Acronym rek
Name rectified diacosipentacontahexazetton,
lattice B8 contact polytope (span of its small roots),
lattice D8 contact polytope (span of its roots)
Circumradius 1
Inradius
wrt. roc
1/2 = 0.5
Inradius
wrt. zee
1/sqrt(2) = 0.707107
Lace city
in approx. ASCII-art
 ©  
o   g   o	-- x3o3o3o3o3o4o (zee)
         
g   r   g	-- o3x3o3o3o3o4o (rez)
         
o   g   o	-- x3o3o3o3o3o4o (zee)

   \   \   \   \   \
     \   \   \   \   +-- o o3o3o3o3o4o (point)
       \   \   \   +---- x x3o3o3o3o4o (geep)
         \   \   +------ compound of:
           \   \         o o3x3o3o3o4o (rag)
             \   \       u o3o3o3o3o4o (u-line)
               \   +---- x x3o3o3o3o4o (geep)
                 +------ o o3o3o3o3o4o (point)

where:
o = o3o3o3o3o4o (point)
g = x3o3o3o3o4o (gee)
r = o3x3o3o3o4o (rag)
  h   H  	-- x3o3o3o3o3o4o (zee)
         
         
r   S   R	-- o3x3o3o3o3o4o (rez)
         
         
  h   H  	-- x3o3o3o3o3o4o (zee)

    \   \   \
     \   \   +- o3x3o3o3o3o3o (roc)
      \   +---- x3o3o3o3o3o3x (suph)
       +------- o3o3o3o3o3x3o (inv. roc)

where:
h = x3o3o3o3o3o (hop)
H = o3o3o3o3o3x (dual hop)
r = o3x3o3o3o3o (ril)
R = o3o3o3o3x3o (inv. ril)
S = x3o3o3o3o3x (staf)
Lace hyper city
in approx. ASCII-art
                         
                         
            o            
          /  \\          
        /  |  \ \        
      /    _ - o_ \      
    / _ - |    |  -_\    
   o _           _ - o   
    \  -_|  _ +     /    
      \  o        /      
        \ \  |  /        
          \\  /          
            o            
                         
                         
                         
                         
                         
         H _             
          \  -_          
        |   \ _H         
            _ \ \        
       |  _     \\       
        _     _ - H      
      |  _ -             
      H                  
                         
                         
                         
                         
           _ - o_        
      _ -     /  \-_     
   o_       /    _ \ o   
    \ -_  / _ -      \\  
  |  \  /o           | \\
      o/   \            o
 |   /|\     \      |  /|
   /     \  I  \     /   
|/   |     \     \ |   | 
o            \   /o      
\\  |      _ - o_/ \  |  
  \\  _ -      /  -_\    
   o_\       /   _ - o   
      -\   /_ -          
         o               
                         
                         
                         
                         
              _ -_H      
         _ -   _         
      H      _   |       
       \\  _             
        \ \     |        
         H_ \            
            -_\|         
               H         
                         
                         
                         
                         
                         
            o            
          /  \\          
        /  |  \ \        
      /    _ - o_ \      
    / _ - |    |  -_\    
   o _           _ - o   
    \  -_|  _ +     /    
      \  o        /      
        \ \  |  /        
          \\  /          
            o            
                         
                         
i.e. the vertex positions of a centered ico plus a concentrical hex

where:
o = o3o3o4o (point)
H = x3o3o4o (hex)
I = o3x3o4o (ico)
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume 31/315 = 0.098413
Surface (480+8 sqrt(2))/315 = 1.559726
Dihedral angles
  • at ril between roc and roc:   arccos(-3/4) = 138.590378°
  • at hop between roc and zee:   arccos[-1/sqrt(8)] = 110.704811°
Confer
uniform relative:
fy   hexdip  
related orbiforms:
idirek  
analogs:
rectified orthoplex rOn  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

o3x3o3o3o3o3o4o

. . . . . . . . | 112    24 |  12  120 |   60  320 |  160   480 |  240  384 |  192  128 |  64  2
----------------+-----+------+----------+-----------+------------+-----------+-----------+-------
. x . . . . . . |   2 | 1344 |   1   10 |   10   40 |   40    80 |   80   80 |   80   32 |  32  1
----------------+-----+------+----------+-----------+------------+-----------+-----------+-------
o3x . . . . . . |   3 |    3 | 448    *    10    0 |   40     0 |   80    0 |   80    0 |  32  0
. x3o . . . . . |   3 |    3 |   * 4480 |    1    8 |    8    24 |   24   32 |   32   16 |  16  1
----------------+-----+------+----------+-----------+------------+-----------+-----------+-------
o3x3o . . . . .    6 |   12 |   4    4 | 1120    *     8     0 |   24    0 |   32    0 |  16  0
. x3o3o . . . .    4 |    6 |   0    4 |    * 8960 |    1     6 |    6   12 |   12    8 |   8  1
----------------+-----+------+----------+-----------+------------+-----------+-----------+-------
o3x3o3o . . . .   10 |   30 |  10   20 |    5    5 | 1792     *     6    0 |   12    0 |   8  0
. x3o3o3o . . .    5 |   10 |   0   10 |    0    5 |    * 10752 |    1    4 |    4    4 |   4  1
----------------+-----+------+----------+-----------+------------+-----------+-----------+-------
o3x3o3o3o . . .   15 |   60 |  20   60 |   15   30 |    6     6 | 1792    * |    4    0 |   4  0
. x3o3o3o3o . .    6 |   15 |   0   20 |    0   15 |    0     6 |    * 7168 |    1    2 |   2  1
----------------+-----+------+----------+-----------+------------+-----------+-----------+-------
o3x3o3o3o3o . .   21 |  105 |  35  140 |   35  105 |   21    42 |    7    7 | 1024    * |   2  0
. x3o3o3o3o3o .    7 |   21 |   0   35 |    0   35 |    0    21 |    0    7 |    * 2048 |   1  1
----------------+-----+------+----------+-----------+------------+-----------+-----------+-------
o3x3o3o3o3o3o .   28 |  168 |  56  280 |   70  280 |   56   168 |   28   56 |    8    8 | 256  *
. x3o3o3o3o3o4o   14 |   84 |   0  280 |    0  560 |    0   672 |    0  448 |    0  128 |   * 16

