Acronym hesa (old: hiss)
Name hemihepteract,
vertex figure of bay,
Gosset polytope 14,1
Circumradius sqrt(7/8) = 0.935414
Lace city
in approx. ASCII-art
 ©  
H   h	where:
     	H = x3o3o *b3o3o (hin)
h   H	h = o3o3x *b3o3o (alt. hin)
     
|   |
|   +-	o3o3x *b3o3o3o (hax)
+-----	x3o3o *b3o3o3o (alt. hax)
o   R   r   o	 -- o3o3x *b3o3o3o (hax)
             
  H   D   h  	 -- x3o3o *b3o3o3o (alt. hax)
             
    \   \   \   \
     \   \   \   +- o3o3o3o3o3o (point)
      \   \   +---- o3x3o3o3o3o (ril)
       \   +------- o3o3o3x3o3o (inv. bril)
        +---------- o3o3o3o3o3x (dual hop)
        
where:
o = o3o3o3o3o (point)
H = x3o3o3o3o (hix)
R = o3x3o3o3o (rix)
D = o3o3x3o3o (dot)
r = o3o3o3x3o (inv. rix)
h = o3o3o3o3x (dual hix)
Lace hyper city
in approx. ASCII-art
  _E---------_O
O----------E  |
|  |       |  |
|  |       |  |
|  |       |  |
| _O-------|-_E
E----------O   

where:
E = x3o3o *b3o (hex)
O = o3o3x *b3o (gyro hex)
Coordinates (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all even permutations, all even changes of sign
Confer
uniform relative:
tethex  
related segmentoexa:
rilpy   rilalbril   hopabril   hexal trahex  
general polytopal classes:
segmentoexa   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

x3o3o *b3o3o3o3o

. . .    . . . . | 64   21 |  105 |  35  140 |  35  105 | 21  42 |  7  7
-----------------+----+-----+------+----------+----------+--------+------
x . .    . . . . |  2 | 672    10 |   5   20 |  10   20 | 10  10 |  5  2
-----------------+----+-----+------+----------+----------+--------+------
x3o .    . . . . |  3 |   3 | 2240 |   1    4 |   4    6 |  6   4 |  4  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o    . . . .   4 |   6 |    4 | 560    *    4    0 |  6   0 |  4  0
x3o . *b3o . . .   4 |   6 |    4 |   * 2240 |   1    3 |  3   3 |  3  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o . . .   8 |  24 |   32 |   8    8 | 280    * |  3   0 |  3  0
x3o . *b3o3o . .   5 |  10 |   10 |   0    5 |   * 1344 |  1   2 |  2  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o3o . .  16 |  80 |  160 |  40   80 |  10   16 | 84   * |  2  0
x3o . *b3o3o3o .   6 |  15 |   20 |   0   15 |   0    6 |  * 448 |  1  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o3o3o .  32 | 240 |  640 | 160  480 |  60  192 | 12  32 | 14  *
x3o . *b3o3o3o3o   7 |  21 |   35 |   0   35 |   0   21 |  0   7 |  * 64

o3o3o3o3o3o4s

demi( . . . . . . . ) | 64   21 |  105 |  35  140 |  35  105 | 21  42 |  7  7
----------------------+----+-----+------+----------+----------+--------+------
      . . . . . o4s   |  2 | 672    10 |   5   20 |  10   20 | 10  10 |  5  2
----------------------+----+-----+------+----------+----------+--------+------
sefa( . . . . o3o4s ) |  3 |   3 | 2240 |   1    4 |   4    6 |  6   4 |  4  1
----------------------+----+-----+------+----------+----------+--------+------
      . . . . o3o4s     4 |   6 |    4 | 560    *    4    0 |  6   0 |  4  0
sefa( . . . o3o3o4s )   4 |   6 |    4 |   * 2240 |   1    3 |  3   3 |  3  1
----------------------+----+-----+------+----------+----------+--------+------
      . . . o3o3o4s     8 |  24 |   32 |   8    8 | 280    * |  3   0 |  3  0
sefa( . . o3o3o3o4s )   5 |  10 |   10 |   0    5 |   * 1344 |  1   2 |  2  1
----------------------+----+-----+------+----------+----------+--------+------
      . . o3o3o3o4s    16 |  80 |  160 |  40   80 |  10   16 | 84   * |  2  0
sefa( . o3o3o3o3o4s )   6 |  15 |   20 |   0   15 |   0    6 |  * 448 |  1  1
----------------------+----+-----+------+----------+----------+--------+------
      . o3o3o3o3o4s    32 | 240 |  640 | 160  480 |  60  192 | 12  32 | 14  *
sefa( o3o3o3o3o3o4s )   7 |  21 |   35 |   0   35 |   0   21 |  0   7 |  * 64

starting figure: o3o3o3o3o3o4x

xo3oo3ox *b3oo3oo3oo&#x   → height = 1/sqrt(2) = 0.707107
(hax || alt hax)

