Acronym octatepe (alt.: tettet octtric)
Name oct atop tepe,
diminished rix,
(tet,tet,oct)-trigonic
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art
    o    		where:
         		o = o3x3o (oct)
t       t		t = x3o3o (tet)
x o3o   o o3x    		- pen
(1)     (2)      
                 
                 
    x o3x   o x3o		- traf
    (4)     (3)  
         \       \
          \       +-- oct
           +--------- tepe
Coordinates
  • (1/sqrt(2), 0, 0, 0, sqrt(3/8))      & all permutations and all changes of sign in first 3 coordinates
    (top base, oct)
  • (1/sqrt(8), 1/sqrt(8), -1/sqrt(8), 1/2, 0)     & all even changes of sign in first 3 coordinates resp. change of sign in 4th
    (bottom base, tepe)
coordinates are centered to the bottom base
Face vector 14, 52, 70, 41, 11
Confer
uniform relative:
rix  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

ox ox3xo3oo&#x   → height = sqrt(3/8) = 0.612372
(oct || tepe)

o. o.3o.3o.    | 6 *   4  4 0  0 | 2 2  2  2  8 0 0 | 1 1  4 4 4 0 0 | 2 2 2 0
.o .o3.o3.o    | * 8 |  0  3 1  3 | 0 0  3  3  3 3 3 | 0 3  3 3 1 3 1 | 3 1 1 1
---------------+-----+------------+------------------+----------------+--------
.. .. x. ..    | 2 0 | 12  * *  * | 1 1  0  0  2 0 0 | 1 0  1 2 2 0 0 | 1 1 2 0
oo oo3oo3oo&#x | 1 1 |  * 24 *  * | 0 0  1  1  2 0 0 | 0 1  2 2 1 0 0 | 2 1 1 0
.x .. .. ..    | 0 2 |  *  * 4  * | 0 0  3  0  0 3 0 | 0 3  3 0 0 3 0 | 3 1 0 1
.. .x .. ..    | 0 2 |  *  * * 12 | 0 0  0  1  0 1 2 | 0 1  0 2 0 2 1 | 2 0 1 1
---------------+-----+------------+------------------+----------------+--------
.. o.3x. ..    | 3 0 |  3  0 0  0 | 4 *  *  *  * * * | 1 0  0 2 0 0 0 | 1 0 2 0
.. .. x.3o.    | 3 0 |  3  0 0  0 | * 4  *  *  * * * | 1 0  0 0 2 0 0 | 0 1 2 0
ox .. .. ..&#x | 1 2 |  0  2 1  0 | * * 12  *  * * * | 0 1  2 0 0 0 0 | 2 1 0 0
.. ox .. ..&#x | 1 2 |  0  2 0  1 | * *  * 12  * * * | 0 1  0 2 0 0 0 | 2 0 1 0
.. .. xo ..&#x | 2 1 |  1  2 0  0 | * *  *  * 24 * * | 0 0  1 1 1 0 0 | 1 1 1 0
.x .x .. ..    | 0 4 |  0  0 2  2 | * *  *  *  * 6 * | 0 1  0 0 0 2 0 | 2 0 0 1
.. .x3.o ..    | 0 3 |  0  0 0  3 | * *  *  *  * * 8 | 0 0  0 1 0 1 1 | 1 0 1 1
---------------+-----+------------+------------------+----------------+--------
.. o.3x.3o.     6 0 | 12  0 0  0 | 4 4  0  0  0 0 0 | 1 *  * * * * * | 0 0 2 0
ox ox .. ..&#x  1 4 |  0  4 2  2 | 0 0  2  2  0 1 0 | * 6  * * * * * | 2 0 0 0
ox .. xo ..&#x  2 2 |  1  4 1  0 | 0 0  2  0  2 0 0 | * * 12 * * * * | 1 1 0 0
.. ox3xo ..&#x  3 3 |  3  6 0  3 | 1 0  0  3  3 0 1 | * *  * 8 * * * | 1 0 1 0
