Acronym thex
Name truncated hexadecachoron,
cantic tesseract
 
©  
Cross sections
 ©
Circumradius sqrt(5/2) = 1.581139
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1x3x3o4o x3x3o .
tut first
x3x . o
{6} first
x . o4o
edge first
. x3o4o
oct first
2 u3o3x . u3o . q u . x4o . u3o4o
3a x3o3u . x3o . Q x . u4o . x3x4o
3b u3x . o U . o4o
4a o3x3x .
opposite tut
o3x . Q o . x4q . u3o4o
4b x3u . o
5a   o3u . q x . u4o . x3o4o
opposite oct
5b U . o4o
6 x3x . o
opposite {6}
u . x4o  
7   x . o4o
opposite edge
 o3o3o *b3o o3o3o    . o3o . *b3o o . o    o . o3o *b3o
1x3x3o *b3o x3x3o    .
tut first
x3x . *b3o
tut first
x . o    o
edge first
. x3o *b3o
oct first
2 u3o3x    . u3o . *b3x u . x    x . u3o *b3o
3a x3o3u    . x3o . *b3u x . u    u . x3x *b3x
3b U . o    o
4a o3x3x    .
opposite tut
o3x . *b3x
opposite tut
o . x    U . u3o *b3o
4b o . U    x
5a     x . u    u . x3o *b3o
opposite oct
5b U . o    o
6 u . x    x  
7 x . o    o
opposite edge
(Q=q+q, U=x+u)
Lace city
in approx. ASCII-art
 ©  
    o4o x4o o4o    
                   
o4o     u4o     o4o
                   
x4o u4o x4q u4o x4o
                   
o4o     u4o     o4o
                   
    o4o x4o o4o    
        x3x        
    u3o     u3o    
x3o     u3x     x3o
                   
o3x     x3u     o3x
    o3u     o3u    
        x3x        
Coordinates (sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: oct thah toe tut
thex 80016
titho 0848
)
Dihedral angles
  • at {3} between oct and tut:   120°
  • at {6} between tut and tut:   120°
Confer
Grünbaumian relatives:
2thex  
related CRFs:
octum   pex thex   pabex thex   pacprit  
decompositions:
hex || thex  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

Note that thex can be thought of as the external blend of 1 hex + 16 tetatuts + 8 octpies. This decomposition is described as the degenerate segmentoteron xx3ox3oo4oo&#x. – Alternatively it can be (subdimensioanlly degenerate) decomposed into 1 rit + 16 tetaltuts + 24 squascs + 8 octacoes according to ox3ox3xo4oo&#x.


Incidence matrix according to Dynkin symbol

x3x3o4o

. . . . | 48 |  1  4 |  4  4 |  4 1
--------+----+-------+-------+-----
x . . . |  2 | 24  * |  4  0 |  4 0
. x . . |  2 |  * 96 |  1  2 |  2 1
--------+----+-------+-------+-----
x3x . . |  6 |  3  3 | 32  * |  2 0
. x3o . |  3 |  0  3 |  * 64 |  1 1
--------+----+-------+-------+-----
x3x3o .  12 |  6 12 |  4  4 | 16 *
. x3o4o   6 |  0 12 |  0  8 |  * 8

snubbed forms: β3x3o4o, x3β3o4o, β3β3o4o

x3x3o4/3o

. . .   . | 48 |  1  4 |  4  4 |  4 1
----------+----+-------+-------+-----
x . .   . |  2 | 24  * |  4  0 |  4 0
. x .   . |  2 |  * 96 |  1  2 |  2 1
----------+----+-------+-------+-----
x3x .   . |  6 |  3  3 | 32  * |  2 0
. x3o   . |  3 |  0  3 |  * 64 |  1 1
----------+----+-------+-------+-----
x3x3o   .  12 |  6 12 |  4  4 | 16 *
. x3o4/3o   6 |  0 12 |  0  8 |  * 8

x3x3/2o4o

. .   . . | 48 |  1  4 |  4  4 |  4 1
----------+----+-------+-------+-----
x .   . . |  2 | 24  * |  4  0 |  4 0
. x   . . |  2 |  * 96 |  1  2 |  2 1
----------+----+-------+-------+-----
x3x   . . |  6 |  3  3 | 32  * |  2 0
. x3/2o . |  3 |  0  3 |  * 64 |  1 1
----------+----+-------+-------+-----
x3x3/2o .  12 |  6 12 |  4  4 | 16 *
. x3/2o4o   6 |  0 12 |  0  8 |  * 8

