Acronym octa tutcup, oct || tutcup
Name oct atop tutcup
Circumradius sqrt(13/8) = 1.274755
Lace city
in approx. ASCII-art
    o3x3o    
             
             
             
o3x3x   x3x3o
Coordinates
  • (2, 0, 0, 0, 3)/sqrt(8)       all permutations in first 3 coords, all changes of sign in first 3 coords
    (upper oct base)
  • (3, 1, 1, 1, 1)/sqrt(8)       all permutations in first 3 coords, even changes of sign in first 4 coords
    (lower tutcup base)
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

xoo3xxx3oox&#x   → height(1,2) = height(2,3) = sqrt(7/5) = 1.183216
                   height(1,3) = sqrt(3/2) = 1.224745
(oct || tutcup)   → height(2,13) = 1/sqrt(2) = 0.707107

o..3o..3o..    | 12 *  * | 1  2  1  2  0  0  0 0 | 2 1 1  2  2  2  1  2 0 0  0 0 0 0 | 1 2 1 2 1 1  2  2  1 0 0 0 0 | 1 1 2 1 1 0
.o.3.o.3.o.    |  * 6  * | 0  0  2  0  4  2  0 0 | 0 0 1  4  0  0  0  4 2 2  4 1 0 0 | 0 2 2 0 0 0  2  4  2 1 2 2 0 | 1 0 2 1 2 1
..o3..o3..o    |  * * 12 | 0  0  0  2  0  1  2 1 | 0 0 0  0  1  2  2  2 0 0  2 1 1 2 | 0 0 0 1 1 2  1  2  2 0 1 2 1 | 0 1 1 1 2 1
---------------+---------+-----------------------+-----------------------------------+------------------------------+------------
x.. ... ...    |  2 0  0 | 6  *  *  *  *  *  * * | 2 0 1  0  2  0  0  0 0 0  0 0 0 0 | 1 2 0 2 1 0  2  0  0 0 0 0 0 | 1 1 2 1 0 0
... x.. ...    |  2 0  0 | * 12  *  *  *  *  * * | 1 1 0  1  0  1  0  0 0 0  0 0 0 0 | 1 1 1 1 0 1  0  1  0 0 0 0 0 | 1 1 1 0 1 0
oo.3oo.3oo.&#x |  1 1  0 | *  * 12  *  *  *  * * | 0 0 1  2  0  0  0  2 0 0  0 0 0 0 | 0 2 1 0 0 0  2  2  1 0 0 0 0 | 1 0 2 1 1 0
o.o3o.o3o.o&#x |  1 0  1 | *  *  * 24  *  *  * * | 0 0 0  0  1  1  1  1 0 0  0 0 0 0 | 0 0 0 1 1 1  1  1  1 0 0 0 0 | 0 1 1 1 1 0
... .x. ...    |  0 2  0 | *  *  *  * 12  *  * * | 0 0 0  1  0  0  0  0 1 1  1 0 0 0 | 0 1 1 0 0 0  0  1  0 1 1 1 0 | 1 0 1 0 1 1
.oo3.oo3.oo&#x |  0 1  1 | *  *  *  *  * 12  * * | 0 0 0  0  0  0  0  2 0 0  2 1 0 0 | 0 0 0 0 0 0  1  2  2 0 1 2 0 | 0 0 1 1 2 1
... ..x ...    |  0 0  2 | *  *  *  *  *  * 12 * | 0 0 0  0  0  1  0  0 0 0  1 0 1 1 | 0 0 0 1 0 1  0  1  0 0 1 1 1 | 0 1 1 0 1 1
... ... ..x    |  0 0  2 | *  *  *  *  *  *  * 6 | 0 0 0  0  0  0  2  0 0 0  0 1 0 2 | 0 0 0 0 1 2  0  0  2 0 0 2 1 | 0 1 0 1 2 1
---------------+---------+-----------------------+-----------------------------------+------------------------------+------------