.. .. xo3oo&#x  3 1 |  3  3 0  0 | 0 1  0  0  3 0 0 | * *  * * 8 * * | 0 1 1 0
.x .x3.o ..     0 6 |  0  0 3  6 | 0 0  0  0  0 3 2 | * *  * * * 4 * | 1 0 0 1
.. .x3.o3.o     0 4 |  0  0 0  6 | 0 0  0  0  0 0 4 | * *  * * * * 2 | 0 0 1 1
---------------+-----+------------+------------------+----------------+--------
ox ox3xo ..&#x  3 6 |  3 12 3  6 | 1 0  6  6  6 3 2 | 0 3  3 2 0 1 0 | 4 * * *
ox .. xo3oo&#x  3 2 |  3  6 1  0 | 0 1  3  0  6 0 0 | 0 0  3 0 2 0 0 | * 4 * *
.. ox3xo3oo&#x  6 4 | 12 12 0  6 | 4 4  0  6 12 0 4 | 1 0  0 4 4 0 1 | * * 2 *
.x .x3.o3.o     0 8 |  0  0 4 12 | 0 0  0  0  0 6 8 | 0 0  0 0 0 4 2 | * * * 1

xox3oxo3ooo&#x   → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569
                   height(1,3) = 1

o..3o..3o..    | 4 * * | 3  3 1  0  0 0 | 3 3  3 3  3 0 0 0  0 0 | 1 3 1 3 3  3 0 0 0 0 | 1 1 3 1 0
.o.3.o.3.o.    | * 6 *  0  2 0  4  2 0 | 0 1  4 0  2 2 2 1  4 0 | 0 2 2 0 1  4 1 2 2 0 | 1 0 2 2 1
..o3..o3..o    | * * 4 | 0  0 1  0  3 3 | 0 0  0 3  3 0 0 3  3 3 | 0 0 0 3 3  3 0 3 1 1 | 0 1 3 1 1
---------------+-------+----------------+------------------------+----------------------+----------
x.. ... ...    | 2 0 0 | 6  * *  *  * * | 2 1  0 1  0 0 0 0  0 0 | 1 2 0 2 1  0 0 0 0 0 | 1 1 2 0 0
oo.3oo.3oo.&#x | 1 1 0 | * 12 *  *  * * | 0 1  2 0  1 0 0 0  0 0 | 0 2 1 0 1  2 0 0 0 0 | 1 0 2 1 0
o.o3o.o3o.o&#x | 1 0 1 | *  * 4  *  * * | 0 0  0 3  3 0 0 0  0 0 | 0 0 0 3 3  3 0 0 0 0 | 0 1 3 1 0
... .x. ...    | 0 2 0 | *  * * 12  * * | 0 0  1 0  0 1 1 0  1 0 | 0 1 1 0 0  1 1 1 1 0 | 1 0 1 1 1
.oo3.oo3.oo&#x | 0 1 1 | *  * *  * 12 * | 0 0  0 0  1 0 0 1  2 0 | 0 0 0 0 1  2 0 2 1 0 | 0 0 2 1 1
..x ... ...    | 0 0 2 | *  * *  *  * 6 | 0 0  0 1  0 0 0 1  0 2 | 0 0 0 2 1  0 0 2 0 1 | 0 1 2 0 1
---------------+-------+----------------+------------------------+----------------------+----------
x..3o.. ...    | 3 0 0 | 3  0 0  0  0 0 | 4 *  * *  * * * *  * * | 1 1 0 1 0  0 0 0 0 0 | 1 1 1 0 0
xo. ... ...&#x | 2 1 0 | 1  2 0  0  0 0 | * 6  * *  * * * *  * * | 0 2 0 0 1  0 0 0 0 0 | 1 0 2 0 0
... ox. ...&#x | 1 2 0 | 0  2 0  1  0 0 | * * 12 *  * * * *  * * | 0 1 1 0 0  1 0 0 0 0 | 1 0 1 1 0
x.x ... ...&#x | 2 0 2 | 1  0 2  0  0 1 | * *  * 6  * * * *  * * | 0 0 0 2 1  0 0 0 0 0 | 0 1 2 0 0
ooo3ooo3ooo&#x | 1 1 1 | 0  1 1  0  1 0 | * *  * * 12 * * *  * * | 0 0 0 0 1  2 0 0 0 0 | 0 0 2 1 0
.o.3.x. ...    | 0 3 0 | 0  0 0  3  0 0 | * *  * *  * 4 * *  * * | 0 1 0 0 0  0 1 1 0 0 | 1 0 1 0 1
... .x.3.o.    | 0 3 0 | 0  0 0  3  0 0 | * *  * *  * * 4 *  * * | 0 0 1 0 0  0 1 0 1 0 | 1 0 0 1 1
