1  0  0  4  0  0  0  0  0 1 | 0 0  0  0  0  2  0  2  0 0 0 0  0  0  0 0 0 | * * * * * 6 *  *  *  * * * * * * | 0 1 0 1 0 0
... x.x3o.x&#x   3  0  6 | 0  3  0  6  0  0  0  0  3 3 | 0 1  0  0  0  0  3  3  0 0 0 0  0  0  0 0 1 | * * * * * * 4  *  *  * * * * * * | 0 1 0 0 1 0
xxo ... ...&#x   2  2  1 | 1  0  2  2  1  0  0  2  0 0 | 0 0  1  0  0  1  0  0  2 0 0 0  1  0  0 0 0 | * * * * * * * 12  *  * * * * * * | 0 0 1 1 0 0
... xxx ...&#x   2  2  2 | 0  1  2  2  0  1  0  2  1 0 | 0 0  0  1  0  0  1  0  2 0 0 0  0  1  0 0 0 | * * * * * * *  * 12  * * * * * * | 0 0 1 0 1 0
... ... oxx&#x   1  2  2 | 0  0  2  2  0  0  1  2  0 1 | 0 0  0  0  1  0  0  1  2 0 0 0  0  0  1 0 0 | * * * * * * *  *  * 12 * * * * * | 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 4 6 4  0  0  0 0 0 | * * * * * * *  *  *  * 1 * * * * | 1 0 0 0 0 1
.xo3.xx ...&#x   0  6  3 | 0  0  0  0  3  3  0  6  3 0 | 0 0  0  0  0  0  0  0  0 1 0 0  3  3  0 1 0 | * * * * * * *  *  *  * * 4 * * * | 0 0 1 0 0 1
.xo ... .xx&#x   0  4  2 | 0  0  0  0  2  0  2  4  0 1 | 0 0  0  0  0  0  0  0  0 0 1 0  2  0  2 0 0 | * * * * * * *  *  *  * * * 6 * * | 0 0 0 1 0 1
... .xx3.xx&#x   0  6  6 | 0  0  0  0  0  3  3  6  3 3 | 0 0  0  0  0  0  0  0  0 0 0 1  0  3  3 0 1 | * * * * * * *  *  *  * * * * 4 * | 0 0 0 0 1 1
..o3..x3..x      0  0 12 | 0  0  0  0  0  0  0  0 12 6 | 0 0  0  0  0  0  0  0  0 0 0 0  0  0  0 4 4 | * * * * * * *  *  *  * * * * * 1 | 0 1 0 0 0 1
---------------+----------+-----------------------------+---------------------------------------------+----------------------------------+------------
xx.3xx.3ox.&#x  12 24  0 | 6 12 24  0 12 12 12  0  0 0 | 4 4 12 12 12  0  0  0  0 4 6 4  0  0  0 0 0 | 1 4 6 4 0 0 0  0  0  0 1 0 0 0 0 | 1 * * * * *
x.o3x.x3o.x&#x  12  0 12 | 6 12  0 24  0  0  0  0 12 6 | 4 4  0  0  0 12 12 12  0 0 0 0  0  0  0 4 4 | 1 0 0 0 4 6 4  0  0  0 0 0 0 0 1 | * 1 * * * *
xxo3xxx ...&#x   6  6  3 | 3  3  6  6  3  3  0  6  3 0 | 1 0  3  3  0  3  3  0  6 1 0 0  3  3  0 1 0 | 0 1 0 0 1 0 0  3  3  0 0 1 0 0 0 | * * 4 * * *
xxo ... oxx&#x   2  4  2 | 1  0  4  4  2  0  2  4  0 1 | 0 0  2  0  2  2  0  2  4 0 1 0  2  0  2 0 0 | 0 0 1 0 0 1 0  2  0  2 0 0 1 0 0 | * * * 6 * *
... xxx3oxx&#x   3  6  6 | 0  3  6  6  0  3  3  6  3 3 | 0 1  0  3  3  0  3  3  6 0 0 1  0  3  3 0 1 | 0 0 0 1 0 0 1  0  3  3 0 0 0 1 0 | * * * * 4 *
.xo3.xx3.xx&#x   0 24 12 | 0  0  0  0 12 12 12 24 12 6 | 0 0  0  0  0  0  0  0  0 4 6 4 12 12 12 4 4 | 0 0 0 0 0 0 0  0  0  0 1 4 6 4 1 | * * * * * 1
or
o..3o..3o..    & | 24  * |  1  2  2  2  0  0 | 2 1  2  2  1  3  2  2 0 0 | 1 2  1 1 3 1  3  2 0 | 1 1 3 1
.o.3.o.3.o.      |  * 24 |  0  0  2  0  2  1 | 0 0  2  2  2  0  0  1 2 1 | 0 2  2 2 0 0  2  1 1 | 2 0 2 1
-----------------+-------+-------------------+---------------------------+----------------------+--------
x.. ... ...    & |  2  0 | 12  *  *  *  *  * | 2 0  2  0  0  2  0  0 0 0 | 1 2  1 0 2 1  2  0 0 | 1 1 2 1
... x.. ...    & |  2  0 |  * 24  *  *  *  * | 1 1  0  1  0  0  1  0 0 0 | 1 1  0 1 2 0  0  1 0 | 1 1 2 0
oo.3oo.3oo.&#x & |  1  1 |  *  * 48  *  *  * | 0 0  1  1  1  0  0  1 0 0 | 0 1  1 1 0 0  2  1 0 | 1 0 2 1