x..3x.. ...    |  6 0  0 | 3  3  0  0  0  0  0 0 | 4 * *  *  *  *  *  * * *  * * * * | 1 1 0 1 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 | * 4 *  *  *  *  *  * * *  * * * * | 1 0 1 0 0 1  0  0  0 0 0 0 0 | 1 1 0 0 1 0
xo. ... ...&#x |  2 1  0 | 1  0  2  0  0  0  0 0 | * * 6  *  *  *  *  * * *  * * * * | 0 2 0 0 0 0  2  0  0 0 0 0 0 | 1 0 2 1 0 0
... xx. ...&#x |  2 2  0 | 0  1  2  0  1  0  0 0 | * * * 12  *  *  *  * * *  * * * * | 0 1 1 0 0 0  0  1  0 0 0 0 0 | 1 0 1 0 1 0
x.o ... ...&#x |  2 0  1 | 1  0  0  2  0  0  0 0 | * * *  * 12  *  *  * * *  * * * * | 0 0 0 1 1 0  1  0  0 0 0 0 0 | 0 1 1 1 0 0
... x.x ...&#x |  2 0  2 | 0  1  0  2  0  0  1 0 | * * *  *  * 12  *  * * *  * * * * | 0 0 0 1 0 1  0  1  0 0 0 0 0 | 0 1 1 0 1 0
... ... o.x&#x |  1 0  2 | 0  0  0  2  0  0  0 1 | * * *  *  *  * 12  * * *  * * * * | 0 0 0 0 1 1  0  0  1 0 0 0 0 | 0 1 0 1 1 0
ooo3ooo3ooo&#x |  1 1  1 | 0  0  1  1  0  1  0 0 | * * *  *  *  *  * 24 * *  * * * * | 0 0 0 0 0 0  1  1  1 0 0 0 0 | 0 0 1 1 1 0
.o.3.x. ...    |  0 3  0 | 0  0  0  0  3  0  0 0 | * * *  *  *  *  *  * 4 *  * * * * | 0 1 0 0 0 0  0  0  0 1 1 0 0 | 1 0 1 0 0 1
... .x.3.o.    |  0 3  0 | 0  0  0  0  3  0  0 0 | * * *  *  *  *  *  * * 4  * * * * | 0 0 1 0 0 0  0  0  0 1 0 1 0 | 1 0 0 0 1 1
... .xx ...&#x |  0 2  2 | 0  0  0  0  1  2  1 0 | * * *  *  *  *  *  * * * 12 * * * | 0 0 0 0 0 0  0  1  0 0 1 1 0 | 0 0 1 0 1 1
... ... .ox&#x |  0 1  2 | 0  0  0  0  0  2  0 1 | * * *  *  *  *  *  * * *  * 6 * * | 0 0 0 0 0 0  0  0  2 0 0 2 0 | 0 0 0 1 2 1
..o3..x ...    |  0 0  3 | 0  0  0  0  0  0  3 0 | * * *  *  *  *  *  * * *  * * 4 * | 0 0 0 1 0 0  0  0  0 0 1 0 1 | 0 1 1 0 0 1
... ..x3..x    |  0 0  6 | 0  0  0  0  0  0  3 3 | * * *  *  *  *  *  * * *  * * * 4 | 0 0 0 0 0 1  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 | 4 4 0  0  0  0  0  0 0 0  0 0 0 0 | 1 * * * * *  *  *  * * * * * | 1 1 0 0 0 0
xo.3xx. ...&#x   6 3  0 | 3  3  6  0  3  0  0 0 | 1 0 3  3  0  0  0  0 1 0  0 0 0 0 | * 4 * * * *  *  *  * * * * * | 1 0 1 0 0 0
... xx.3oo.&#x   3 3  0 | 0  3  3  0  3  0  0 0 | 0 1 0  3  0  0  0  0 0 1  0 0 0 0 | * * 4 * * *  *  *  * * * * * | 1 0 0 0 1 0
x.o3x.x ...&#x   6 0  3 | 3  3  0  6  0  0  3 0 | 1 0 0  0  3  3  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 1 | 0 0 0  0  2  0  2  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  3 3 | 0 1 0  0  0  3  3  0 0 0  0 0 0 1 | * * * * * 4  *  *  * * * * * | 0 1 0 0 1 0