o.3o.3o. *b3o.3o.3o.    | 32  *   15   6   0 |  60  30  15   0 |  20  60  60  15  20   0   0 | 15  30  20  60  15  0   0 |  6  6 15  30   6  0  0 | 1  6  6  1 0
.o3.o3.o *b3.o3.o3.o    |  * 32    0   6  15 |   0  15  30  60 |   0   0  20  15  60  20  60 |  0   0  20  15  60 15  30 |  0  0 15   6  30  6  6 | 0  6  1  6 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x. .. ..    .. .. ..    |  2  0 | 240   *   *    8   2   0   0 |   4  12   8   1   0   0   0 |  6   8   4  12   0  0   0 |  4  2  6   8   0  0  0 | 1  4  2  0 0
oo3oo3oo *b3oo3oo3oo&#x |  1  1 |   * 192   *    0   5   5   0 |   0   0  10   5  10   0   0 |  0   0  10  10  10  0   0 |  0  0 10   5   5  0  0 | 0  5  1  1 0
.. .. .x    .. .. ..    |  0  2 |   *   * 240    0   0   2   8 |   0   0   0   1   8   4  12 |  0   0   4   0  12  6   8 |  0  0  6   0   8  4  2 | 0  4  0  2 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o. ..    .. .. ..    |  3  0 |   3   0   0 | 640   *   *   * |   1   3   1   0   0   0   0 |  3   3   1   3   0  0   0 |  3  1  3   3   0  0  0 | 1  3  1  0 0
xo .. ..    .. .. ..&#x |  2  1 |   1   2   0 |   * 480   *   * |   0   0   4   1   0   0   0 |  0   0   4   6   0  0   0 |  0  0  6   4   0  0  0 | 0  4  1  0 0
.. .. ox    .. .. ..&#x |  1  2 |   0   2   1 |   *   * 480   * |   0   0   0   1   4   0   0 |  0   0   4   0   6  0   0 |  0  0  6   0   4  0  0 | 0  4  0  1 0
.. .o3.x    .. .. ..    |  0  3 |   0   0   3 |   *   *   * 640 |   0   0   0   0   1   1   3 |  0   0   1   0   3  3   3 |  0  0  3   0   3  3  1 | 0  3  0  1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o.    .. .. ..      4  0 |   6   0   0 |   4   0   0   0 | 160   *   *   *   *   *   *   3   0   1   0   0  0   0 |  3  0  3   0   0  0  0 | 1  3  0  0 0
x.3o. .. *b3o. .. ..      4  0 |   6   0   0 |   4   0   0   0 |   * 480   *   *   *   *   * |  1   2   0   1   0  0   0 |  2  1  1   2   0  0  0 | 1  2  1  0 0
xo3oo ..    .. .. ..&#x   3  1 |   3   3   0 |   1   3   0   0 |   *   * 640   *   *   *   * |  0   0   1   3   0  0   0 |  0  0  3   3   0  0  0 | 0  3  1  0 0
xo .. ox    .. .. ..&#x   2  2 |   1   4   1 |   0   2   2   0 |   *   *   * 240   *   *   *   0   0   4   0   0  0   0 |  0  0  6   0   0  0  0 | 0  4  0  0 0
.. oo3ox    .. .. ..&#x   1  3 |   0   3   3 |   0   0   3   1 |   *   *   *   * 640   *   * |  0   0   1   0   3  0   0 |  0  0  3   0   3  0  0 | 0  3  0  1 0
.o3.o3.x    .. .. ..      0  4 |   0   0   6 |   0   0   0   4 |   *   *   *   *   * 160   *   0   0   1   0   0  3   0 |  0  0  3   0   0  3  0 | 0  3  0  0 1
.. .o3.x *b3.o .. ..      0  4 |   0   0   6 |   0   0   0   4 |   *   *   *   *   *   * 480 |  0   0   0   0   1  1   2 |  0  0  1   0   2  2  1 | 0  2  0  1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o. *b3o. .. ..      8  0 |  24   0   0 |  32   0   0   0 |   8   8   0   0   0   0   0 | 60   *   *   *   *  *   * |  2  0  1   0   0  0  0 | 1  2  0  0 0
x.3o. .. *b3o.3o. ..      5  0 |  10   0   0 |  10   0   0   0 |   0   5   0   0   0   0   0 |  * 192   *   *   *  *   * |  1  1  0   1   0  0  0 | 1  1  1  0 0
xo3oo3ox    .. .. ..&#x   4  4 |   6  12   6 |   4  12  12   4 |   1   0   4   6   4   1   0 |  *   * 160   *   *  *   * |  0  0  3   0   0  0  0 | 0  3  0  0 0
xo3oo .. *b3oo .. ..&#x   4  1 |   6   4   0 |   4   6   0   0 |   0   1   4   0   0   0   0 |  *   *   * 480   *  *   * |  0  0  1   2   0  0  0 | 0  2  1  0 0
.. oo3ox *b3oo .. ..&#x   1  4 |   0   4   6 |   0   0   6   4 |   0   0   0   0   4   0   1 |  *   *   *   * 480  *   * |  0  0  1   0   2  0  0 | 0  2  0  1 0
.o3.o3.x *b3.o .. ..      0  8 |   0   0  24 |   0   0   0  32 |   0   0   0   0   0   8   8 |  *   *   *   *   * 60   * |  0  0  1   0   0  2  0 | 0  2  0  0 1
.. .o3.x *b3.o3.o ..      0  5 |   0   0  10 |   0   0   0  10 |   0   0   0   0   0   0   5 |  *   *   *   *   *  * 192 |  0  0  0   0   1  1  1 | 0  1  0  1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o. *b3o.3o. ..     16  0 |  80   0   0 | 160   0   0   0 |  40  80   0   0   0   0   0 | 10  16   0   0   0  0   0 | 12  *  *   *   *  *  * | 1  1  0  0 0
x.3o. .. *b3o.3o.3o.      6  0 |  15   0   0 |  20   0   0   0 |   0  15   0   0   0   0   0 |  0   6   0   0   0  0   0 |  * 32  *   *   *  *  * | 1  0  1  0 0
xo3oo3ox *b3oo .. ..&#x   8  8 |  24  32  24 |  32  48  48  32 |   8   8  32  24  32   8   8 |  1   0   8   8   8  1   0 |  *  * 60   *   *  *  * | 0  2  0  0 0
xo3oo .. *b3oo3oo ..&#x   5  1 |  10   5   0 |  10  10   0   0 |   0   5  10   0   0   0   0 |  0   1   0   5   0  0   0 |  *  *  * 192   *  *  * | 0  1  1  0 0
.. oo3ox *b3oo3oo ..&#x   1  5 |   0   5  10 |   0   0  10  10 |   0   0   0   0  10   0   5 |  0   0   0   0   5  0   1 |  *  *  *   * 192  *  * | 0  1  0  1 0
.o3.o3.x *b3.o3.o ..      0 16 |   0   0  80 |   0   0   0 160 |   0   0   0   0   0  40  80 |  0   0   0   0   0 10  16 |  *  *  *   *   * 12  * | 0  1  0  0 1
.. .o3.x *b3.o3.o3.o      0  6 |   0   0  15 |   0   0   0  20 |   0   0   0   0   0   0  15 |  0   0   0   0   0  0   6 |  *  *  *   *   *  * 32 | 0  0  0  1 1
------------------------+-------+-------------+-----------------+-----------------------------+---------------------------+------------------------+-------------
x.3o.3o. *b3o.3o.3o.     32  0 | 240   0   0 | 640   0   0   0 | 160 480   0   0   0   0   0 | 60 192   0   0   0  0   0 | 12 32  0   0   0  0  0 | 1  *  *  * *
xo3oo3ox *b3oo3oo ..&#x  16 16 |  80  80  80 | 160 160 160 160 |  40  80 160  80 160  40  80 | 10  16  40  80  80 10  16 |  1  0 10  16  16  1  0 | * 12  *  * *
xo3oo .. *b3oo3oo3oo&#x   6  1 |  15   6   0 |  20  15   0   0 |   0  15  20   0   0   0   0 |  0   6   0  15   0  0   0 |  0  1  0   6   0  0  0 | *  * 32  * *
.. oo3ox *b3oo3oo3oo&#x   1  6 |   0   6  15 |   0   0  15  20 |   0   0   0   0  20   0  15 |  0   0   0   0  15  0   6 |  0  0  0   0   6  0  1 | *  *  * 32 *
.o3.o3.x *b3.o3.o3.o      0 32 |   0   0 240 |   0   0   0 640 |   0   0   0   0   0 160 480 |  0   0   0   0   0 60 192 |  0  0  0   0   0 12 32 | *  *  *  * 1