.ox ... ...&#x | 0 1 2 | 0  0 0  0  2 1 | * *  * *  * * * 6  * * | 0 0 0 0 1  0 0 2 0 0 | 0 0 2 0 1
... .xo ...&#x | 0 2 1 | 0  0 0  1  2 0 | * *  * *  * * * * 12 * | 0 0 0 0 0  1 0 1 1 0 | 0 0 1 1 1
..x3..o ...    | 0 0 3 | 0  0 0  0  0 3 | * *  * *  * * * *  * 4 | 0 0 0 1 0  0 0 1 0 1 | 0 1 1 0 1
---------------+-------+----------------+------------------------+----------------------+----------
x..3o..3o..     4 0 0 | 6  0 0  0  0 0 | 4 0  0 0  0 0 0 0  0 0 | 1 * * * *  * * * * * | 1 1 0 0 0
xo.3ox. ...&#x  3 3 0 | 3  6 0  3  0 0 | 1 3  3 0  0 1 0 0  0 0 | * 4 * * *  * * * * * | 1 0 1 0 0
... ox.3oo.&#x  1 3 0 | 0  3 0  3  0 0 | 0 0  3 0  0 0 1 0  0 0 | * * 4 * *  * * * * * | 1 0 0 1 0
x.x3o.o ...&#x  3 0 3 | 3  0 3  0  0 3 | 1 0  0 3  0 0 0 0  0 1 | * * * 4 *  * * * * * | 0 1 1 0 0
xox ... ...&#x  2 1 2 | 1  2 2  0  2 1 | 0 1  0 1  2 0 0 1  0 0 | * * * * 6  * * * * * | 0 0 2 0 0
... oxo ...&#x  1 2 1 | 0  2 1  1  2 0 | 0 0  1 0  2 0 0 0  1 0 | * * * * * 12 * * * * | 0 0 1 1 0
.o.3.x.3.o.     0 6 0 | 0  0 0 12  0 0 | 0 0  0 0  0 4 4 0  0 0 | * * * * *  * 1 * * * | 1 0 0 0 1
.ox3.xo ...&#x  0 3 3 | 0  0 0  3  6 3 | 0 0  0 0  0 1 0 3  3 1 | * * * * *  * * 4 * * | 0 0 1 0 1
... .xo3.oo&#x  0 3 1 | 0  0 0  3  3 0 | 0 0  0 0  0 0 1 0  3 0 | * * * * *  * * * 4 * | 0 0 0 1 1
..x3..o3..o     0 0 4 | 0  0 0  0  0 6 | 0 0  0 0  0 0 0 0  0 4 | * * * * *  * * * * 1 | 0 1 0 0 1
---------------+-------+----------------+------------------------+----------------------+----------
xo.3ox.3oo.&#x  4 6 0 | 6 12 0 12  0 0 | 4 6 12 0  0 4 4 0  0 0 | 1 4 4 0 0  0 1 0 0 0 | 1 * * * *
x.x3o.o3o.o&#x  4 0 4 | 6  0 4  0  0 6 | 4 0  0 6  0 0 0 0  0 4 | 1 0 0 4 0  0 0 0 0 1 | * 1 * * *
xox3oxo ...&#x  3 3 3 | 3  6 3  3  6 3 | 1 3  3 3  6 1 0 3  3 1 | 0 1 0 1 3  3 0 1 0 0 | * * 4 * *
... oxo3ooo&#x  1 3 1 | 0  3 1  3  3 0 | 0 0  3 0  3 0 1 0  3 0 | 0 0 1 0 0  3 0 0 1 0 | * * * 4 *
.ox3.xo3.oo&#x  0 6 4 | 0  0 0 12 12 6 | 0 0  0 0  0 4 4 6 12 4 | 0 0 0 0 0  0 1 4 4 1 | * * * * 1
or
o..3o..3o..    & | 8 * |  3  3 1  0 | 3  3  3 3  3 0 0 | 1 3 1 3 3  3 0 | 1 1 3 1
.o.3.o.3.o.      | * 6   0  4 0  4 | 0  2  8 0  2 2 2 | 0 4 4 0 1  4 1 | 2 0 2 2
-----------------+-----+------------+------------------+----------------+--------
x.. ... ...    & | 2 0 | 12  * *  * | 2  1  0 1  0 0 0 | 1 2 0 2 1  0 0 | 1 1 2 0
oo.3oo.3oo.&#x & | 1 1 |  * 24 *  * | 0  1  2 0  1 0 0 | 0 2 1 0 1  2 0 | 1 0 2 1
o.o3o.o3o.o&#x   | 2 0 |  *  * 4  * | 0  0  0 3  3 0 0 | 0 0 0 3 3  3 0 | 0 1 3 1
... .x. ...      | 0 2 |  *  * * 12 | 0  0  2 0  0 1 1 | 0 2 2 0 0  1 1 | 2 0 1 1
-----------------+-----+------------+------------------+----------------+--------