o3o3o *b3o3o3o3x3o

. . .    . . . . . | 112    24 |  120  12 |  320   60 |   480  160 |  384  240 |   64   64  192 |  2  32  32
-------------------+-----+------+----------+-----------+------------+-----------+----------------+-----------
. . .    . . . x . |   2 | 1344 |   10   1 |   40   10 |    80   40 |   80   80 |   16   16   80 |  1  16  16
-------------------+-----+------+----------+-----------+------------+-----------+----------------+-----------
. . .    . . o3x . |   3 |    3 | 4480   * |    8    1 |    24    8 |   32   24 |    8    8   32 |  1   8   8
. . .    . . . x3o |   3 |    3 |    * 448     0   10 |     0   40 |    0   80 |    0    0   80 |  0  16  16
-------------------+-----+------+----------+-----------+------------+-----------+----------------+-----------
. . .    . o3o3x .    4 |    6 |    4   0 | 8960    * |     6    1 |   12    6 |    4    4   12 |  1   4   4
. . .    . . o3x3o    6 |   12 |    4   4 |    * 1120      0    8 |    0   24 |    0    0   32 |  0   8   8
-------------------+-----+------+----------+-----------+------------+-----------+----------------+-----------
. . .    o3o3o3x .    5 |   10 |   10   0 |    5    0 | 10752    * |    4    1 |    2    2    4 |  1   2   2
. . .    . o3o3x3o   10 |   30 |   20  10 |    5    5 |     * 1792     0    6 |    0    0   12 |  0   4   4
-------------------+-----+------+----------+-----------+------------+-----------+----------------+-----------
. o . *b3o3o3o3x .    6 |   15 |   20   0 |   15    0 |     6    0 | 7168    * |    1    1    1 |  1   1   1
. . .    o3o3o3x3o   15 |   60 |   60  20 |   30   15 |     6    6 |    * 1792 |    0    0    4 |  0   2   2
-------------------+-----+------+----------+-----------+------------+-----------+----------------+-----------
o3o . *b3o3o3o3x .    7 |   21 |   35   0 |   35    0 |    21    0 |    7    0 | 1024    *    * |  1   1   0
. o3o *b3o3o3o3x .    7 |   21 |   35   0 |   35    0 |    21    0 |    7    0 |    * 1024    * |  1   0   1
. o . *b3o3o3o3x3o   21 |  105 |  140  35 |  105   35 |    42   21 |    7    7 |    *    * 1024 |  0   1   1
-------------------+-----+------+----------+-----------+------------+-----------+----------------+-----------
o3o3o *b3o3o3o3x .   14 |   84 |  280   0 |  560    0 |   672    0 |  448    0 |   64   64    0 | 16   *   *
o3o . *b3o3o3o3x3o   28 |  168 |  280  56 |  280   70 |   168   56 |   56   28 |    8    0    8 |  * 128   *
. o3o *b3o3o3o3x3o   28 |  168 |  280  56 |  280   70 |   168   56 |   56   28 |    0    8    8 |  *   * 128

xox3oxo3ooo3ooo3ooo3ooo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(zee || pseudo rez || zee)