oooo3oxoo3oooo3ooxo3oooo3ooox&#xt   → all heights = sqrt(2/7) = 0.534522
(pt || (pseudo) ril || (pseudo) inv bril || dual hop)

o...3o...3o...3o...3o...3o...     | 1  *  * *  21   0   0   0   0  0 | 105  0   0   0   0   0   0   0   0  0 | 35 140   0   0   0   0   0   0   0  0   0   0   0  0  0 | 35 105  0   0   0   0   0   0  0   0   0  0  0 | 21 42 0   0  0   0  0  0   0 0 | 7 7  0 0  0 0
.o..3.o..3.o..3.o..3.o..3.o..     | * 21  * *   1  10  10   0   0  0 |  10  5  20  40  30   0   0   0   0  0 |  5  20  20  20  20  60  10  20   0  0   0   0   0  0  0 | 10  20 10  30  20  40   5   5  0   0   0  0  0 | 10 10 2  20 10  10  1  0   0 0 | 5 2  5 2  0 0
..o.3..o.3..o.3..o.3..o.3..o.     | *  * 35 *   0   0   6  12   3  0 |   0  0   0  12  36  18  12  24   3  0 |  0   0   0   4   4  36  18  36  12  4  36  12  12  1  0 |  1   0  0  12  12  36  18  12  3  24  18  4  0 |  3  0 0  12 12  12  6  6  12 0 | 3 0  4 4  3 0
...o3...o3...o3...o3...o3...o     | *  *  * 7   0   0   0   0  15  6 |   0  0   0   0   0   0   0  60  30 15 |  0   0   0   0   0   0   0   0   0  0  60  20  60 15 20 |  0   0  0   0   0   0  15   0  0  30  60 20 25 |  0  0 0   0  6   0 15  6  30 6 | 1 0  0 6  6 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
oo..3oo..3oo..3oo..3oo..3oo..&#x  | 1  1  0 0 | 21   *   *   *   *  *   10  0   0   0   0   0   0   0   0  0 |  5  20   0   0   0   0   0   0   0  0   0   0   0  0  0 | 10  20  0   0   0   0   0   0  0   0   0  0  0 | 10 10 0   0  0   0  0  0   0 0 | 5 2  0 0  0 0
.... .x.. .... .... .... ....     | 0  2  0 0 |  * 105   *   *   *  *    1  1   4   4   0   0   0   0   0  0 |  1   4   6   4   4   6   0   0   0  0   0   0   0  0  0 |  4   6  4   6   6   4   0   0  0   0   0  0  0 |  6  4 1   4  4   1  0  0   0 0 | 4 1  1 1  0 0
.oo.3.oo.3.oo.3.oo.3.oo.3.oo.&#x  | 0  1  1 0 |  *   * 210   *   *  *    0  0   0   4   6   0   0   0   0  0 |  0   0   0   2   2  12   3   6   0  0   0   0   0  0  0 |  1   0  0   6   6  12   3   2  0   0   0  0  0 |  3  0 0   6  6   4  1  0   0 0 | 3 0  2 2  0 0
.... .... .... ..x. .... ....     | 0  0  2 0 |  *   *   * 210   *  *    0  0   0   0   3   3   2   2   0  0 |  0   0   0   0   0   3   3   6   3  1   6   2   1  0  0 |  0   0  0   1   3   6   6   3  1   6   3  1  0 |  1  0 0   2  6   3  3  2   3 0 | 2 0  1 3  1 0
..oo3..oo3..oo3..oo3..oo3..oo&#x  | 0  0  1 1 |  *   *   *   * 105  *    0  0   0   0   0   0   0   8   2  0 |  0   0   0   0   0   0   0   0   0  0  12   4   8  1  0 |  0   0  0   0   0   0   6   0  0   8  12  4  0 |  0  0 0   0  4   0  6  2   8 0 | 1 0  0 4  2 0
.... .... .... .... .... ...x     | 0  0  0 2 |  *   *   *   *   * 21    0  0   0   0   0   0   0   0   5  5 |  0   0   0   0   0   0   0   0   0  0   0   0  10  5 10 |  0   0  0   0   0   0   0   0  0   0  10 10 10 |  0  0 0   0  0   0 10  0   5 5 | 0 0  0 5  1 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
.... ox.. .... .... .... ....&#x  | 1  2  0 0 |  2   1   0   0   0  0 | 105  *   *   *   *   *   *   *   *  * |  1   4   0   0   0   0   0   0   0  0   0   0   0  0  0 |  4   6  0   0   0   0   0   0  0   0   0  0  0 |  6  4 0   0  0   0  0  0   0 0 | 4 1  0 0  0 0
.o..3.x.. .... .... .... ....     | 0  3  0 0 |  0   3   0   0   0  0 |   * 35   *   *   *   *   *   *   *  * |  1   0   0   4   0   0   0   0   0  0   0   0   0  0  0 |  4   0  0   6   0   0   0   0  0   0   0  0  0 |  6  0 0   4  0   0  0  0   0 0 | 4 0  1 0  0 0