x..3o.. ...    & | 3 0 |  3  0 0  0 | 8  *  * *  * * * | 1 1 0 1 0  0 0 | 1 1 1 0
xo. ... ...&#x & | 2 1 |  1  2 0  0 | * 12  * *  * * * | 0 2 0 0 1  0 0 | 1 0 2 0
... ox. ...&#x & | 1 2 |  0  2 0  1 | *  * 24 *  * * * | 0 1 1 0 0  1 0 | 1 0 1 1
x.x ... ...&#x   | 4 0 |  2  0 2  0 | *  *  * 6  * * * | 0 0 0 2 1  0 0 | 0 1 2 0
ooo3ooo3ooo&#x   | 2 1 |  0  2 1  0 | *  *  * * 12 * * | 0 0 0 0 1  2 0 | 0 0 2 1
.o.3.x. ...      | 0 3 |  0  0 0  3 | *  *  * *  * 4 * | 0 2 0 0 0  0 1 | 2 0 1 0
... .x.3.o.      | 0 3 |  0  0 0  3 | *  *  * *  * * 4 | 0 0 2 0 0  0 1 | 2 0 0 1
-----------------+-----+------------+------------------+----------------+--------
x..3o..3o..    &  4 0 |  6  0 0  0 | 4  0  0 0  0 0 0 | 2 * * * *  * * | 1 1 0 0
xo.3ox. ...&#x &  3 3 |  3  6 0  3 | 1  3  3 0  0 1 0 | * 8 * * *  * * | 1 0 1 0
... ox.3oo.&#x &  1 3 |  0  3 0  3 | 0  0  3 0  0 0 1 | * * 8 * *  * * | 1 0 0 1
x.x3o.o ...&#x    6 0 |  6  0 3  0 | 2  0  0 3  0 0 0 | * * * 4 *  * * | 0 1 1 0
xox ... ...&#x    4 1 |  2  4 2  0 | 0  2  0 1  2 0 0 | * * * * 6  * * | 0 0 2 0
... oxo ...&#x    2 2 |  0  4 1  1 | 0  0  2 0  2 0 0 | * * * * * 12 * | 0 0 1 1
.o.3.x.3.o.       0 6 |  0  0 0 12 | 0  0  0 0  0 4 4 | * * * * *  * 1 | 2 0 0 0
-----------------+-----+------------+------------------+----------------+--------
xo.3ox.3oo.&#x &  4 6 |  6 12 0 12 | 4  6 12 0  0 4 4 | 1 4 4 0 0  0 1 | 2 * * *
x.x3o.o3o.o&#x    8 0 | 12  0 4  0 | 8  0  0 6  0 0 0 | 2 0 0 4 0  0 0 | * 1 * *
xox3oxo ...&#x    6 3 |  6 12 3  3 | 2  6  6 3  6 1 0 | 0 2 0 1 3  3 0 | * * 4 *
... oxo3ooo&#x    2 3 |  0  6 1  3 | 0  0  6 0  3 0 1 | 0 0 2 0 0  3 0 | * * * 4

oxoxo oxoox oooxx&#xr   → all exist. heights = 1/sqrt(2) = 0.707107

o.... o.... o....     & | 2 * *  4 4 0  0 0 0 0 | 4  8 2 2 0 0 0 0 0 0 | 1 4 4 4 1 0 0 0 0 | 2 2 2 0
.o... .o... .o...       | * 4 *  2 0 2  4 0 0 0 | 4  4 0 0 4 2 2 0 0 0 | 1 4 4 2 0 2 1 0 0 | 2 2 2 0
...o. ...o. ...o.     & | * * 8 | 0 1 0  2 1 1 2 | 0  2 1 1 1 2 2 1 3 2 | 0 1 3 2 1 1 2 1 3 | 1 3 1 1
------------------------+-------+----------------+----------------------+-------------------+--------
oo... oo... oo...&#x  & | 1 1 0 | 8 * *  * * * * | 2  2 0 0 0 0 0 0 0 0 | 1 2 2 1 0 0 0 0 0 | 2 1 1 0
o...o o...o o...o&#x  & | 1 0 1 | * 8 *  * * * * | 0  2 1 1 0 0 0 0 0 0 | 0 1 2 2 1 0 0 0 0 | 1 2 1 0
.x... ..... .....     & | 0 2 0 | * * 4  * * * * | 2  0 0 0 2 0 0 0 0 0 | 1 2 2 0 0 1 0 0 0 | 2 1 1 0
.o.o. .o.o. .o.o.&#x  & | 0 1 1 | * * * 16 * * * | 0  1 0 0 1 1 1 0 0 0 | 0 1 2 1 0 1 1 0 0 | 1 2 1 0