o..3o..3o..3o..3o..3o..4o..     & | 28  *   12  12   0 |  60  12   60   0    0 |  160  60  160   0    0 |  240  160  240   0    0 | 192  240  192   0   0 |  64 192   64   0 | 1  64  1
.o.3.o.3.o.3.o.3.o.3.o.4.o.       |  * 84    0   4  20 |   0   2   40  10   80 |    0  20  160  40  160 |    0   80  320  80  160 |   0  160  320  80  64 |   0 160  128  32 | 0  64  2
----------------------------------+-------+-------------+-----------------------+------------------------+-------------------------+-----------------------+------------------+---------
x.. ... ... ... ... ... ...     & |  2  0 | 168   *   * |  10   1    0   0    0 |   40  10    0   0    0 |   80   40    0   0    0 |  80   80    0   0   0 |  32  80    0   0 | 1  32  0
oo.3oo.3oo.3oo.3oo.3oo.4oo.&#x  & |  1  1 |   * 336   * |   0   1   10   0    0 |    0  10   40   0    0 |    0   40   80   0    0 |   0   80   80   0   0 |   0  80   30   0 | 0  32  1
... .x. ... ... ... ... ...       |  0  2 |   *   * 840 |   0   0    2   1    8 |    0   2   16   8   24 |    0   16   48  24   32 |   0   48   64  32  16 |   0  64   32  16 | 0  32  1
----------------------------------+-------+-------------+-----------------------+------------------------+-------------------------+-----------------------+------------------+---------
x..3o.. ... ... ... ... ...     & |  3  0 |   3   0   0 | 560   *    *   *    * |    8   1    0   0    0 |   24    8    0   0    0 |  32   24    0   0   0 |  16  32    0   0 | 1  16  0
xo. ... ... ... ... ... ...&#x  & |  2  1 |   1   2   0 |   * 168    *   *    *     0  10    0   0    0 |    0   40    0   0    0 |   0   80    0   0   0 |   0  80    0   0 | 0  32  0
... ox. ... ... ... ... ...&#x  & |  1  2 |   0   2   1 |   *   * 1680   *    * |    0   1    8   0    0 |    0    8   24   0    0 |   0   24   32   0   0 |   0  32   16   0 | 0  16  1
.o.3.x. ... ... ... ... ...       |  0  3 |   0   0   3 |   *   *    * 280    *     0   2    0   8    0 |    0   16    0  24    0 |   0   48    0  32   0 |   0  64    0  16 | 0  32  0
... .x.3.o. ... ... ... ...       |  0  3 |   0   0   3 |   *   *    *   * 2240 |    0   0    2   1    6 |    0    2   12   6   12 |   0   12   24  12   8 |   0  24   16   8 | 0  16  1
----------------------------------+-------+-------------+-----------------------+------------------------+-------------------------+-----------------------+------------------+---------
x..3o..3o.. ... ... ... ...     &   4  0 |   6   0   0 |   4   0    0   0    0 | 1120   *    *   *    * |    6    1    0   0    0 |  12    6    0   0   0 |   8  12    0   0 | 1   8  0
xo.3ox. ... ... ... ... ...&#x  &   3  3 |   3   6   3 |   1   3    3   1    0 |    * 560    *   *    *     0    8    0   0    0 |   0   24    0   0   0 |   0  32    0   0 | 0  16  0
... ox.3oo. ... ... ... ...&#x  &   1  3 |   0   3   3 |   0   0    3   0    1 |    *   * 4480   *    * |    0    1    6   0    0 |   0    6   12   0   0 |   0  12    8   0 | 0   8  1
.o.3.x.3.o. ... ... ... ...         0  6 |   0   0  12 |   0   0    0   4    4 |    *   *    * 560    *     0    2    0   6    0 |   0   12    0  12   0 |   0  24    0   8 | 0  16  0
... .x.3.o.3.o. ... ... ...         0  4 |   0   0   6 |   0   0    0   0    4 |    *   *    *   * 3360 |    0    0    2   1    4 |   0    2    8   4   4 |   0   8    8   4 | 0   8  1
----------------------------------+-------+-------------+-----------------------+------------------------+-------------------------+-----------------------+------------------+---------
x..3o..3o..3o.. ... ... ...     &   5  0 |  10   0   0 |  10   0    0   0    0 |    5   0    0   0    0 | 1344    *    *   *    * |   4    1    0   0   0 |   4   4    0   0 | 1   4  0
xo.3ox.3oo. ... ... ... ...&#x  &   4  6 |   6  12  12 |   4   6   12   4    4 |    1   4    4   1    0 |    * 1120    *   *    *    0    6    0   0   0 |   0  12    0   0 | 0   8  0
... ox.3oo.3oo. ... ... ...&#x  &   1  4 |   0   4   6 |   0   0    6   0    4 |    0   0    4   0    1 |    *    * 6720   *    * |   0    1    4   0   0 |   0   4    4   0 | 0   4  1
.o.3.x.3.o.3.o. ... ... ...         0 10 |   0   0  30 |   0   0    0  10   20 |    0   0    0   5    5 |    *    *    * 672    *    0    2    0   4   0 |   0   8    0   4 | 0   8  0
... .x.3.o.3.o.3.o. ... ...         0  5 |   0   0  10 |   0   0    0   0   10 |    0   0    0   0    5 |    *    *    *   * 2688 |   0    0    2   1   2 |   0   2    4   2 | 0   4  1
----------------------------------+-------+-------------+-----------------------+------------------------+-------------------------+-----------------------+------------------+---------
x..3o..3o..3o..3o.. ... ...     &   6  0 |  15   0   0 |  20   0    0   0    0 |   15   0    0   0    0 |    6    0    0   0    0 | 896    *    *   *   * |   2   1    0   0 | 1   2  0
xo.3ox.3oo.3oo. ... ... ...&#x  &   5 10 |  10  20  30 |  10  10   30  10   20 |    5  10   20   5    5 |    1    5    5   1    0 |   * 1344    *   *   * |   0   4    0   0 | 0   4  0
... ox.3oo.3oo.3oo. ... ...&#x  &   1  5 |   0   5  10 |   0   0   10   0   10 |    0   0   10   0    5 |    0    0    5   0    1 |   *    * 5376   *   * |   0   1    2   0 | 0   2  1
.o.3.x.3.o.3.o.3.o. ... ...         0 15 |   0   0  60 |   0   0    0  20   60 |    0   0    0  15   30 |    0    0    0   6    6 |   *    *    * 448   * |   0   2    0   2 | 0   4  0
... .x.3.o.3.o.3.o.3.o. ...         0  6 |   0   0  15 |   0   0    0   0   20 |    0   0    0   0   15 |    0    0    0   0    6 |   *    *    *   * 896 |   0   0    2   1 | 0   2  1
----------------------------------+-------+-------------+-----------------------+------------------------+-------------------------+-----------------------+------------------+---------
x..3o..3o..3o..3o..3o.. ...     &   7  0 |  21   0   0 |  35   0    0   0    0 |   35   0    0   0    0 |   21    0    0   0    0 |   7    0    0   0   0 | 256   *    *   * | 1   1  0
xo.3ox.3oo.3oo.3oo. ... ...&#x  &   6 15 |  15  30  60 |  20  15   60  20   60 |   15  20   60  15   30 |    6   15   30   6    6 |   1    6    6   1   0 |   * 896    *   * | 0   2  0
... ox.3oo.3oo.3oo.3oo. ...&#x  &   1  6 |   0   6  15 |   0   0   15   0   20 |    0   0   20   0   15 |    0    0   15   0    6 |   0    0    6   0   1 |   *   * 1792   * | 0   1  1
.o.3.x.3.o.3.o.3.o.3.o. ...         0 21 |   0   0 105 |   0   0    0  35  140 |    0   0    0  35  105 |    0    0    0  21   42 |   0    0    0   7   7 |   *   *    * 128 | 0   2  0
----------------------------------+-------+-------------+-----------------------+------------------------+-------------------------+-----------------------+------------------+---------
x..3o..3o..3o..3o..3o..4o..     &  14  0 |  84   0   0 | 280   0    0   0    0 |  560   0    0   0    0 |  672    0    0   0    0 | 448    0    0   0   0 | 128   0    0   0 | 2   *  *
xo.3ox.3oo.3oo.3oo.3oo. ...&#x  &   7 21 |  21  42 105 |  35  21  105  35  140 |   35  35  140  35  105 |   21   35  105  21   42 |   7   21   42   7   7 |   1   7    7   1 | * 256  *
... oxo3ooo3ooo3ooo3ooo4ooo&#xt     2 12 |   0  24  60 |   0   0  120   0  160 |    0   0  320   0  240 |    0    0  480   0  192 |   0    0  384   0  64 |   0   0  128   0 | *   * 14