.... .x..3.o.. .... .... ....     | 0  3  0 0 |  0   3   0   0   0  0 |   *  * 140   *   *   *   *   *   *  * |  0   1   3   0   1   0   0   0   0  0   0   0   0  0  0 |  1   3  3   0   3   0   0   0  0   0   0  0  0 |  3  3 1   0  3   0  0  0   0 0 | 3 1  0 1  0 0
.... .xo. .... .... .... ....&#x  | 0  2  1 0 |  0   1   2   0   0  0 |   *  *   * 420   *   *   *   *   *  * |  0   0   0   1   1   3   0   0   0  0   0   0   0  0  0 |  1   0  0   3   3   3   0   0  0   0   0  0  0 |  3  0 0   3  3   1  0  0   0 0 | 3 0  1 1  0 0
.... .... .... .ox. .... ....&#x  | 0  1  2 0 |  0   0   2   1   0  0 |   *  *   *   * 630   *   *   *   *  * |  0   0   0   0   0   2   1   2   0  0   0   0   0  0  0 |  0   0  0   1   2   1   2   1  0   0   0  0  0 |  1  0 0   2  4   2  1  0   0 0 | 2 0  1 2  0 0
.... .... ..o.3..x. .... ....     | 0  0  3 0 |  0   0   0   3   0  0 |   *  *   *   *   * 210   *   *   *  * |  0   0   0   0   0   0   1   0   2  0   2   0   0  0  0 |  0   0  0   0   2   0   2   0  1   4   1  0  0 |  1  0 0   0  4   0  1  2   2 0 | 2 0  0 2  1 0
.... .... .... ..x.3..o. ....     | 0  0  3 0 |  0   0   0   3   0  0 |   *  *   *   *   *   * 140   *   *  * |  0   0   0   0   0   0   0   3   0  1   0   1   0  0  0 |  0   0  0   0   0   3   3   3  0   0   0  1  0 |  0  0 0   1  3   3  3  0   0 0 | 1 0  1 3  0 0
.... .... .... ..xo .... ....&#x  | 0  0  2 1 |  0   0   0   1   2  0 |   *  *   *   *   *   *   * 420   *  * |  0   0   0   0   0   0   0   0   0  0   3   1   1  0  0 |  0   0  0   0   0   0   3   0  0   3   3  1  0 |  0  0 0   0  3   0  3  1   3 0 | 1 0  0 3  1 0
.... .... .... .... .... ..ox&#x  | 0  0  1 2 |  0   0   0   0   2  1 |   *  *   *   *   *   *   *   * 105  * |  0   0   0   0   0   0   0   0   0  0   0   0   4  1  0 |  0   0  0   0   0   0   0   0  0   0   6  4  0 |  0  0 0   0  0   0  6  0   4 0 | 0 0  0 4  1 0
.... .... .... .... ...o3...x     | 0  0  0 3 |  0   0   0   0   0  3 |   *  *   *   *   *   *   *   *   * 35 |  0   0   0   0   0   0   0   0   0  0   0   0   0  1  4 |  0   0  0   0   0   0   0   0  0   0   0  4  6 |  0  0 0   0  0   0  6  0   0 4 | 0 0  0 4  0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
oo..3ox.. .... .... .... ....&#x   1  3  0 0 |  3   3   0   0   0  0 |   3  1   0   0   0   0   0   0   0  0 | 35   *   *   *   *   *   *   *   *  *   *   *   *  *  *   4   0  0   0   0   0   0   0  0   0   0  0  0 |  6  0 0   0  0   0  0  0   0 0 | 4 0  0 0  0 0
.... ox..3oo.. .... .... ....&#x   1  3  0 0 |  3   3   0   0   0  0 |   3  0   1   0   0   0   0   0   0  0 |  * 140   *   *   *   *   *   *   *  *   *   *   *  *  * |  1   3  0   0   0   0   0   0  0   0   0  0  0 |  3  3 0   0  0   0  0  0   0 0 | 3 1  0 0  0 0
.... .x..3.o..3.o.. .... ....      0  4  0 0 |  0   6   0   0   0  0 |   0  0   4   0   0   0   0   0   0  0 |  *   * 105   *   *   *   *   *   *  *   *   *   *  *  * |  0   1  2   0   1   0   0   0  0   0   0  0  0 |  1  2 1   0  2   0  0  0   0 0 | 2 1  0 1  0 0
.oo.3.xo. .... .... .... ....&#x   0  3  1 0 |  0   3   3   0   0  0 |   0  1   0   3   0   0   0   0   0  0 |  *   *   * 140   *   *   *   *   *  *   *   *   *  *  * |  1   0  0   3   0   0   0   0  0   0   0  0  0 |  3  0 0   3  0   0  0  0   0 0 | 3 0  1 0  0 0
.... .xo.3.oo. .... .... ....&#x   0  3  1 0 |  0   3   3   0   0  0 |   0  0   1   3   0   0   0   0   0  0 |  *   *   *   * 140   *   *   *   *  *   *   *   *  *  *   1   0  0   0   3   0   0   0  0   0   0  0  0 |  3  0 0   0  3   0  0  0   0 0 | 3 0  0 1  0 0