x3x3/2o4/3o

. .   .   . | 48 |  1  4 |  4  4 |  4 1
------------+----+-------+-------+-----
x .   .   . |  2 | 24  * |  4  0 |  4 0
. x   .   . |  2 |  * 96 |  1  2 |  2 1
------------+----+-------+-------+-----
x3x   .   . |  6 |  3  3 | 32  * |  2 0
. x3/2o   . |  3 |  0  3 |  * 64 |  1 1
------------+----+-------+-------+-----
x3x3/2o   .  12 |  6 12 |  4  4 | 16 *
. x3/2o4/3o   6 |  0 12 |  0  8 |  * 8

x3x3o *b3o

. . .    . | 48 |  1  4 |  4  2  2 | 2 2 1
-----------+----+-------+----------+------
x . .    . |  2 | 24  * |  4  0  0 | 2 2 0
. x .    . |  2 |  * 96 |  1  1  1 | 1 1 1
-----------+----+-------+----------+------
x3x .    . |  6 |  3  3 | 32  *  * | 1 1 0
. x3o    . |  3 |  0  3 |  * 32  * | 1 0 1
. x . *b3o |  3 |  0  3 |  *  * 32 | 0 1 1
-----------+----+-------+----------+------
x3x3o    .  12 |  6 12 |  4  4  0 | 8 * *
x3x . *b3o  12 |  6 12 |  4  0  4 | * 8 *
. x3o *b3o   6 |  0 12 |  0  4  4 | * * 8

snubbed forms: β3x3o *b3o, x3β3o *b3o, β3β3o *b3o

x3x3o *b3/2o

. . .      . | 48 |  1  4 |  4  2  2 | 2 2 1
-------------+----+-------+----------+------
x . .      . |  2 | 24  * |  4  0  0 | 2 2 0
. x .      . |  2 |  * 96 |  1  1  1 | 1 1 1
-------------+----+-------+----------+------
x3x .      . |  6 |  3  3 | 32  *  * | 1 1 0
. x3o      . |  3 |  0  3 |  * 32  * | 1 0 1
. x . *b3/2o |  3 |  0  3 |  *  * 32 | 0 1 1
-------------+----+-------+----------+------
x3x3o      .  12 |  6 12 |  4  4  0 | 8 * *
x3x . *b3/2o  12 |  6 12 |  4  0  4 | * 8 *
. x3o *b3/2o   6 |  0 12 |  0  4  4 | * * 8

x3x3/2o *b3/2o

. .   .      . | 48 |  1  4 |  4  2  2 | 2 2 1
---------------+----+-------+----------+------
x .   .      . |  2 | 24  * |  4  0  0 | 2 2 0
. x   .      . |  2 |  * 96 |  1  1  1 | 1 1 1
---------------+----+-------+----------+------
x3x   .      . |  6 |  3  3 | 32  *  * | 1 1 0
. x3/2o      . |  3 |  0  3 |  * 32  * | 1 0 1
. x   . *b3/2o |  3 |  0  3 |  *  * 32 | 0 1 1
---------------+----+-------+----------+------
x3x3/2o      .  12 |  6 12 |  4  4  0 | 8 * *
x3x   . *b3/2o  12 |  6 12 |  4  0  4 | * 8 *
. x3/2o *b3/2o   6 |  0 12 |  0  4  4 | * * 8

s4o3x3o

demi( . . . . ) | 48 |  1  4 |  2  2  4 | 2 1 2
----------------+----+-------+----------+------
      s4o . .   |  2 | 24  * |  0  0  4 | 2 0 2
demi( . . x . ) |  2 |  * 96 |  1  1  1 | 1 1 1
----------------+----+-------+----------+------
demi( . o3x . ) |  3 |  0  3 | 32  *  * | 1 1 0
demi( . . x3o ) |  3 |  0  3 |  * 32  * | 0 1 1
sefa( s4o3x . ) |  6 |  3  3 |  *  * 32 | 1 0 1
----------------+----+-------+----------+------
      s4o3x .    12 |  6 12 |  4  0  4 | 8 * *
demi( . o3x3o )   6 |  0 12 |  4  4  0 | * 8 *
sefa( s4o3x3o )  12 |  6 12 |  0  4  4 | * * 8