oxo3oox3ooo3ooo3ooo3xoo3oxo&#xt   → both heights = 1/2
(roc || pseudo suph || inv. roc)

... 

oox3xoo3ooo4ooo oox3oxo3ooo4ooo&#zx   → heights = 0
(tegum sum of 2 perp icoes and a hexdip)

o..3o..3o..4o.. o..3o..3o..4o..     & | 48  *    8  16   0 |  4   8   8   64   48   0 |  4  32  24   64  192   64   0 |  32  128  192  256   32 | 112  128  256  128 |  192  128 |  64  2
..o3..o3..o4..o ..o3..o3..o4..o       |  * 64    0  12  12 |  0   0  12   24   72  24 |  0  24  36   16  144  144  16 |  16  144   96  288   96 |  96  144  192  192 |  192  128 |  64  2
--------------------------------------+-------+-------------+--------------------------+-------------------------------+-------------------------+--------------------+-----------+-------
... x.. ... ... ... ... ... ...     & |  2  0 | 192   *   * |  1   2   0    8    0   0 |  2   8   0   16   24    0   0 |  16   24   48   32    0 |  48   32   64   16 |   80   32 |  32  1
o.o3o.o3o.o4o.o o.o3o.o3o.o4o.o&#x  & |  1  1 |   * 768   * |  0   0   1    4    6   0 |  0   4   6    4   24   12   0 |   4   36   24   48    8 |  32   48   48   32 |   80   32 |  32  1
..x ... ... ... ... ... ... ...     & |  0  2 |   *   * 384 |  0   0   1    0    6   4 |  0   4   6    0   12   24   4 |   4   36    8   48   24 |  32   48   32   48 |   80   32 |  32  1
--------------------------------------+-------+-------------+--------------------------+-------------------------------+-------------------------+--------------------+-----------+-------
o..3x.. ... ... ... ... ... ...     & |  3  0 |   3   0   0 | 64   *   *    *    *   *   2   8   0    0    0    0   0 |  16   24    0    0    0 |  48   32    0    0 |   80    0 |  32  0
... x..3o.. ... ... ... ... ...     & |  3  0 |   3   0   0 |  * 128   *    *    *   * |  1   0   0    8    0    0   0 |   8    0   24    0    0 |  24    0   32    0 |   32   16 |  16  1
o.x ... ... ... ... ... ... ...&#x  & |  1  2 |   0   2   1 |  *   * 384    *    *   *   0   4   6    0    0    0   0 |   4   36    0    0    0 |  32   48    0    0 |   80    0 |  32  0
... x.o ... ... ... ... ... ...&#x  & |  2  1 |   1   2   0 |  *   *   * 1536    *   * |  0   1   0    2    6    0   0 |   2    6   12   12    0 |  12   12   24    8 |   32   16 |  16  1
... ... ... ... o.x ... ... ...&#x  & |  1  2 |   0   2   1 |  *   *   *    * 2304   * |  0   0   1    0    4    4   0 |   0    8    4   16    4 |   8   16   16   16 |   32   16 |  16  1
..x3..o ... ... ... ... ... ...     & |  0  3 |   0   0   3 |  *   *   *    *    * 512 |  0   1   0    0    0    6   2 |   2    6    0   12   12 |  12   12    8   24 |   32   16 |  16  1
--------------------------------------+-------+-------------+--------------------------+-------------------------------+-------------------------+--------------------+-----------+-------
o..3x..3o.. ... ... ... ... ...     &   6  0 |  12   0   0 |  4   4   0    0    0   0 | 32   *   *    *    *    *   *    8    0    0    0    0 |  24    0    0    0 |   32    0 |  16  0
o.x3x.o ... ... ... ... ... ...&#x  &   3  3 |   3   6   3 |  1   0   3    3    0   1 |  * 512   *    *    *    *   *    2    6    0    0    0 |  12   12    0    0 |   32    0 |  16  0
oox ... ... ... oox ... ... ...&#xt     2  4 |   0   8   4 |  0   0   4    0    4   0 |  *   * 576    *    *    *   *    0    8    0    0    0 |   8   16    0    0 |   32    0 |  16  0 tower: A-C-B
... x.o3o.o ... ... ... ... ...&#x  &   3  1 |   3   3   0 |  0   1   0    3    0   0 |  *   *   * 1024    *    *   * |   1    0    6    0    0 |   6    0   12    0 |   12    8 |   8  1
... x.o ... ... o.x ... ... ...&#x  &   2  2 |   1   4   1 |  0   0   0    2    2   0 |  *   *   *    * 4608    *   * |   0    1    2    4    0 |   2    4    8    4 |   12    8 |   8  1