.... .xo. .... .ox. .... ....&#x   0  2  2 0 |  0   1   4   1   0  0 |   0  0   0   2   2   0   0   0   0  0 |  *   *   *   *   * 630   *   *   *  *   *   *   *  *  * |  0   0  0   1   1   2   0   0  0   0   0  0  0 |  1  0 0   2  2   1  0  0   0 0 | 2 0  1 1  0 0
.... .... .oo.3.ox. .... ....&#x   0  1  3 0 |  0   0   3   3   0  0 |   0  0   0   0   3   1   0   0   0  0 |  *   *   *   *   *   * 210   *   *  *   *   *   *  *  *   0   0  0   0   2   0   2   0  0   0   0  0  0 |  1  0 0   0  4   0  1  0   0 0 | 2 0  0 2  0 0
.... .... .... .ox.3.oo. ....&#x   0  1  3 0 |  0   0   3   3   0  0 |   0  0   0   0   3   0   1   0   0  0 |  *   *   *   *   *   *   * 420   *  *   *   *   *  *  * |  0   0  0   0   0   2   1   1  0   0   0  0  0 |  0  0 0   1  2   2  1  0   0 0 | 1 0  1 2  0 0
.... ..o.3..o.3..x. .... ....      0  0  4 0 |  0   0   0   6   0  0 |   0  0   0   0   0   4   0   0   0  0 |  *   *   *   *   *   *   *   * 105  *   *   *   *  *  * |  0   0  0   0   1   0   0   0  1   2   0  0  0 |  1  0 0   0  2   0  0  2   1 0 | 2 0  0 1  1 0
.... .... .... ..x.3..o.3..o.      0  0  4 0 |  0   0   0   6   0  0 |   0  0   0   0   0   0   4   0   0  0 |  *   *   *   *   *   *   *   *   * 35   *   *   *  *  * |  0   0  0   0   0   0   0   3  0   0   0  1  0 |  0  0 0   0  0   3  3  0   0 0 | 0 0  1 3  0 0
.... .... ..oo3..xo .... ....&#x   0  0  3 1 |  0   0   0   3   3  0 |   0  0   0   0   0   1   0   3   0  0 |  *   *   *   *   *   *   *   *   *  * 420   *   *  *  * |  0   0  0   0   0   0   1   0  0   2   1  0  0 |  0  0 0   0  2   0  1  1   2 0 | 1 0  0 2  1 0
.... .... .... ..xo3..oo ....&#x   0  0  3 1 |  0   0   0   3   3  0 |   0  0   0   0   0   0   1   3   0  0 |  *   *   *   *   *   *   *   *   *  *   * 140   *  *  *   0   0  0   0   0   0   3   0  0   0   0  1  0 |  0  0 0   0  3   0  3  0   0 0 | 1 0  0 3  0 0
.... .... .... ..xo .... ..ox&#x   0  0  2 2 |  0   0   0   1   4  1 |   0  0   0   0   0   0   0   2   2  0 |  *   *   *   *   *   *   *   *   *  *   *   * 210  *  * |  0   0  0   0   0   0   0   0  0   0   3  1  0 |  0  0 0   0  0   0  3  0   3 0 | 0 0  0 3  1 0
.... .... .... .... ..oo3..ox&#x   0  0  1 3 |  0   0   0   0   3  3 |   0  0   0   0   0   0   0   0   3  1 |  *   *   *   *   *   *   *   *   *  *   *   *   * 35  *   0   0  0   0   0   0   0   0  0   0   0  4  0 |  0  0 0   0  0   0  6  0   0 0 | 0 0  0 4  0 0
.... .... .... ...o3...o3...x      0  0  0 4 |  0   0   0   0   0  6 |   0  0   0   0   0   0   0   0   0  4 |  *   *   *   *   *   *   *   *   *  *   *   *   *  * 35 |  0   0  0   0   0   0   0   0  0   0   0  1  3 |  0  0 0   0  0   0  3  0   0 3 | 0 0  0 3  0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
ooo.3oxo.3ooo. .... .... ....&#xt  1  6  1 0 |  6  12   6   0   0  0 |  12  4   4  12   0   0   0   0   0  0 |  4   4   0   4   4   0   0   0   0  0   0   0   0  0  0 | 35   *  *   *   *   *   *   *  *   *   *  *  * |  3  0 0   0  0   0  0  0   0 0 | 3 0  0 0  0 0
.... ox..3oo..3oo.. .... ....&#x   1  4  0 0 |  4   6   0   0   0  0 |   6  0   4   0   0   0   0   0   0  0 |  0   4   1   0   0   0   0   0   0  0   0   0   0  0  0 |  * 105  *   *   *   *   *   *  *   *   *  *  * |  1  2 0   0  0   0  0  0   0 0 | 2 1  0 0  0 0
.... .x..3.o..3.o..3.o.. ....      0  5  0 0 |  0  10   0   0   0  0 |   0  0  10   0   0   0   0   0   0  0 |  0   0   5   0   0   0   0   0   0  0   0   0   0  0  0 |  *   * 42   *   *   *   *   *  *   *   *  *  * |  0  1 1   0  1   0  0  0   0 0 | 1 1  0 1  0 0
.oo.3.xo. .... .ox. .... ....&#x   0  3  2 0 |  0   3   6   1   0  0 |   0  1   0   6   3   0   0   0   0  0 |  0   0   0   2   0   3   0   0   0  0   0   0   0  0  0 |  *   *  * 210   *   *   *   *  *   *   *  *  * |  1  0 0   2  0   0  0  0   0 0 | 2 0  1 0  0 0