...x. ..... .....     & | 0 0 2 | * * *  * 4 * * | 0  0 1 0 0 0 0 1 2 0 | 0 0 2 0 1 0 0 1 2 | 1 2 0 1
..... ..... ...x.       | 0 0 2 | * * *  * * 4 * | 0  0 0 1 0 2 0 1 0 2 | 0 0 0 2 1 1 2 0 3 | 0 3 1 1
...oo ...oo ...oo&#x    | 0 0 2 | * * *  * * * 8 | 0  0 0 0 0 0 1 0 2 1 | 0 0 2 0 0 0 1 1 2 | 1 2 0 1
------------------------+-------+----------------+----------------------+-------------------+--------
ox... ..... .....&#x  & | 1 2 0 | 2 0 1  0 0 0 0 | 8  * * * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0
oo..o oo..o oo..o&#x  & | 1 1 1 | 1 1 0  1 0 0 0 | * 16 * * * * * * * * | 0 1 1 1 0 0 0 0 0 | 1 1 1 0
..... o...x .....&#x  & | 1 0 2 | 0 2 0  0 1 0 0 | *  * 4 * * * * * * * | 0 0 2 0 1 0 0 0 0 | 1 2 0 0
..... ..... o...x&#x  & | 1 0 2 | 0 2 0  0 0 1 0 | *  * * 4 * * * * * * | 0 0 0 2 1 0 0 0 0 | 0 2 1 0
..... .x.o. .....&#x  & | 0 2 1 | 0 0 1  2 0 0 0 | *  * * * 8 * * * * * | 0 1 1 0 0 1 0 0 0 | 1 1 1 0
..... ..... .o.x.&#x  & | 0 1 2 | 0 0 0  2 0 1 0 | *  * * * * 8 * * * * | 0 0 0 1 0 1 1 0 0 | 0 2 1 0
.o.oo .o.oo .o.oo&#x    | 0 1 2 | 0 0 0  2 0 0 1 | *  * * * * * 8 * * * | 0 0 2 0 0 0 1 0 0 | 1 2 0 0
...x. ..... ...x.     & | 0 0 4 | 0 0 0  0 2 2 0 | *  * * * * * * 2 * * | 0 0 0 0 1 0 0 0 2 | 0 2 0 1
...xo ..... .....&#x  & | 0 0 3 | 0 0 0  0 1 0 2 | *  * * * * * * * 8 * | 0 0 1 0 0 0 0 1 1 | 1 1 0 1
..... ..... ...xx&#x    | 0 0 4 | 0 0 0  0 0 2 2 | *  * * * * * * * * 4 | 0 0 0 0 0 0 1 0 2 | 0 2 0 1
------------------------+-------+----------------+----------------------+-------------------+--------
oxo.. oxo.. .....&#xt    2 4 0 | 8 0 4  0 0 0 0 | 8  0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * | 2 0 0 0
ox..o ..... .....&#x  &  1 2 1 | 2 1 1  2 0 0 0 | 1  2 0 0 1 0 0 0 0 0 | * 8 * * * * * * * | 1 0 1 0
..... ox.ox .....&#xr &  1 2 3 | 2 2 1  4 1 0 2 | 1  2 1 0 1 0 2 0 1 0 | * * 8 * * * * * * | 1 1 0 0
..... ..... oo..x&#x  &  1 1 2 | 1 2 0  2 0 1 0 | 0  2 0 1 0 1 0 0 0 0 | * * * 8 * * * * * | 0 1 1 0
..... o...x o...x&#x  &  1 0 4 | 0 4 0  0 2 2 0 | 0  0 2 2 0 0 0 1 0 0 | * * * * 2 * * * * | 0 2 0 0
..... .x.o. .o.x.&#x  &  0 2 2 | 0 0 1  4 0 1 0 | 0  0 0 0 2 2 0 0 0 0 | * * * * * 4 * * * | 0 1 1 0
..... ..... .o.xx&#x     0 1 4 | 0 0 0  4 0 2 2 | 0  0 0 0 0 2 2 0 0 1 | * * * * * * 4 * * | 0 2 0 0
...xo ...ox .....&#x     0 0 4 | 0 0 0  0 2 0 4 | 0  0 0 0 0 0 0 0 4 0 | * * * * * * * 2 * | 1 0 0 1
...xo ..... ...xx&#x  &  0 0 6 | 0 0 0  0 2 3 4 | 0  0 0 0 0 0 0 1 2 2 | * * * * * * * * 4 | 0 1 0 1
------------------------+-------+----------------+----------------------+-------------------+--------