... ... ... ... o.x3o.o ... ...     &   1  3 |   0   3   3 |  0   0   0    0    3   1 |  *   *   *    *    * 3072   * |   0    1    0    4    2 |   2    4    4    8 |   12    8 |   8  1
..x3..o3..o ... ... ... ... ...     &   0  4 |   0   0   6 |  0   0   0    0    0   4 |  *   *   *    *    *    * 256 |   1    0    0    0    6 |   6    0    0   12 |   12    8 |   8  1
--------------------------------------+-------+-------------+--------------------------+-------------------------------+-------------------------+--------------------+-----------+-------
o.x3x.o3o.o ... ... ... ... ...&#x  &   6  4 |  12  12   6 |  4   4   6   12    0   4 |  1   4   0    4    0    0   1 | 256    *    *    *    *    6    0    0    0 |   12    0 |   8  0
oox3xoo ... ... oox ... ... ...&#xt &   4  6 |   3  18   9 |  1   0   9    6   12   2 |  0   2   3    0    3    2   0 |   * 1536    *    *    *    2    4    0    0 |   12    0 |   8  0
... x.o3o.o ... o.x ... ... ...&#x  &   3  2 |   3   6   1 |  0   1   0    6    3   0 |  0   0   0    2    3    0   0 |   *    * 3072    *    * |   1    0    4    0 |    4    4 |   4  1
... x.o ... ... o.x3o.o ... ...&#x  &   2  3 |   1   6   3 |  0   0   0    3    6   1 |  0   0   0    0    3    2   0 |   *    *    * 6144    * |   0    1    2    2 |    4    4 |   4  1
... ... ... ... o.x3o.o3o.o ...&#x  &   1  4 |   0   4   6 |  0   0   0    0    6   4 |  0   0   0    0    0    4   1 |   *    *    *    * 1536 |   1    0    0    4 |    4    4 |   4  1
--------------------------------------+-------+-------------+--------------------------+-------------------------------+-------------------------+--------------------+-----------+-------
oox3xoo3ooo ... oox ... ... ...&#xt &   7  8 |  12  32  16 |  4   4  16   24   24   8 |  1   8   6    8   12    8   2 |   2    4    4    0    2 | 768    *    *    * |    4    0 |   4  0 tower: A-C-B
oox3xoo ... ... oox3oxo ... ...&#xt &   6  9 |   6  36  18 |  2   0  18   18   36   6 |  0   6   9    0   18   12   0 |   0    6    0    6    0 |   * 1024    *    * |    4    0 |   4  0 tower: A-C-B
... x.o3o.o ... o.x3o.o ... ...&#x  &   3  3 |   3   9   3 |  0   1   0    9    9   1 |  0   0   0    3    9    3   0 |   0    0    3    3    0 |   *    * 4096    * |    1    2 |   2  1
... x.o ... ... o.x3o.o3o.o ...&#x  &   2  4 |   1   8   6 |  0   0   0    4   12   4 |  0   0   0    0    6    8   1 |   0    0    0    4    2 |   *    *    * 3072 |    1    2 |   2  1
--------------------------------------+-------+-------------+--------------------------+-------------------------------+-------------------------+--------------------+-----------+-------
oox3xoo3ooo ... oox3oxo ... ...&#xt &   9 12 |  15  60  30 |  5   4  30   48   72  16 |  1  16  18   12   54   36   3 |   3   18   12   24    6 |   3    4    4    3 | 1024    * |   2  0 tower: A-C-B
... x.o3o.o ... o.x3o.o3o.o ...&#x  &   3  4 |   3  12   6 |  0   1   0   12   18   4 |  0   0   0    4   18   12   1 |   0    0    6   12    3 |   0    0    4    3 |    * 2048 |   1  1
--------------------------------------+-------+-------------+--------------------------+-------------------------------+-------------------------+--------------------+-----------+-------
oox3xoo3ooo ... oox3oxo3ooo ...&#xt    12 16 |  24  96  48 |  8   8  48   96  144  32 |  2  32  36   32  144   96   8 |   8   48   48   96   24 |  12   16   32   24 |    8    8 | 256  *
... x.o3o.o4o.o o.x3o.o3o.o4o.o&#zx &   6  8 |  12  48  24 |  0   8   0   96  144  32 |  0   0   0   64  288  192  16 |   0    0  192  384   96 |   0    0  256  192 |    0  128 |   * 16

oox3xoo3ooo *b3ooo oox3oxo3ooo *f3ooo&#zx   → heights = 0
(tegum sum of 2 perp icoes and a hexdip)