.... .xo.3.oo.3.ox. .... ....&#x   0  4  4 0 |  0   6  12   6   0  0 |   0  0   4  12  12   4   0   0   0  0 |  0   0   1   0   4   6   4   0   1  0   0   0   0  0  0 |  *   *  *   * 105   *   *   *  *   *   *  *  * |  1  0 0   0  2   0  0  0   0 0 | 2 0  0 1  0 0
.... .xo. .... .ox.3.oo. ....&#x   0  2  3 0 |  0   1   6   3   0  0 |   0  0   0   3   6   0   1   0   0  0 |  0   0   0   0   0   3   0   2   0  0   0   0   0  0  0 |  *   *  *   *   * 420   *   *  *   *   *  *  * |  0  0 0   1  1   1  0  0   0 0 | 1 0  1 1  0 0
.... .... .ooo3.oxo3.ooo ....&#xt  0  1  6 1 |  0   0   6  12   6  0 |   0  0   0   0  12   4   4  12   0  0 |  0   0   0   0   0   0   4   4   0  0   4   4   0  0  0 |  *   *  *   *   *   * 105   *  *   *   *  *  * |  0  0 0   0  2   0  1  0   0 0 | 1 0  0 2  0 0
.... .... .... .ox.3.oo.3.oo.&#x   0  1  4 0 |  0   0   4   6   0  0 |   0  0   0   0   6   0   4   0   0  0 |  0   0   0   0   0   0   0   4   0  1   0   0   0  0  0 |  *   *  *   *   *   *   * 105  *   *   *  *  * |  0  0 0   0  0   2  1  0   0 0 | 0 0  1 2  0 0
..o.3..o.3..o.3..x. .... ....      0  0  5 0 |  0   0   0  10   0  0 |   0  0   0   0   0  10   0   0   0  0 |  0   0   0   0   0   0   0   0   5  0   0   0   0  0  0 |  *   *  *   *   *   *   *   * 21   *   *  *  * |  1  0 0   0  0   0  0  2   0 0 | 2 0  0 0  1 0
.... ..oo3..oo3..xo .... ....&#x   0  0  4 1 |  0   0   0   6   4  0 |   0  0   0   0   0   4   0   6   0  0 |  0   0   0   0   0   0   0   0   1  0   4   0   0  0  0 |  *   *  *   *   *   *   *   *  * 210   *  *  * |  0  0 0   0  1   0  0  1   1 0 | 1 0  0 1  1 0
.... .... ..oo3..xo .... ..ox&#x   0  0  3 2 |  0   0   0   3   6  1 |   0  0   0   0   0   1   0   6   3  0 |  0   0   0   0   0   0   0   0   0  0   2   0   3  0  0 |  *   *  *   *   *   *   *   *  *   * 210  *  * |  0  0 0   0  0   0  1  0   2 0 | 0 0  0 2  1 0
.... .... .... ..xo3..oo3..ox&#x   0  0  4 4 |  0   0   0   6  12  6 |   0  0   0   0   0   0   4  12  12  4 |  0   0   0   0   0   0   0   0   0  1   0   4   6  4  1 |  *   *  *   *   *   *   *   *  *   *   * 35  * |  0  0 0   0  0   0  3  0   0 0 | 0 0  0 3  0 0
.... .... ...o3...o3...o3...x      0  0  0 5 |  0   0   0   0   0 10 |   0  0   0   0   0   0   0   0   0 10 |  0   0   0   0   0   0   0   0   0  0   0   0   0  0  5 |  *   *  *   *   *   *   *   *  *   *   *  * 21 |  0  0 0   0  0   0  1  0   0 2 | 0 0  0 2  0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
ooo.3oxo.3ooo.3oox. .... ....&#xt  1 10  5 0 | 10  30  30  10   0  0 |  30 10  20  60  30  10   0   0   0  0 | 10  20   5  20  20  30  10   0   5  0   0   0   0  0  0 |  5   5  0  10   5   0   0   0  1   0   0  0  0 | 21  * *   *  *   *  *  *   * * | 2 0  0 0  0 0
.... ox..3oo..3oo..3oo.. ....&#x   1  5  0 0 |  5  10   0   0   0  0 |  10  0  10   0   0   0   0   0   0  0 |  0  10   5   0   0   0   0   0   0  0   0   0   0  0  0 |  0   5  1   0   0   0   0   0  0   0   0  0  0 |  * 42 *   *  *   *  *  *   * * | 1 1  0 0  0 0
.... .x..3.o..3.o..3.o..3.o..      0  6  0 0 |  0  15   0   0   0  0 |   0  0  20   0   0   0   0   0   0  0 |  0   0  15   0   0   0   0   0   0  0   0   0   0  0  0 |  0   0  6   0   0   0   0   0  0   0   0  0  0 |  *  * 7   *  *   *  *  *   * * | 0 1  0 1  0 0
.oo.3.xo. .... .ox.3.oo. ....&#x   0  3  3 0 |  0   3   9   3   0  0 |   0  1   0   9   9   0   1   0   0  0 |  0   0   0   3   0   9   0   3   0  0   0   0   0  0  0 |  0   0  0   3   0   3   0   0  0   0   0  0  0 |  *  * * 140  *   *  *  *   * * | 1 0  1 0  0 0