xoo ... ...&#x   2 1  1 | 1  0  2  2  0  1  0 0 | 0 0 1  0  1  0  0  2 0 0  0 0 0 0 | * * * * * * 12  *  * * * * * | 0 0 1 1 0 0
... xxx ...&#x   2 2  2 | 0  1  2  2  1  2  1 0 | 0 0 0  1  0  1  0  2 0 0  1 0 0 0 | * * * * * *  * 12  * * * * * | 0 0 1 0 1 0
... ... oox&#x   1 1  2 | 0  0  1  2  0  2  0 1 | 0 0 0  0  0  0  1  2 0 0  0 1 0 0 | * * * * * *  *  * 12 * * * * | 0 0 0 1 1 0
.o.3.x.3.o.      0 6  0 | 0  0  0  0 12  0  0 0 | 0 0 0  0  0  0  0  0 4 4  0 0 0 0 | * * * * * *  *  *  * 1 * * * | 1 0 0 0 0 1
.oo3.xx ...&#x   0 3  3 | 0  0  0  0  3  3  3 0 | 0 0 0  0  0  0  0  0 1 0  3 0 1 0 | * * * * * *  *  *  * * 4 * * | 0 0 1 0 0 1
... .xx3.ox&#x   0 3  6 | 0  0  0  0  3  6  3 3 | 0 0 0  0  0  0  0  0 0 1  3 3 0 1 | * * * * * *  *  *  * * * 4 * | 0 0 0 0 1 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 0 4 4 | * * * * * *  *  *  * * * * 1 | 0 1 0 0 0 1
---------------+---------+-----------------------+-----------------------------------+------------------------------+------------
xo.3xx.3oo.&#x  12 6  0 | 6 12 12  0 12  0  0 0 | 4 4 6 12  0  0  0  0 4 4  0 0 0 0 | 1 4 4 0 0 0  0  0  0 1 0 0 0 | 1 * * * * *
x.o3x.x3o.x&#x  12 0 12 | 6 12  0 24  0  0 12 6 | 4 4 0  0 12 12 12  0 0 0  0 0 4 4 | 1 0 0 4 6 4  0  0  0 0 0 0 1 | * 1 * * * *
xoo3xxx ...&#x   6 3  3 | 3  3  6  6  3  3  3 0 | 1 0 3  3  3  3  0  6 1 0  3 0 1 0 | 0 1 0 1 0 0  3  3  0 0 1 0 0 | * * 4 * * *
xoo ... oox&#x   2 1  2 | 1  0  2  4  0  2  0 1 | 0 0 1  0  2  0  2  4 0 0  0 1 0 0 | 0 0 0 0 1 0  2  0  2 0 0 0 0 | * * * 6 * *
... xxx3oox&#x   3 3  6 | 0  3  3  6  3  6  3 3 | 0 1 0  3  0  3  3  6 0 1  3 3 0 1 | 0 0 1 0 0 1  0  3  3 0 0 1 0 | * * * * 4 *
.oo3.xx3.ox&#x   0 6 12 | 0  0  0  0 12 12 12 6 | 0 0 0  0  0  0  0  0 4 4 12 6 4 4 | 0 0 0 0 0 0  0  0  0 1 4 4 1 | * * * * * 1
or
o..3o..3o..    & | 24 * |  1  2  1  2  0 | 2 1  1  2  3  2  2 0 | 1 2 1 3 1  3  2 0 | 1 1 3 1
.o.3.o.3.o.      |  * 6 |  0  0  4  0  4 | 0 0  2  8  0  0  4 4 | 0 4 4 0 0  4  4 1 | 2 0 4 1
-----------------+------+----------------+----------------------+-------------------+--------
x.. ... ...    & |  2 0 | 12  *  *  *  * | 2 0  1  0  2  0  0 0 | 1 2 0 2 1  2  0 0 | 1 1 2 1
... x.. ...    & |  2 0 |  * 24  *  *  * | 1 1  0  1  0  1  0 0 | 1 1 1 2 0  0  1 0 | 1 1 2 0
oo.3oo.3oo.&#x & |  1 1 |  *  * 24  *  * | 0 0  1  2  0  0  2 0 | 0 2 1 0 0  3  2 0 | 1 0 3 1