o..3o..3o..    o.. o..3o..3o..    o..     & | 48  *    8  16   0 |  4  4  4   8   64   48   0 |  2  2  32  24  32  32  192   64   0   0 |  16  16  128   96   96  256  16  16 |  56  56  128  128  128   64   64 |  96  96  32  32  32  32 | 16  32 16  2
..o3..o3..o    ..o ..o3..o3..o    ..o       |  * 64    0  12  12 |  0  0  0  12   24   72  24 |  0  0  24  36   8   8  144  144   8   8 |   8   8  144   48   48  288  48  48 |  48  48  144   96   96   96   96 |  96  96  32  32  32  32 | 16  32 16  2
--------------------------------------------+-------+-------------+----------------------------+-----------------------------------------+-------------------------------------+----------------------------------+-------------------------+-------------
... x.. ...    ... ... ... ...    ...     & |  2  0 | 192   *   * |  1  1  1   0    8    0   0 |  1  1   8   0   8   8   24    0   0   0 |   8   8   24   24   24   32   0   0 |  24  24   32   32   32    8    8 |  40  40   8   8   8   8 |  8  16  8  1
o.o3o.o3o.o *b3o.o o.o3o.o3o.o *f3o.o&#x  & |  1  1 |   * 768   * |  0  0  0   1    4    6   0 |  0  0   4   6   2   2   24   12   0   0 |   2   2   36   12   12   48   4   4 |  16  16   48   24   24   16   16 |  40  40   8   8   8   8 |  8  16  8  1
..x ... ...    ... ... ... ...    ...     & |  0  2 |   *   * 384 |  0  0  0   1    0    6   4 |  0  0   4   6   0   0   12   24   2   2 |   2   2   36    4    4   48  12  12 |  16  16   48   16   16   24   24 |  40  40   8   8   8   8 |  8  16  8  1
--------------------------------------------+-------+-------------+----------------------------+-----------------------------------------+-------------------------------------+----------------------------------+-------------------------+-------------
o..3x.. ...    ... ... ... ...    ...     & |  3  0 |   3   0   0 | 64  *  *   *    *    *   *   1  1   8   0   0   0    0    0   0   0 |   8   8   24    0    0    0   0   0 |  24  24   32    0    0    0    0 |  40  40   0   0   0   0 |  8  16  8  0
... x..3o..    ... ... ... ...    ...     & |  3  0 |   3   0   0 |  * 64  *   *    *    *   * |  1  0   0   0   8   0    0    0   0   0 |   8   0    0   24    0    0   0   0 |  24   0    0   32    0    0    0 |  32   0   8   8   0   0 |  8   8  0  1
... x.. ... *b3o.. ... ... ...    ...     & |  3  0 |   3   0   0 |  *  * 64   *    *    *   * |  0  1   0   0   0   8    0    0   0   0 |   0   8    0    0   24    0   0   0 |   0  24    0    0   32    0    0 |   0  32   0   0   8   8 |  0   8  8  1
o.x ... ...    ... ... ... ...    ...&#x  & |  1  2 |   0   2   1 |  *  *  * 384    *    *   *   0  0   4   6   0   0    0    0   0   0 |   2   2   36    0    0    0   0   0 |  16  16   48    0    0    0    0 |  40  40   0   0   0   0 |  8  16  8  0
... x.o ...    ... ... ... ...    ...&#x  & |  2  1 |   1   2   0 |  *  *  *   * 1536    *   * |  0  0   1   0   1   1    6    0   0   0 |   1   1    6    6    6   12   0   0 |   6   6   12   12   12    4    4 |  16  16   4   4   4   4 |  4   8  4  1
... ... ...    ... o.x ... ...    ...&#x  & |  1  2 |   0   2   1 |  *  *  *   *    * 2304   * |  0  0   0   1   0   0    4    4   0   0 |   0   0    8    2    2   16   2   2 |   4   4   16    8    8    8    8 |  16  16   4   4   4   4 |  4   8  4  1
..x3..o ...    ... ... ... ...    ...     & |  0  3 |   0   0   3 |  *  *  *   *    *    * 512 |  0  0   1   0   0   0    0    6   1   1 |   1   1    6    0    0   12   6   6 |   6   6   12    4    4   12   12 |  16  16   4   4   4   4 |  4   8  4  1
--------------------------------------------+-------+-------------+----------------------------+-----------------------------------------+-------------------------------------+----------------------------------+-------------------------+-------------
o..3x..3o..    ... ... ... ...    ...     &   6  0 |  12   0   0 |  4  4  0   0    0    0   0 | 16  *   *   *   *   *    *    *   *   *    8   0    0    0    0    0   0   0 |  24   0    0    0    0    0    0 |  32   0   0   0   0   0 |  8   8  0  0
o..3x.. ... *b3o.. ... ... ...    ...     &   6  0 |  12   0   0 |  4  0  4   0    0    0   0 |  * 16   *   *   *   *    *    *   *   *    0   8    0    0    0    0   0   0 |   0  24    0    0    0    0    0 |   0  32   0   0   0   0 |  0   8  8  0
o.x3x.o ...    ... ... ... ...    ...&#x  &   3  3 |   3   6   3 |  1  0  0   3    3    0   1 |  *  * 512   *   *   *    *    *   *   *    1   1    6    0    0    0   0   0 |   6   6   12    0    0    0    0 |  16  16   0   0   0   0 |  4   8  4  0