.... .xoo3.ooo3.oxo3.ooo ....&#xt  0  5 10 1 |  0  10  30  30  10  0 |   0  0  10  30  60  20  10  30   0  0 |  0   0   5   0  10  30  20  20   5  0  20  10   0  0  0 |  0   0  1   0   5  10   5   0  0   5   0  0  0 |  *  * *   * 42   *  *  *   * * | 1 0  0 1  0 0
.... .xo. .... .ox.3.oo.3.oo.&#x   0  2  4 0 |  0   1   8   6   0  0 |   0  0   0   4  12   0   4   0   0  0 |  0   0   0   0   0   6   0   8   0  1   0   0   0  0  0 |  0   0  0   0   0   4   0   2  0   0   0  0  0 |  *  * *   *  * 105  *  *   * * | 0 0  1 1  0 0
.... .... .ooo3.oxo3.ooo3.oox&#xt  0  1 10 5 |  0   0  10  30  30 10 |   0  0   0   0  30  10  20  60  30 10 |  0   0   0   0   0   0  10  20   0  5  20  20  30 10  5 |  0   0  0   0   0   0   5   5  0   0  10  5  1 |  *  * *   *  *   * 21  *   * * | 0 0  0 2  0 0
..oo3..oo3..oo3..xo .... ....&#x   0  0  5 1 |  0   0   0  10   5  0 |   0  0   0   0   0  10   0  10   0  0 |  0   0   0   0   0   0   0   0   5  0  10   0   0  0  0 |  0   0  0   0   0   0   0   0  1   5   0  0  0 |  *  * *   *  *   *  * 42   * * | 1 0  0 0  1 0
.... ..oo3..oo3..xo .... ..ox&#x   0  0  4 2 |  0   0   0   6   8  1 |   0  0   0   0   0   4   0  12   4  0 |  0   0   0   0   0   0   0   0   1  0   8   0   6  0  0 |  0   0  0   0   0   0   0   0  0   2   4  0  0 |  *  * *   *  *   *  *  * 105 * | 0 0  0 1  1 0
.... ...o3...o3...o3...o3...x      0  0  0 6 |  0   0   0   0   0 15 |   0  0   0   0   0   0   0   0   0 20 |  0   0   0   0   0   0   0   0   0  0   0   0   0  0 15 |  0   0  0   0   0   0   0   0  0   0   0  0  6 |  *  * *   *  *   *  *  *   * 7 | 0 0  0 1  0 1
----------------------------------+-----------+-----------------------+---------------------------------------+---------------------------------------------------------+------------------------------------------------+--------------------------------+--------------
oooo3oxoo3oooo3ooxo3oooo ....&#xt  1 15 15 1 | 15  60  90  60  15  0 |  60 20  60 180 180  60  20  60   0  0 | 20  60  30  60  60 180  60  60  30  0  60  20   0  0  0 | 15  30  6  60  30  60  15   0  6  30   0  0  0 |  6  6 0  20  6   0  0  6   0 0 | 7 *  * *  * *
.... ox..3oo..3oo..3oo..3oo..&#x   1  6  0 0 |  6  15   0   0   0  0 |  15  0  20   0   0   0   0   0   0  0 |  0  20  15   0   0   0   0   0   0  0   0   0   0  0  0 |  0  15  6   0   0   0   0   0  0   0   0  0  0 |  0  6 1   0  0   0  0  0   0 0 | * 7  * *  * *
.oo.3.xo. .... .ox.3.oo.3.oo.&#x   0  3  4 0 |  0   3  12   6   0  0 |   0  1   0  12  18   0   4   0   0  0 |  0   0   0   4   0  18   0  12   0  1   0   0   0  0  0 |  0   0  0   6   0  12   0   3  0   0   0  0  0 |  0  0 0   4  0   3  0  0   0 0 | * * 35 *  * *
.... .xoo3.ooo3.oxo3.ooo3.oox&#xt  0  6 20 6 |  0  15  60  90  60 15 |   0  0  20  60 180  60  60 180  60 20 |  0   0  15   0  20  90  60 120  15 15 120  60  90 20 15 |  0   0  6   0  15  60  30  30  0  30  60 15  6 |  0  0 1   0  6  15  6  0  15 1 | * *  * 7  * *
..oo3..oo3..oo3..xo .... ..ox&#x   0  0  5 2 |  0   0   0  10  10  1 |   0  0   0   0   0  10   0  20   5  0 |  0   0   0   0   0   0   0   0   5  0  20   0  10  0  0 |  0   0  0   0   0   0   0   0  1  10  10  0  0 |  0  0 0   0  0   0  0  2   5 0 | * *  * * 21 *
...o3...o3...o3...o3...o3...x      0  0  0 7 |  0   0   0   0   0 21 |   0  0   0   0   0   0   0   0   0 35 |  0   0   0   0   0   0   0   0   0  0   0   0   0  0 35 |  0   0  0   0   0   0   0   0  0   0   0  0 21 |  0  0 0   0  0   0  0  0   0 7 | * *  * *  * 1