oxoxo oxoox .....&#xr    2 4 4 | 8 4 4  8 2 0 4 | 8  8 2 0 4 0 4 0 4 0 | 1 4 4 0 0 0 0 1 0 | 2 * * *
..... ox.ox oo.xx&#xr &  1 2 6 | 2 4 1  8 2 3 4 | 1  4 2 2 2 4 4 1 2 2 | 0 0 2 2 1 1 2 0 1 | * 4 * *
ox..o ..... oo..x&#x  &  1 2 2 | 2 2 1  4 0 1 0 | 1  4 0 1 2 2 0 0 0 0 | 0 2 0 2 0 1 0 0 0 | * * 4 *
...xo ...ox ...xx&#x     0 0 8 | 0 0 0  0 4 4 8 | 0  0 0 0 0 0 0 2 8 4 | 0 0 0 0 0 0 0 2 4 | * * * 1

xoox ooxo3oxox&#xr   → height(1,2) = height(3,4) = sqrt(5/12) = 0.645497
                       height(1,4) = height(2,3) = sqrt(2/3) = 0.816497
                       height(12,34) = sqrt(3/5) = 0.774597 (pen || traf)
                       height(14,23) = sqrt(3/8) = 0.612372 (oct || tepe)

o... o...3o...     | 2 * * * | 1 3 3 0 0 0 0  0 0 0 | 3 3 3 3 3 0 0 0  0 0 0 0 0 0 0 0 | 3 1 3 3 3 1 0 0 0 0 0 0 0 | 1 3 1 1 0 0
.o.. .o..3.o..     | * 3 * *  0 2 0 2 2 2 0  0 0 0 | 1 4 2 0 0 1 1 2  4 1 0 0 0 0 0 0 | 2 2 1 4 0 0 1 2 2 0 0 0 0 | 1 2 2 0 1 0
..o. ..o.3..o.     | * * 3 *  0 0 0 0 2 0 2  4 0 0 | 0 0 0 0 0 0 2 1  4 0 1 2 4 2 0 0 | 0 0 0 2 0 0 1 2 4 2 1 2 0 | 0 1 2 0 2 1
...o ...o3...o     | * * * 6 | 0 0 1 0 0 1 0  2 1 2 | 0 0 1 1 2 0 0 0  2 1 0 2 1 2 2 1 | 0 0 1 2 2 1 0 2 1 1 2 1 1 | 0 2 1 1 1 1
-------------------+---------+----------------------+----------------------------------+---------------------------+------------
x... .... ....     | 2 0 0 0 | 1 * * * * * *  * * * | 3 0 0 3 0 0 0 0  0 0 0 0 0 0 0 0 | 3 0 3 0 3 0 0 0 0 0 0 0 0 | 1 3 0 1 0 0
oo.. oo..3oo..&#x  | 1 1 0 0 | * 6 * * * * *  * * * | 1 2 1 0 0 0 0 0  0 0 0 0 0 0 0 0 | 2 1 1 2 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0
o..o o..o3o..o&#x  | 1 0 0 1 | * * 6 * * * *  * * * | 0 0 1 1 2 0 0 0  0 0 0 0 0 0 0 0 | 0 0 1 2 2 1 0 0 0 0 0 0 0 | 0 2 1 1 0 0
.... .... .x..     | 0 2 0 0 | * * * 3 * * *  * * * | 0 2 0 0 0 1 0 1  0 0 0 0 0 0 0 0 | 1 2 0 2 0 0 1 0 0 0 0 0 0 | 1 1 2 0 0 0
.oo. .oo.3.oo.&#x  | 0 1 1 0 | * * * * 6 * *  * * * | 0 0 0 0 0 0 1 1  2 0 0 0 0 0 0 0 | 0 0 0 2 0 0 1 1 2 0 0 0 0 | 0 1 2 0 1 0
.o.o .o.o3.o.o&#x  | 0 1 0 1 | * * * * * 6 *  * * * | 0 0 1 0 0 0 0 0  2 1 0 0 0 0 0 0 | 0 0 1 2 0 0 0 2 1 0 0 0 0 | 0 2 1 0 1 0
.... ..x. ....     | 0 0 2 0 | * * * * * * 3  * * * | 0 0 0 0 0 0 1 0  0 0 1 0 2 0 0 0 | 0 0 0 0 0 0 1 0 2 1 0 2 0 | 0 0 2 0 1 1
..oo ..oo3..oo&#x  | 0 0 1 1 | * * * * * * * 12 * * | 0 0 0 0 0 0 0 0  1 0 0 1 1 1 0 0 | 0 0 0 1 0 0 0 1 1 1 1 1 0 | 0 1 1 0 1 1
...x .... ....     | 0 0 0 2 | * * * * * * *  * 3 * | 0 0 0 1 0 0 0 0  0 1 0 2 0 0 2 0 | 0 0 1 0 2 0 0 2 0 1 2 0 1 | 0 2 0 1 1 1