starting figure: x4o3x3o

xuxo3xoox3oxux&#xt   → all heights = 1/sqrt(2) = 0.707107
(tut || pseudo (u,x)-co || pseudo inv (u,x)-co || inv tut)

o...3o...3o...     | 12  *  *  * | 1  2  2  0  0  0  0  0 0 | 2 1  2  2  1 0  0 0  0  0 0 0 | 1 2 1 1 0 0 0
.o..3.o..3.o..     |  * 12  *  * | 0  0  2  2  1  0  0  0 0 | 0 0  2  1  2 1  2 0  0  0 0 0 | 0 1 2 1 1 0 0
..o.3..o.3..o.     |  *  * 12  * | 0  0  0  0  1  2  2  0 0 | 0 0  2  0  0 0  2 1  2  1 0 0 | 0 1 2 0 1 1 0
...o3...o3...o     |  *  *  * 12 | 0  0  0  0  0  0  2  2 1 | 0 0  0  0  0 0  2 0  1  2 1 2 | 0 0 1 0 2 1 1
-------------------+-------------+--------------------------+-------------------------------+--------------
x... .... ....     |  2  0  0  0 | 6  *  *  *  *  *  *  * * | 2 0  2  0  0 0  0 0  0  0 0 0 | 1 2 1 0 0 0 0
.... x... ....     |  2  0  0  0 | * 12  *  *  *  *  *  * * | 1 1  0  1  0 0  0 0  0  0 0 0 | 1 1 0 1 0 0 0
oo..3oo..3oo..&#x  |  1  1  0  0 | *  * 24  *  *  *  *  * * | 0 0  1  1  1 0  0 0  0  0 0 0 | 0 1 1 1 0 0 0
.... .... .x..     |  0  2  0  0 | *  *  * 12  *  *  *  * * | 0 0  0  0  1 1  1 0  0  0 0 0 | 0 0 1 1 1 0 0
.oo.3.oo.3.oo.&#x  |  0  1  1  0 | *  *  *  * 12  *  *  * * | 0 0  2  0  0 0  2 0  0  0 0 0 | 0 1 2 0 1 0 0
..x. .... ....     |  0  0  2  0 | *  *  *  *  * 12  *  * * | 0 0  1  0  0 0  0 1  1  0 0 0 | 0 1 1 0 0 1 0
..oo3..oo3..oo&#x  |  0  0  1  1 | *  *  *  *  *  * 24  * * | 0 0  0  0  0 0  1 0  1  1 0 0 | 0 0 1 0 1 1 0
.... ...x ....     |  0  0  0  2 | *  *  *  *  *  *  * 12 * | 0 0  0  0  0 0  0 0  0  1 1 1 | 0 0 0 0 1 1 1
.... .... ...x     |  0  0  0  2 | *  *  *  *  *  *  *  * 6 | 0 0  0  0  0 0  2 0  0  0 0 2 | 0 0 1 0 2 0 1
-------------------+-------------+--------------------------+-------------------------------+--------------
x...3x... ....     |  6  0  0  0 | 3  3  0  0  0  0  0  0 0 | 4 *  *  *  * *  * *  *  * * * | 1 1 0 0 0 0 0
.... x...3o...     |  3  0  0  0 | 0  3  0  0  0  0  0  0 0 | * 4  *  *  * *  * *  *  * * * | 1 0 0 1 0 0 0
xux. .... ....&#xt |  2  2  2  0 | 1  0  2  0  2  1  0  0 0 | * * 12  *  * *  * *  *  * * * | 0 1 1 0 0 0 0
.... xo.. ....&#x  |  2  1  0  0 | 0  1  2  0  0  0  0  0 0 | * *  * 12  * *  * *  *  * * * | 0 1 0 1 0 0 0
.... .... ox..&#x  |  1  2  0  0 | 0  0  2  1  0  0  0  0 0 | * *  *  * 12 *  * *  *  * * * | 0 0 1 1 0 0 0
.... .o..3.x..     |  0  3  0  0 | 0  0  0  3  0  0  0  0 0 | * *  *  *  * 4  * *  *  * * * | 0 0 0 1 1 0 0
.... .... .xux&#xt |  0  2  2  2 | 0  0  0  1  2  0  2  0 1 | * *  *  *  * * 12 *  *  * * * | 0 0 1 0 1 0 0
..x.3..o. ....     |  0  0  3  0 | 0  0  0  0  0  3  0  0 0 | * *  *  *  * *  * 4  *  * * * | 0 1 0 0 0 1 0
..xo .... ....&#x  |  0  0  2  1 | 0  0  0  0  0  1  2  0 0 | * *  *  *  * *  * * 12  * * * | 0 0 1 0 0 1 0