oox ... ...    ... oox ... ...    ...&#xt     2  4 |   0   8   4 |  0  0  0   4    0    4   0 |  *  *   * 576   *   *    *    *   *   *    0   0    8    0    0    0   0   0 |   4   4   16    0    0    0    0 |  16  16   0   0   0   0 |  4   8  4  0 tower: A-C-B
... x.o3o.o    ... ... ... ...    ...&#x  &   3  1 |   3   3   0 |  0  1  0   0    3    0   0 |  *  *   *   * 512   *    *    *   *   * |   1   0    0    6    0    0   0   0 |   6   0    0   12    0    0    0 |  12   0   4   4   0   0 |  4   4  0  1
... x.o ... *b3o.o ... ... ...    ...&#x  &   3  1 |   3   3   0 |  0  0  1   0    3    0   0 |  *  *   *   *   * 512    *    *   *   * |   0   1    0    0    6    0   0   0 |   0   6    0    0   12    0    0 |   0  12   0   0   4   4 |  0   4  4  1
... x.o ...    ... o.x ... ...    ...&#x  &   2  2 |   1   4   1 |  0  0  0   0    2    2   0 |  *  *   *   *   *   * 4608    *   *   * |   0   0    1    1    1    4   0   0 |   1   1    4    4    4    2    2 |   6   6   2   2   2   2 |  2   4  2  1
... ... ...    ... o.x3o.o ...    ...     &   1  3 |   0   3   3 |  0  0  0   0    0    3   1 |  *  *   *   *   *   *    * 3072   *   * |   0   0    1    0    0    4   1   1 |   1   1    4    2    2    4    4 |   6   6   2   2   2   2 |  2   4  2  1
..x3..o3..o    ... ... ... ...    ...     &   0  4 |   0   0   6 |  0  0  0   0    0    0   4 |  *  *   *   *   *   *    *    * 128   * |   1   0    0    0    0    0   6   0 |   6   0    0    0    0   12    0 |  12   0   4   0   4   0 |  4   4  0  1
..x3..o ... *b3..o ... ... ...    ...     &   0  4 |   0   0   6 |  0  0  0   0    0    0   4 |  *  *   *   *   *   *    *    *   * 128 |   0   1    0    0    0    0   0   6 |   0   6    0    0    0    0   12 |   0  12   0   4   0   4 |  0   4  4  1
--------------------------------------------+-------+-------------+----------------------------+-----------------------------------------+-------------------------------------+----------------------------------+-------------------------+-------------
o.x3x.o3o.o    ... ... ... ...    ...&#x  &   6  4 |  12  12   6 |  4  4  0   6   12    0   4 |  1  0   4   0   4   0    0    0   1   0 | 128   *    *    *    *    *   *   *    6   0    0    0    0    0    0 |  12   0   0   0   0   0 |  4   4  0  0
o.x3x.o ... *b3o.o ... ... ...    ...&#x  &   6  4 |  12  12   6 |  4  0  4   6   12    0   4 |  0  1   4   0   0   4    0    0   0   1 |   * 128    *    *    *    *   *   *    0   6    0    0    0    0    0 |   0  12   0   0   0   0 |  0   4  4  0
oox3xoo ...    ... oox ... ...    ...&#xt &   4  6 |   3  18   9 |  1  0  0   9    6   12   2 |  0  0   2   3   0   0    3    2   0   0 |   *   * 1536    *    *    *   *   *    1   1    4    0    0    0    0 |   6   6   0   0   0   0 |  2   4  2  0
... x.o3o.o    ... o.x ... ...    ...&#x  &   3  2 |   3   6   1 |  0  1  0   0    6    3   0 |  0  0   0   0   2   0    3    0   0   0 |   *   *    * 1536    *    *   *   * |   1   0    0    4    0    0    0 |   4   0   2   2   0   0 |  2   2  0  1
... x.o ... *b3o.o o.x ... ...    ...&#x  &   3  2 |   3   6   1 |  0  0  1   0    6    3   0 |  0  0   0   0   0   2    3    0   0   0 |   *   *    *    * 1536    *   *   * |   0   1    0    0    4    0    0 |   0   4   0   0   2   2 |  0   2  2  1
... x.o ...    ... o.x3o.o ...    ...&#x  &   2  3 |   1   6   3 |  0  0  0   0    3    6   1 |  0  0   0   0   0   0    3    2   0   0 |   *   *    *    *    * 6144   *   * |   0   0    1    1    1    1    1 |   2   2   1   1   1   1 |  1   2  1  1
... ... ...    ... o.x3o.o3o.o    ...&#x  &   1  4 |   0   4   6 |  0  0  0   0    0    6   4 |  0  0   0   0   0   0    0    4   1   0 |   *   *    *    *    *    * 768   * |   1   0    0    0    0    4    0 |   4   0   2   0   2   0 |  2   2  0  1
... ... ...    ... o.x3o.o ... *f3o.o&#x  &   1  4 |   0   4   6 |  0  0  0   0    0    6   4 |  0  0   0   0   0   0    0    4   0   1 |   *   *    *    *    *    *   * 768 |   0   1    0    0    0    0    4 |   0   4   0   2   0   2 |  0   2  2  1
--------------------------------------------+-------+-------------+----------------------------+-----------------------------------------+-------------------------------------+----------------------------------+-------------------------+-------------
oox3xoo3ooo    ... oox ... ...    ...&#xt &   7  8 |  12  32  16 |  4  4  0  16   24   24   8 |  1  0   8   6   8   0   12    8   2   0 |   2   0    4    4    0    0   2   0 | 384   *    *    *    *    *    * |   4   0   0   0   0   0 |  2   2  0  0 tower: A-C-B