.... .... ...x     | 0 0 0 2 | * * * * * * *  * * 6 | 0 0 0 0 1 0 0 0  0 0 0 0 0 1 1 1 | 0 0 0 1 1 1 0 0 0 0 1 1 1 | 0 1 1 1 0 1
-------------------+---------+----------------------+----------------------------------+---------------------------+------------
xo.. .... ....&#x  | 2 1 0 0 | 1 2 0 0 0 0 0  0 0 0 | 3 * * * * * * *  * * * * * * * * | 2 0 1 0 0 0 0 0 0 0 0 0 0 | 1 2 0 0 0 0
.... .... ox..&#x  | 1 2 0 0 | 0 2 0 1 0 0 0  0 0 0 | * 6 * * * * * *  * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo.o oo.o3oo.o&#x  | 1 1 0 1 | 0 1 1 0 0 1 0  0 0 0 | * * 6 * * * * *  * * * * * * * * | 0 0 1 2 0 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0
x..x .... ....&#x  | 2 0 0 2 | 1 0 2 0 0 0 0  0 1 0 | * * * 3 * * * *  * * * * * * * * | 0 0 1 0 2 0 0 0 0 0 0 0 0 | 0 2 0 1 0 0
.... .... o..x&#x  | 1 0 0 2 | 0 0 2 0 0 0 0  0 0 1 | * * * * 6 * * *  * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
.... .o..3.x..     | 0 3 0 0 | 0 0 0 3 0 0 0  0 0 0 | * * * * * 1 * *  * * * * * * * * | 0 2 0 0 0 0 1 0 0 0 0 0 0 | 1 0 2 0 0 0
.... .ox. ....&#x  | 0 1 2 0 | 0 0 0 0 2 0 1  0 0 0 | * * * * * * 3 *  * * * * * * * * | 0 0 0 0 0 0 1 0 2 0 0 0 0 | 0 0 2 0 1 0
.... .... .xo.&#x  | 0 2 1 0 | 0 0 0 1 2 0 0  0 0 0 | * * * * * * * 3  * * * * * * * * | 0 0 0 2 0 0 1 0 0 0 0 0 0 | 0 1 2 0 0 0
.ooo .ooo3.ooo&#x  | 0 1 1 1 | 0 0 0 0 1 1 0  1 0 0 | * * * * * * * * 12 * * * * * * * | 0 0 0 1 0 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
.o.x .... ....&#x  | 0 1 0 2 | 0 0 0 0 0 2 0  0 1 0 | * * * * * * * *  * 3 * * * * * * | 0 0 1 0 0 0 0 2 0 0 0 0 0 | 0 2 0 0 1 0
.... ..x.3..o.     | 0 0 3 0 | 0 0 0 0 0 0 3  0 0 0 | * * * * * * * *  * * 1 * * * * * | 0 0 0 0 0 0 1 0 0 0 0 2 0 | 0 0 2 0 0 1
..ox .... ....&#x  | 0 0 1 2 | 0 0 0 0 0 0 0  2 1 0 | * * * * * * * *  * * * 6 * * * * | 0 0 0 0 0 0 0 1 0 1 1 0 0 | 0 1 0 0 1 1
.... ..xo ....&#x  | 0 0 2 1 | 0 0 0 0 0 0 1  2 0 0 | * * * * * * * *  * * * * 6 * * * | 0 0 0 0 0 0 0 0 1 1 0 1 0 | 0 0 1 0 1 1
.... .... ..ox&#x  | 0 0 1 2 | 0 0 0 0 0 0 0  2 0 1 | * * * * * * * *  * * * * * 6 * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 1 1 0 0 1
...x .... ...x     | 0 0 0 4 | 0 0 0 0 0 0 0  0 2 2 | * * * * * * * *  * * * * * * 3 * | 0 0 0 0 1 0 0 0 0 0 1 0 1 | 0 1 0 1 0 1
.... ...o3...x     | 0 0 0 3 | 0 0 0 0 0 0 0  0 0 3 | * * * * * * * *  * * * * * * * 2 | 0 0 0 0 0 1 0 0 0 0 0 1 1 | 0 0 1 1 0 1
-------------------+---------+----------------------+----------------------------------+---------------------------+------------
xo.. .... ox..&#x   2 2 0 0 | 1 4 0 1 0 0 0  0 0 0 | 2 2 0 0 0 0 0 0  0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * | 1 1 0 0 0 0