.... ..ox ....&#x  |  0  0  1  2 | 0  0  0  0  0  0  2  1 0 | * *  *  *  * *  * *  * 12 * * | 0 0 0 0 1 1 0
...o3...x ....     |  0  0  0  3 | 0  0  0  0  0  0  0  3 0 | * *  *  *  * *  * *  *  * 4 * | 0 0 0 0 0 1 1
.... ...x3...x     |  0  0  0  6 | 0  0  0  0  0  0  0  3 3 | * *  *  *  * *  * *  *  * * 4 | 0 0 0 0 1 0 1
-------------------+-------------+--------------------------+-------------------------------+--------------
x...3x...3o...      12  0  0  0 | 6 12  0  0  0  0  0  0 0 | 4 4  0  0  0 0  0 0  0  0 0 0 | 1 * * * * * *
xux.3xoo. ....&#xt   6  3  3  0 | 3  3  6  0  3  3  0  0 0 | 1 0  3  3  0 0  0 1  0  0 0 0 | * 4 * * * * *
xuxo .... oxux&#xt   2  4  4  2 | 1  0  4  2  4  2  4  0 1 | 0 0  2  0  2 0  2 0  2  0 0 0 | * * 6 * * * *
.... xo..3ox..&#x    3  3  0  0 | 0  3  6  3  0  0  0  0 0 | 0 1  0  3  3 1  0 0  0  0 0 0 | * * * 4 * * *
.... .oox3.xux&#xt   0  3  3  6 | 0  0  0  3  3  0  6  3 3 | 0 0  0  0  0 1  3 0  0  3 0 1 | * * * * 4 * *
..xo3..ox ....&#x    0  0  3  3 | 0  0  0  0  0  3  6  3 0 | 0 0  0  0  0 0  0 1  3  3 1 0 | * * * * * 4 *
...o3...x3...x       0  0  0 12 | 0  0  0  0  0  0  0 12 6 | 0 0  0  0  0 0  0 0  0  0 4 4 | * * * * * * 1
or
o...3o...3o...      & | 24  * |  1  2  2  0  0 | 2 1  2  2  1 0 | 1 2 1 1
.o..3.o..3.o..      & |  * 24 |  0  0  2  2  1 | 0 0  4  1  2 1 | 0 2 2 1
----------------------+-------+----------------+----------------+--------
x... .... ....      & |  2  0 | 12  *  *  *  * | 2 0  2  0  0 0 | 1 2 1 0
.... x... ....      & |  2  0 |  * 24  *  *  * | 1 1  0  1  0 0 | 1 1 0 1
oo..3oo..3oo..&#x   & |  1  1 |  *  * 48  *  * | 0 0  1  1  1 0 | 0 1 1 1
.... .... .x..      & |  0  2 |  *  *  * 24  * | 0 0  1  0  1 1 | 0 1 1 1
.oo.3.oo.3.oo.&#x     |  0  2 |  *  *  *  * 12 | 0 0  4  0  0 0 | 0 2 2 0
----------------------+-------+----------------+----------------+--------
x...3x... ....      & |  6  0 |  3  3  0  0  0 | 8 *  *  *  * * | 1 1 0 0
.... x...3o...      & |  3  0 |  0  3  0  0  0 | * 8  *  *  * * | 1 0 0 1
xux. .... ....&#xt  & |  2  4 |  1  0  2  1  2 | * * 24  *  * * | 0 1 1 0
.... xo.. ....&#x   & |  2  1 |  0  1  2  0  0 | * *  * 24  * * | 0 1 0 1
.... .... ox..&#x   & |  1  2 |  0  0  2  1  0 | * *  *  * 24 * | 0 0 1 1
.... .o..3.x..      & |  0  3 |  0  0  0  3  0 | * *  *  *  * 8 | 0 1 0 1
----------------------+-------+----------------+----------------+--------
x...3x...3o...      &  12  0 |  6 12  0  0  0 | 4 4  0  0  0 0 | 2 * * *
xux.3xoo. ....&#xt  &   6  6 |  3  3  6  3  3 | 1 0  3  3  0 1 | * 8 * *
xuxo .... oxux&#xt      4  8 |  2  0  8  4  4 | 0 0  4  0  4 0 | * * 6 *
.... xo..3ox..&#x   &   3  3 |  0  3  6  3  0 | 0 1  0  3  3 1 | * * * 8