o.o3o.o3o.o&#x   |  2 0 |  *  *  * 24  * | 0 0  0  0  2  1  1 0 | 0 0 0 2 1  2  1 0 | 0 1 2 1
... .x. ...      |  0 2 |  *  *  *  * 12 | 0 0  0  2  0  0  0 2 | 0 2 2 0 0  0  1 1 | 2 0 2 0
-----------------+------+----------------+----------------------+-------------------+--------
x..3x.. ...    & |  6 0 |  3  3  0  0  0 | 8 *  *  *  *  *  * * | 1 1 0 1 0  0  0 0 | 1 1 1 0
... x..3o..    & |  3 0 |  0  3  0  0  0 | * 8  *  *  *  *  * * | 1 0 1 1 0  0  0 0 | 1 1 1 0
xo. ... ...&#x & |  2 1 |  1  0  2  0  0 | * * 12  *  *  *  * * | 0 2 0 0 0  2  0 0 | 1 0 2 1
... xx. ...&#x & |  2 2 |  0  1  2  0  1 | * *  * 24  *  *  * * | 0 1 1 0 0  0  1 0 | 1 0 2 0
x.o ... ...&#x & |  3 0 |  1  0  0  2  0 | * *  *  * 24  *  * * | 0 0 0 1 1  1  0 0 | 0 1 1 1
... x.x ...&#x   |  4 0 |  0  2  0  2  0 | * *  *  *  * 12  * * | 0 0 0 2 0  0  1 0 | 0 1 2 0
ooo3ooo3ooo&#x   |  2 1 |  0  0  2  1  0 | * *  *  *  *  * 24 * | 0 0 0 0 0  2  1 0 | 0 0 2 1
.o.3.x. ...    & |  0 3 |  0  0  0  0  3 | * *  *  *  *  *  * 8 | 0 1 1 0 0  0  0 1 | 2 0 1 0
-----------------+------+----------------+----------------------+-------------------+--------
x..3x..3o..    &  12 0 |  6 12  0  0  0 | 4 4  0  0  0  0  0 0 | 2 * * * *  *  * * | 1 1 0 0
xo.3xx. ...&#x &   6 3 |  3  3  6  0  3 | 1 0  3  3  0  0  0 1 | * 8 * * *  *  * * | 1 0 1 0
... xx.3oo.&#x &   3 3 |  0  3  3  0  3 | 0 1  0  3  0  0  0 1 | * * 8 * *  *  * * | 1 0 1 0
x.o3x.x ...&#x &   9 0 |  3  6  0  6  0 | 1 1  0  0  3  3  0 0 | * * * 8 *  *  * * | 0 1 1 0
x.o ... o.x&#x     4 0 |  2  0  0  4  0 | 0 0  0  0  4  0  0 0 | * * * * 6  *  * * | 0 1 0 1
xoo ... ...&#x &   3 1 |  1  0  3  2  0 | 0 0  1  0  1  0  2 0 | * * * * * 24  * * | 0 0 1 1
... xxx ...&#x     4 2 |  0  2  4  2  1 | 0 0  0  2  0  1  2 0 | * * * * *  * 12 * | 0 0 2 0
.o.3.x.3.o.        0 6 |  0  0  0  0 12 | 0 0  0  0  0  0  0 8 | * * * * *  *  * 1 | 2 0 0 0
-----------------+------+----------------+----------------------+-------------------+--------
xo.3xx.3oo.&#x &  12 6 |  6 12 12  0 12 | 4 4  6 12  0  0  0 8 | 1 4 4 0 0  0  0 1 | 2 * * *
x.o3x.x3o.x&#x    24 0 | 12 24  0 24  0 | 8 8  0  0 24 12  0 0 | 1 0 0 8 6  0  0 0 | * 1 * *
xoo3xxx ...&#x &   9 3 |  3  6  9  6  3 | 1 1  3  6  3  3  6 1 | 0 1 1 1 0  3  3 0 | * * 8 *
xoo ... oox&#x     4 1 |  2  0  4  4  0 | 0 0  2  0  4  0  4 0 | 0 0 0 0 1  4  0 0 | * * * 6

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