.... oo..3ox..&#x   1 3 0 0 | 0 3 0 3 0 0 0  0 0 0 | 0 3 0 0 0 1 0 0  0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * | 1 0 1 0 0 0
xo.x .... ....&#x   2 1 0 2 | 1 2 2 0 0 2 0  0 1 0 | 1 0 2 1 0 0 0 0  0 1 0 0 0 0 0 0 | * * 3 * * * * * * * * * * | 0 2 0 0 0 0
.... .... oxox&#xr  1 2 1 2 | 0 2 2 1 2 2 0  2 0 1 | 0 1 2 0 1 0 0 1  2 0 0 0 0 1 0 0 | * * * 6 * * * * * * * * * | 0 1 1 0 0 0
x..x .... o..x&#x   2 0 0 4 | 1 0 4 0 0 0 0  0 2 2 | 0 0 0 2 2 0 0 0  0 0 0 0 0 0 1 0 | * * * * 3 * * * * * * * * | 0 1 0 1 0 0
.... o..o3o..x&#x   1 0 0 3 | 0 0 3 0 0 0 0  0 0 3 | 0 0 0 0 3 0 0 0  0 0 0 0 0 0 0 1 | * * * * * 2 * * * * * * * | 0 0 1 1 0 0
.... .ox.3.xo.&#x   0 3 3 0 | 0 0 0 3 6 0 3  0 0 0 | 0 0 0 0 0 1 3 3  0 0 1 0 0 0 0 0 | * * * * * * 1 * * * * * * | 0 0 2 0 0 0
.oox .... ....&#x   0 1 1 2 | 0 0 0 0 1 2 0  2 1 0 | 0 0 0 0 0 0 0 0  2 1 0 1 0 0 0 0 | * * * * * * * 6 * * * * * | 0 1 0 0 1 0
.... .oxo ....&#x   0 1 2 1 | 0 0 0 0 2 1 1  2 0 0 | 0 0 0 0 0 0 1 0  2 0 0 0 1 0 0 0 | * * * * * * * * 6 * * * * | 0 0 1 0 1 0
..ox ..xo ....&#x   0 0 2 2 | 0 0 0 0 0 0 1  4 1 0 | 0 0 0 0 0 0 0 0  0 0 0 2 2 0 0 0 | * * * * * * * * * 3 * * * | 0 0 0 0 1 1
..ox .... ..ox&#x   0 0 1 4 | 0 0 0 0 0 0 0  4 2 2 | 0 0 0 0 0 0 0 0  0 0 0 2 0 2 1 0 | * * * * * * * * * * 3 * * | 0 1 0 0 0 1
.... ..xo3..ox&#x   0 0 3 3 | 0 0 0 0 0 0 3  6 0 3 | 0 0 0 0 0 0 0 0  0 0 1 0 3 3 0 1 | * * * * * * * * * * * 2 * | 0 0 1 0 0 1
...x ...o3...x      0 0 0 6 | 0 0 0 0 0 0 0  0 3 6 | 0 0 0 0 0 0 0 0  0 0 0 0 0 0 3 2 | * * * * * * * * * * * * 1 | 0 0 0 1 0 1
-------------------+---------+----------------------+----------------------------------+---------------------------+------------
xo.. oo..3ox..&#x   2 3 0 0 | 1 6 0 3 0 0 0  0 0 0 | 3 6 0 0 0 1 0 0  0 0 0 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xoox .... oxox&#xr  2 2 1 4 | 1 4 4 1 2 4 0  4 2 2 | 2 2 4 2 2 0 0 1  4 2 0 2 0 2 1 0 | 1 0 2 2 1 0 0 2 0 0 1 0 0 | * 3 * * * *
.... ooxo3oxox&#xr  1 3 3 3 | 0 3 3 3 6 3 3  6 0 3 | 0 3 3 0 3 1 3 3  6 0 1 0 3 3 0 1 | 0 1 0 3 0 1 1 0 3 0 0 1 0 | * * 2 * * *
x..x o..o3o..x&#x   2 0 0 6 | 1 0 6 0 0 0 0  0 3 6 | 0 0 0 3 6 0 0 0  0 0 0 0 0 0 3 2 | 0 0 0 0 3 2 0 0 0 0 0 0 1 | * * * 1 * *
.oox .oxo ....&#x   0 1 2 2 | 0 0 0 0 2 2 1  4 1 0 | 0 0 0 0 0 0 1 0  4 1 0 2 2 0 0 0 | 0 0 0 0 0 0 0 2 2 1 0 0 0 | * * * * 3 *
..ox ..xo3..ox&#x   0 0 3 6 | 0 0 0 0 0 0 3 12 3 6 | 0 0 0 0 0 0 0 0  0 0 1 6 6 6 3 2 | 0 0 0 0 0 0 0 0 0 3 3 2 1 | * * * * * 1

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