oox3xoo ... *b3ooo oox ... ...    ...&#xt &   7  8 |  12  32  16 |  4  0  4  16   24   24   8 |  0  1   8   6   0   8   12    8   0   2 |   0   2    4    0    4    0   0   2 |   * 384    *    *    *    *    * |   0   4   0   0   0   0 |  0   2  2  0 tower: A-C-B
oox3xoo ...    ... oox3oxo ...    ...&#xt &   6  9 |   6  36  18 |  2  0  0  18   18   36   6 |  0  0   6   9   0   0   18   12   0   0 |   0   0    6    0    0    6   0   0 |   *   * 1024    *    *    *    * |   2   2   0   0   0   0 |  1   2  1  0 tower: A-C-B
... x.o3o.o    ... o.x3o.o ...    ...&#x  &   3  3 |   3   9   3 |  0  1  0   0    9    9   1 |  0  0   0   0   3   0    9    3   0   0 |   0   0    0    3    0    3   0   0 |   *   *    * 2048    *    *    * |   1   0   1   1   0   0 |  1   1  0  1
... x.o ... *b3o.o o.x3o.o ...    ...&#x  &   3  3 |   3   9   3 |  0  0  1   0    9    9   1 |  0  0   0   0   0   3    9    3   0   0 |   0   0    0    0    3    3   0   0 |   *   *    *    * 2048    *    * |   0   1   0   0   1   1 |  0   1  1  1
... x.o ...    ... o.x3o.o3o.o    ...&#x  &   2  4 |   1   8   6 |  0  0  0   0    4   12   4 |  0  0   0   0   0   0    6    8   1   0 |   0   0    0    0    0    4   2   0 |   *   *    *    *    * 1536    * |   1   0   1   0   1   0 |  1   1  0  1
... x.o ...    ... o.x3o.o ... *f3o.o&#x  &   2  4 |   1   8   6 |  0  0  0   0    4   12   4 |  0  0   0   0   0   0    6    8   0   1 |   0   0    0    0    0    4   0   2 |   *   *    *    *    *    * 1536 |   0   1   0   1   0   1 |  0   1  1  1
--------------------------------------------+-------+-------------+----------------------------+-----------------------------------------+-------------------------------------+----------------------------------+-------------------------+-------------
oox3xoo3ooo    ... oox3oxo ...    ...&#xt &   9 12 |  15  60  30 |  5  4  0  30   48   72  16 |  1  0  16  18  12   0   54   36   3   0 |   3   0   18   12    0   24   6   0 |   3   0    4    4    0    3    0 | 512   *   *   *   *   * |  1   1  0  0 tower: A-C-B
oox3xoo ... *b3ooo oox3oxo ...    ...&#xt &   9 12 |  15  60  30 |  5  0  4  30   48   72  16 |  0  1  16  18   0  12   54   36   0   3 |   0   3   18    0   12   24   0   6 |   0   3    4    0    4    0    3 |   * 512   *   *   *   * |  0   1  1  0 tower: A-C-B
... x.o3o.o    ... o.x3o.o3o.o    ...&#x  &   3  4 |   3  12   6 |  0  1  0   0   12   18   4 |  0  0   0   0   4   0   18   12   1   0 |   0   0    0    6    0   12   3   0 |   0   0    0    4    0    3    0 |   *   * 512   *   *   * |  1   0  0  1
... x.o3o.o    ... o.x3o.o ... *f3o.o&#x  &   3  4 |   3  12   6 |  0  1  0   0   12   18   4 |  0  0   0   0   4   0   18   12   0   1 |   0   0    0    6    0   12   0   3 |   0   0    0    4    0    0    3 |   *   *   * 512   *   * |  0   1  0  1
... x.o ... *b3o.o o.x3o.o3o.o    ...&#x  &   3  4 |   3  12   6 |  0  0  1   0   12   18   4 |  0  0   0   0   0   4   18   12   1   0 |   0   0    0    0    6   12   3   0 |   0   0    0    0    4    3    0 |   *   *   *   * 512   * |  0   1  0  1
... x.o ... *b3o.o o.x3o.o ... *f3o.o&#x  &   3  4 |   3  12   6 |  0  0  1   0   12   18   4 |  0  0   0   0   0   4   18   12   0   1 |   0   0    0    0    6   12   0   3 |   0   0    0    0    4    0    3 |   *   *   *   *   * 512 |  0   0  1  1
--------------------------------------------+-------+-------------+----------------------------+-----------------------------------------+-------------------------------------+----------------------------------+-------------------------+-------------
oox3xoo3ooo    ... oox3oxo3ooo    ...&#xt    12 16 |  24  96  48 |  8  8  0  48   96  144  32 |  2  0  32  36  32   0  144   96   8   0 |   8   0   48   48    0   96  24   0 |  12   0   16   32    0   24    0 |   8   0   8   0   0   0 | 64   *  *  *
oox3xoo3ooo    ... oox3oxo ... *f3ooo&#xt &  12 16 |  24  96  48 |  8  4  4  48   96  144  32 |  1  1  32  36  16  16  144   96   4   4 |   4   4   48   24   24   96  12  12 |   6   6   16   16   16   12   12 |   4   4   0   4   4   0 |  * 128  *  *
oox3xoo ... *b3ooo oox3oxo ... *f3ooo&#xt    12 16 |  24  96  48 |  8  0  8  48   96  144  32 |  0  2  32  36   0  32  144   96   0   8 |   0   8   48    0   48   96   0  24 |   0  12   16    0   32    0   24 |   0   8   0   0   0   8 |  *   * 64  *
... x.o3o.o *b3o.o o.x3o.o3o.o *f3o.o&#zx &   6  8 |  12  48  24 |  0  4  4   0   96  144  32 |  0  0   0   0  32  32  288  192   0  16 |   0   0    0   96   96  384  48  48 |   0   0    0  128  128   96   96 |   0   0  32  32  32  32 |  *   *  * 16

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