o.o3o.o3o.o&#x   |  2  0 |  *  *  * 24  *  * | 0 0  0  0  0  2  1  1 0 0 | 0 0  0 0 2 1  2  1 0 | 0 1 2 1
.x. ... ...    & |  0  2 |  *  *  *  * 24  * | 0 0  1  0  1  0  0  0 1 1 | 0 1  2 1 0 0  1  0 1 | 2 0 1 1
... .x. ...      |  0  2 |  *  *  *  *  * 12 | 0 0  0  2  0  0  0  0 2 0 | 0 2  0 2 0 0  0  1 1 | 2 0 2 0
-----------------+-------+-------------------+---------------------------+----------------------+--------
x..3x.. ...    & |  6  0 |  3  3  0  0  0  0 | 8 *  *  *  *  *  *  * * * | 1 1  0 0 1 0  0  0 0 | 1 1 1 0
... x..3o..    & |  3  0 |  0  3  0  0  0  0 | * 8  *  *  *  *  *  * * * | 1 0  0 1 1 0  0  0 0 | 1 1 1 0
xx. ... ...&#x & |  2  2 |  1  0  2  0  1  0 | * * 24  *  *  *  *  * * * | 0 1  1 0 0 0  1  0 0 | 1 0 1 1
... xx. ...&#x & |  2  2 |  0  1  2  0  0  1 | * *  * 24  *  *  *  * * * | 0 1  0 1 0 0  0  1 0 | 1 0 2 0
... ... ox.&#x & |  1  2 |  0  0  2  0  1  0 | * *  *  * 24  *  *  * * * | 0 0  1 1 0 0  1  0 0 | 1 0 1 1
x.o ... ...&#x & |  3  0 |  1  0  0  2  0  0 | * *  *  *  * 24  *  * * * | 0 0  0 0 1 1  1  0 0 | 0 1 1 1
... x.x ...&#x   |  4  0 |  0  2  0  2  0  0 | * *  *  *  *  * 12  * * * | 0 0  0 0 2 0  0  1 0 | 0 1 2 0
ooo3ooo3ooo&#x   |  2  1 |  0  0  2  1  0  0 | * *  *  *  *  *  * 24 * * | 0 0  0 0 0 0  2  1 0 | 0 0 2 1
.x.3.x. ...    & |  0  6 |  0  0  0  0  3  3 | * *  *  *  *  *  *  * 8 * | 0 1  0 1 0 0  0  0 1 | 2 0 1 0
.x. ... .x.      |  0  4 |  0  0  0  0  4  0 | * *  *  *  *  *  *  * * 6 | 0 0  2 0 0 0  0  0 1 | 2 0 0 1
-----------------+-------+-------------------+---------------------------+----------------------+--------
x..3x..3o..    &  12  0 |  6 12  0  0  0  0 | 4 4  0  0  0  0  0  0 0 0 | 2 *  * * * *  *  * * | 1 1 0 0
xx.3xx. ...&#x &   6  6 |  3  3  6  0  3  3 | 1 0  3  3  0  0  0  0 1 0 | * 8  * * * *  *  * * | 1 0 1 0
xx. ... ox.&#x &   2  4 |  1  0  4  0  4  0 | 0 0  2  0  2  0  0  0 0 1 | * * 12 * * *  *  * * | 1 0 0 1
... xx.3ox.&#x &   3  6 |  0  3  6  0  3  3 | 0 1  0  3  3  0  0  0 1 0 | * *  * 8 * *  *  * * | 1 0 1 0
x.o3x.x ...&#x &   9  0 |  3  6  0  6  0  0 | 1 1  0  0  0  3  3  0 0 0 | * *  * * 8 *  *  * * | 0 1 1 0
x.o ... o.x&#x     4  0 |  2  0  0  4  0  0 | 0 0  0  0  0  4  0  0 0 0 | * *  * * * 6  *  * * | 0 1 0 1
xxo ... ...&#x &   3  2 |  1  0  4  2  1  0 | 0 0  1  0  1  1  0  2 0 0 | * *  * * * * 24  * * | 0 0 1 1
... xxx ...&#x     4  2 |  0  2  4  2  0  1 | 0 0  0  2  0  0  1  2 0 0 | * *  * * * *  * 12 * | 0 0 2 0
.x.3.x.3.x.        0 24 |  0  0  0  0 24 12 | 0 0  0  0  0  0  0  0 8 6 | * *  * * * *  *  * 1 | 2 0 0 0
-----------------+-------+-------------------+---------------------------+----------------------+--------
xx.3xx.3ox.&#x &  12 24 |  6 12 24  0 24 12 | 4 4 12 12 12  0  0  0 8 6 | 1 4  6 4 0 0  0  0 1 | 2 * * *
x.o3x.x3o.x&#x    24  0 | 12 24  0 24  0  0 | 8 8  0  0  0 24 12  0 0 0 | 2 0  0 0 8 6  0  0 0 | * 1 * *
xxo3xxx ...&#x &   9  6 |  3  6 12  6  3  3 | 1 1  3  6  3  3  3  6 1 0 | 0 1  0 1 1 0  3  3 0 | * * 8 *
xxo ... oxx&#x     4  4 |  2  0  8  4  4  0 | 0 0  4  0  4  4  0  4 0 1 | 0 0  2 0 0 1  4  0 0 | * * * 6

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