xuxux3ooxoo4ooooo&#xt   → all heights = 1/sqrt(2) = 0.707107
(oct || pseudo u-oct || pseudo toe || pseudo u-oct || oct)

o....3o....4o....     | 6 *  * * * |  4 1  0  0  0  0 0  0 | 4  4  0 0  0  0 0 | 1 4 0 0 0
.o...3.o...4.o...     | * 6  * * * |  0 1  4  0  0  0 0  0 | 0  4  4 0  0  0 0 | 0 4 1 0 0
..o..3..o..4..o..     | * * 24 * * |  0 0  1  1  2  1 0  0 | 0  1  2 2  1  2 0 | 0 2 1 2 0
...o.3...o.4...o.     | * *  * 6 * |  0 0  0  0  0  4 1  0 | 0  0  0 0  4  4 0 | 0 0 1 4 0
....o3....o4....o     | * *  * * 6 |  0 0  0  0  0  0 1  4 | 0  0  0 0  4  0 4 | 0 0 0 4 1
----------------------+------------+-----------------------+-------------------+----------
x.... ..... .....     | 2 0  0 0 0 | 12 *  *  *  *  * *  * | 2  1  0 0  0  0 0 | 1 2 0 0 0
oo...3oo...4oo...&#x  | 1 1  0 0 0 |  * 6  *  *  *  * *  * | 0  4  0 0  0  0 0 | 0 4 0 0 0
.oo..3.oo..4.oo..&#x  | 0 1  1 0 0 |  * * 24  *  *  * *  * | 0  1  2 0  0  0 0 | 0 2 1 0 0
..x.. ..... .....     | 0 0  2 0 0 |  * *  * 12  *  * *  * | 0  1  0 2  1  0 0 | 0 2 0 2 0
..... ..x.. .....     | 0 0  2 0 0 |  * *  *  * 24  * *  * | 0  0  1 1  0  1 0 | 0 1 1 1 0
..oo.3..oo.4..oo.&#x  | 0 0  1 1 0 |  * *  *  *  * 24 *  * | 0  0  0 0  1  2 0 | 0 0 1 2 0
...oo3...oo4...oo&#x  | 0 0  0 1 1 |  * *  *  *  *  * 6  * | 0  0  0 0  4  0 0 | 0 0 0 4 0
....x ..... .....     | 0 0  0 0 2 |  * *  *  *  *  * * 12 | 0  0  0 0  1  0 2 | 0 0 0 2 1
----------------------+------------+-----------------------+-------------------+----------
x....3o.... .....     | 3 0  0 0 0 |  3 0  0  0  0  0 0  0 | 8  *  * *  *  * * | 1 1 0 0 0
xux.. ..... .....&#xt | 2 2  2 0 0 |  1 2  2  1  0  0 0  0 | * 12  * *  *  * * | 0 2 0 0 0
..... .ox.. .....&#x  | 0 1  2 0 0 |  0 0  2  0  1  0 0  0 | *  * 24 *  *  * * | 0 1 1 0 0
..x..3..x.. .....     | 0 0  6 0 0 |  0 0  0  3  3  0 0  0 | *  *  * 8  *  * * | 0 1 0 1 0
..xux ..... .....&#xt | 0 0  2 2 2 |  0 0  0  1  0  2 2  1 | *  *  * * 12  * * | 0 0 0 2 0
..... ..xo. .....&#x  | 0 0  2 1 0 |  0 0  0  0  1  2 0  0 | *  *  * *  * 24 * | 0 0 1 1 0
....x3....o .....     | 0 0  0 0 3 |  0 0  0  0  0  0 0  3 | *  *  * *  *  * 8 | 0 0 0 1 1
----------------------+------------+-----------------------+-------------------+----------
x....3o....4o....      6 0  0 0 0 | 12 0  0  0  0  0 0  0 | 8  0  0 0  0  0 0 | 1 * * * *
xux..3oox.. .....&#xt  3 3  6 0 0 |  3 3  6  3  3  0 0  0 | 1  3  3 1  0  0 0 | * 8 * * *
..... .oxo.4.ooo.&#xt  0 1  4 1 0 |  0 0  4  0  4  4 0  0 | 0  0  4 0  0  4 0 | * * 6 * *
..xux3..xoo .....&#xt  0 0  6 3 3 |  0 0  0  3  3  6 3  3 | 0  0  0 1  3  3 1 | * * * 8 *
....x3....o4....o      0 0  0 0 6 |  0 0  0  0  0  0 0 12 | 0  0  0 0  0  0 8 | * * * * 1
or
o....3o....4o....      & | 12  *  * |  4  1  0  0  0 |  4  4  0 0 | 1  4 0
.o...3.o...4.o...      & |  * 12  * |  0  1  4  0  0 |  0  4  4 0 | 0  4 1
..o..3..o..4..o..        |  *  * 24 |  0  0  2  1  2 |  0  2  4 2 | 0  4 1
-------------------------+----------+----------------+------------+-------
x.... ..... .....      & |  2  0  0 | 24  *  *  *  * |  2  1  0 0 | 1  2 0
oo...3oo...4oo...&#x   & |  1  1  0 |  * 12  *  *  * |  0  4  0 0 | 0  4 0
.oo..3.oo..4.oo..&#x   & |  0  1  1 |  *  * 48  *  * |  0  1  2 0 | 0  2 1
..x.. ..... .....        |  0  0  2 |  *  *  * 12  * |  0  2  0 2 | 0  4 0
..... ..x.. .....        |  0  0  2 |  *  *  *  * 24 |  0  0  2 1 | 0  2 1
-------------------------+----------+----------------+------------+-------
x....3o.... .....      & |  3  0  0 |  3  0  0  0  0 | 16  *  * * | 1  1 0
xux.. ..... .....&#xt  & |  2  2  2 |  1  2  2  1  0 |  * 24  * * | 0  2 0
..... .ox.. .....&#x   & |  0  1  2 |  0  0  2  0  1 |  *  * 48 * | 0  1 1
..x..3..x.. .....        |  0  0  6 |  0  0  0  3  3 |  *  *  * 8 | 0  2 0
-------------------------+----------+----------------+------------+-------
x....3o....4o....      &   6  0  0 | 12  0  0  0  0 |  8  0  0 0 | 2  * *
xux..3oox.. .....&#xt  &   3  3  6 |  3  3  6  3  3 |  1  3  3 1 | * 16 *
..... .oxo.4.ooo.&#xt      0  2  4 |  0  0  8  0  4 |  0  0  8 0 | *  * 6

ooxoo3xuxux3ooxoo&#xt   → all heights = 1/sqrt(2) = 0.707107
(oct || pseudo u-oct || pseudo toe || pseudo u-oct || oct)

o....3o....3o....     | 6 *  * * * |  4 1  0  0  0  0  0 0  0 | 2 2  4  0  0 0 0  0  0  0 0 0 | 1 2 2 0 0 0 0
.o...3.o...3.o...     | * 6  * * * |  0 1  4  0  0  0  0 0  0 | 0 0  4  2  2 0 0  0  0  0 0 0 | 0 2 2 1 0 0 0
..o..3..o..3..o..     | * * 24 * * |  0 0  1  1  1  1  1 0  0 | 0 0  1  1  1 1 1  1  1  1 0 0 | 0 1 1 1 1 1 0
...o.3...o.3...o.     | * *  * 6 * |  0 0  0  0  0  0  4 1  0 | 0 0  0  0  0 0 0  2  4  2 0 0 | 0 0 0 1 2 2 0
....o3....o3....o     | * *  * * 6 |  0 0  0  0  0  0  0 1  4 | 0 0  0  0  0 0 0  0  4  0 2 2 | 0 0 0 0 2 2 1
----------------------+------------+--------------------------+-------------------------------+--------------
..... x.... .....     | 2 0  0 0 0 | 12 *  *  *  *  *  * *  * | 1 1  1  0  0 0 0  0  0  0 0 0 | 1 1 1 0 0 0 0
oo...3oo...3oo...&#x  | 1 1  0 0 0 |  * 6  *  *  *  *  * *  * | 0 0  4  0  0 0 0  0  0  0 0 0 | 0 2 2 0 0 0 0
.oo..3.oo..3.oo..&#x  | 0 1  1 0 0 |  * * 24  *  *  *  * *  * | 0 0  1  1  1 0 0  0  0  0 0 0 | 0 1 1 1 0 0 0
..x.. ..... .....     | 0 0  2 0 0 |  * *  * 12  *  *  * *  * | 0 0  0  1  0 1 0  1  0  0 0 0 | 0 1 0 1 1 0 0
..... ..x.. .....     | 0 0  2 0 0 |  * *  *  * 12  *  * *  * | 0 0  1  0  0 1 1  0  1  0 0 0 | 0 1 1 0 1 1 0
..... ..... ..x..     | 0 0  2 0 0 |  * *  *  *  * 12  * *  * | 0 0  0  0  1 0 1  0  0  1 0 0 | 0 0 1 1 0 1 0
..oo.3..oo.3..oo.&#x  | 0 0  1 1 0 |  * *  *  *  *  * 24 *  * | 0 0  0  0  0 0 0  1  1  1 0 0 | 0 0 0 1 1 1 0
...oo3...oo3...oo&#x  | 0 0  0 1 1 |  * *  *  *  *  *  * 6  * | 0 0  0  0  0 0 0  0  4  0 0 0 | 0 0 0 0 2 2 0
..... ....x .....     | 0 0  0 0 2 |  * *  *  *  *  *  * * 12 | 0 0  0  0  0 0 0  0  1  0 1 1 | 0 0 0 0 1 1 1
----------------------+------------+--------------------------+-------------------------------+--------------
o....3x.... .....     | 3 0  0 0 0 |  3 0  0  0  0  0  0 0  0 | 4 *  *  *  * * *  *  *  * * * | 1 1 0 0 0 0 0
..... x....3o....     | 3 0  0 0 0 |  3 0  0  0  0  0  0 0  0 | * 4  *  *  * * *  *  *  * * * | 1 0 1 0 0 0 0
..... xux.. .....&#xt | 2 2  2 0 0 |  1 2  2  0  1  0  0 0  0 | * * 12  *  * * *  *  *  * * * | 0 1 1 0 0 0 0
.ox.. ..... .....&#x  | 0 1  2 0 0 |  0 0  2  1  0  0  0 0  0 | * *  * 12  * * *  *  *  * * * | 0 1 0 1 0 0 0
..... ..... .ox..&#x  | 0 1  2 0 0 |  0 0  2  0  0  1  0 0  0 | * *  *  * 12 * *  *  *  * * * | 0 0 1 1 0 0 0
..x..3..x.. .....     | 0 0  6 0 0 |  0 0  0  3  3  0  0 0  0 | * *  *  *  * 4 *  *  *  * * * | 0 1 0 0 1 0 0
..... ..x..3..x..     | 0 0  6 0 0 |  0 0  0  0  3  3  0 0  0 | * *  *  *  * * 4  *  *  * * * | 0 0 1 0 0 1 0
..xo. ..... .....&#x  | 0 0  2 1 0 |  0 0  0  1  0  0  2 0  0 | * *  *  *  * * * 12  *  * * * | 0 0 0 1 1 0 0
..... ..xux .....&#xt | 0 0  2 2 2 |  0 0  0  0  1  0  2 2  1 | * *  *  *  * * *  * 12  * * * | 0 0 0 0 1 1 0
..... ..... ..xo.&#x  | 0 0  2 1 0 |  0 0  0  0  0  1  2 0  0 | * *  *  *  * * *  *  * 12 * * | 0 0 0 1 0 1 0
....o3....x .....     | 0 0  0 0 3 |  0 0  0  0  0  0  0 0  3 | * *  *  *  * * *  *  *  * 4 * | 0 0 0 0 1 0 1
..... ....x3....o     | 0 0  0 0 3 |  0 0  0  0  0  0  0 0  3 | * *  *  *  * * *  *  *  * * 4 | 0 0 0 0 0 1 1
----------------------+------------+--------------------------+-------------------------------+--------------
o....3x....3o....      6 0  0 0 0 | 12 0  0  0  0  0  0 0  0 | 4 4  0  0  0 0 0  0  0  0 0 0 | 1 * * * * * *
oox..3xux.. .....&#xt  3 3  6 0 0 |  3 3  6  3  3  0  0 0  0 | 1 0  3  3  0 1 0  0  0  0 0 0 | * 4 * * * * *
..... xux..3oox..&#xt  3 3  6 0 0 |  3 3  6  0  3  3  0 0  0 | 0 1  3  0  3 0 1  0  0  0 0 0 | * * 4 * * * *
.oxo. ..... .oxo.&#xt  0 1  4 1 0 |  0 0  4  2  0  2  4 0  0 | 0 0  0  2  2 0 0  2  0  2 0 0 | * * * 6 * * *
..xoo3..xux .....&#xt  0 0  6 3 3 |  0 0  0  3  3  0  6 3  3 | 0 0  0  0  0 1 0  3  3  0 1 0 | * * * * 4 * *
..... ..xux3..xoo&#xt  0 0  6 3 3 |  0 0  0  0  3  3  6 3  3 | 0 0  0  0  0 0 1  0  3  3 0 1 | * * * * * 4 *
....o3....x3....o      0 0  0 0 6 |  0 0  0  0  0  0  0 0 12 | 0 0  0  0  0 0 0  0  0  0 4 4 | * * * * * * 1
or
o....3o....3o....      & | 12  *  * |  4  1  0  0  0  0 | 2 2  4  0  0 0 0 | 1 2 2 0
.o...3.o...3.o...      & |  * 12  * |  0  1  4  0  0  0 | 0 0  4  2  2 0 0 | 0 2 2 1
..o..3..o..3..o..        |  *  * 24 |  0  0  2  1  1  1 | 0 0  2  2  2 1 1 | 0 2 2 1
-------------------------+----------+-------------------+------------------+--------
..... x.... .....      & |  2  0  0 | 24  *  *  *  *  * | 1 1  1  0  0 0 0 | 1 1 1 0
oo...3oo...3oo...&#x   & |  1  1  0 |  * 12  *  *  *  * | 0 0  4  0  0 0 0 | 0 2 2 0
.oo..3.oo..3.oo..&#x   & |  0  1  1 |  *  * 48  *  *  * | 0 0  1  1  1 0 0 | 0 1 1 1
..x.. ..... .....        |  0  0  2 |  *  *  * 12  *  * | 0 0  0  2  0 1 0 | 0 2 0 1
..... ..x.. .....        |  0  0  2 |  *  *  *  * 12  * | 0 0  2  0  0 1 1 | 0 2 2 0
..... ..... ..x..        |  0  0  2 |  *  *  *  *  * 12 | 0 0  0  0  2 0 1 | 0 0 2 1
-------------------------+----------+-------------------+------------------+--------
o....3x.... .....      & |  3  0  0 |  3  0  0  0  0  0 | 8 *  *  *  * * * | 1 1 0 0
..... x....3o....      & |  3  0  0 |  3  0  0  0  0  0 | * 8  *  *  * * * | 1 0 1 0
..... xux.. .....&#xt  & |  2  2  2 |  1  2  2  0  1  0 | * * 24  *  * * * | 0 1 1 0
.ox.. ..... .....&#x   & |  0  1  2 |  0  0  2  1  0  0 | * *  * 24  * * * | 0 1 0 1
..... ..... .ox..&#x   & |  0  1  2 |  0  0  2  0  0  1 | * *  *  * 24 * * | 0 0 1 1
..x..3..x.. .....        |  0  0  6 |  0  0  0  3  3  0 | * *  *  *  * 4 * | 0 2 0 0
..... ..x..3..x..        |  0  0  6 |  0  0  0  0  3  3 | * *  *  *  * * 4 | 0 0 2 0
-------------------------+----------+-------------------+------------------+--------
o....3x....3o....      &   6  0  0 | 12  0  0  0  0  0 | 4 4  0  0  0 0 0 | 2 * * *
oox..3xux.. .....&#xt  &   3  3  6 |  3  3  6  3  3  0 | 1 0  3  3  0 1 0 | * 8 * *
..... xux..3oox..&#xt  &   3  3  6 |  3  3  6  0  3  3 | 0 1  3  0  3 0 1 | * * 8 *
.oxo. ..... .oxo.&#xt      0  2  4 |  0  0  8  2  0  2 | 0 0  0  4  4 0 0 | * * * 6

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