oxoo3ooxo xoxo3oooo3oxox *d3oooo&#xt   → all heights = 1/sqrt(6) = 0.408248
(hex || pseudo hex-alt. trahex || pseudo {3}-dual trahex || hex-alt. hex)

o...3o... o...3o...3o... *d3o...     & | 16  *   6  12  3  0   0   0 | 12  12  36  18  24  3  0   0   0   0 |  4  4  4  36  36  16  12  12  12  36  1  0  0   0   0   0 | 1 12  36 12 12  3  16  16  24  4 0   0  0  0 | 12 12 3 12  12  6  6  0 0 |  4 3  3 4
.o..3.o.. .o..3.o..3.o.. *d3.o..     & |  * 48   0   4  1  2   6   8 |  0   8   6  12  16  2  1  12  12  36 |  0  0  4  12   4   6  12  12  12  36  1  4  4  24  32  12 | 0  6   8  4  1  4  18  24  32  4 1  20  8 10 |  4  2 1 12  20 10  6  6 2 |  1 3  6 4
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x... .... ....    ....     & |  2  0 | 48   *  *  *   *   *   4   0   6   0   0  0  0   0   0   0 |  2  2  0   6  12   3   0   0   0   0  0  0  0   0   0   0 | 1  2  12  6  6  0   3   0   0  0 0   0  0  0 |  4  6 3  6   0  0  1  0 0 |  2 3  0 2
oo..3oo.. oo..3oo..3oo.. *d3oo..&#x  & |  1  1 |  * 192  *  *   *   *   0   2   3   3   2  0  0   0   0   0 |  0  0  1   6   3   3   3   2   1   6  0  0  0   0   0   0 | 0  3   6  3  1  1   6   3   6  1 0   0  0  0 |  3  2 1  6   3  2  3  0 0 |  1 2  1 3
o.o.3o.o. o.o.3o.o.3o.o. *d3o.o.&#x  & |  1  1 |  *   * 48  *   *   *   0   0   0   0   8  2  0   0   0   0 |  0  0  0   0   0   0   0   4   8  16  1  0  0   0   0   0 | 0  0   0  0  0  0   6  12   8  4 0   0  0  0 |  0  0 0  4   8  2  6  0 0 |  0 1  2 4
.x.. .... .... .... ....    ....     & |  0  2 |  *   *  * 48   *   *   0   4   0   0   0  1  1   0   4   0 |  0  0  4   6   0   0   0   4   4   0  1  0  0   6   0   0 | 0  6   4  0  0  0   6   6   0  4 0   4  0  0 |  4  1 0  4   4  0  6  1 0 |  1 1  1 4
.... .... .... .... .x..    ....     & |  0  2 |  *   *  *  * 144   *   0   0   0   2   0  0  0   4   0   4 |  0  0  0   0   0   1   4   0   0   4  0  2  2   2   8   2 | 0  0   0  2  0  2   3   2   8  0 1   4  4  4 |  0  0 1  6   4  4  1  2 2 |  0 3  2 2
.oo.3.oo. .oo.3.oo.3.oo. *d3.oo.&#x    |  0  2 |  *   *  *  *   * 192   0   0   0   0   2  0  0   0   2   6 |  0  0  0   0   0   0   0   2   2   6  0  0  0   6   6   3 | 0  0   0  0  0  0   6   6   6  1 0   6  3  2 |  0  0 0  6   6  2  3  2 1 |  0 2  2 3
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x...3o... ....    ....     & |  3  0 |  3   0  0  0   0   0 | 64   *   *   *   *  *  *   *   *   * |  1  1  0   0   3   0   0   0   0   0  0  0  0   0   0   0 | 1  0   3  3  3  0   0   0   0  0 0   0  0  0 |  1  3 3  3   0  0  0  0 0 |  1 3  0 1
ox.. .... .... .... ....    ....&#x  & |  1  2 |  0   2  0  1   0   0 |  * 192   *   *   *  *  *   *   *   * |  0  0  1   3   0   0   0   1   0   0  0  0  0   0   0   0 | 0  3   3  0  0  0   3   0   0  1 0   0  0  0 |  3  1 0  3   0  0  3  0 0 |  1 1  0 3
.... .... xo.. .... ....    ....&#x  & |  2  1 |  1   2  0  0   0   0 |  *   * 288   *   *  *  *   *   *   * |  0  0  0   2   2   1   0   0   0   0  0  0  0   0   0   0 | 0  1   4  2  1  0   2   0   0  0 0   0  0  0 |  2  2 1  4   0  0  1  0 0 |  1 2  0 2
.... .... .... .... ox..    ....&#x  & |  1  2 |  0   2  0  0   1   0 |  *   *   * 288   *  *  *   *   *   * |  0  0  0   0   0   1   2   0   0   2  0  0  0   0   0   0 | 0  0   0  2  0  1   2   1   4  0 0   0  0  0 |  0  0 1  4   2  2  1  0 0 |  0 2  1 2
ooo.3ooo. ooo.3ooo.3ooo. *d3ooo.&#x  & |  1  2 |  0   1  1  0   0   1 |  *   *   *   * 384  *  *   *   *   * |  0  0  0   0   0   0   0   1   1   3  0  0  0   0   0   0 | 0  0   0  0  0  0   3   3   3  1 0   0  0  0 |  0  0 0  3   3  1  3  0 0 |  0 1  1 3
.... o.x. .... .... ....    ....&#x  & |  1  2 |  0   0  2  1   0   0 |  *   *   *   *   * 48  *   *   *   * |  0  0  0   0   0   0   0   0   4   0  1  0  0   0   0   0 | 0  0   0  0  0  0   0   6   0  4 0   0  0  0 |  0  0 0  0   4  0  6  0 0 |  0 0  1 4
.x..3.o.. .... .... ....    ....     & |  0  3 |  0   0  0  3   0   0 |  *   *   *   *   *  * 16   *   *   * |  0  0  4   0   0   0   0   0   0   0  1  0  0   0   0   0 | 0  6   0  0  0  0   0   0   0  4 0   0  0  0 |  4  0 0  0   0  0  6  0 0 |  1 0  0 4
.... .... .... .o..3.x..    ....     & |  0  3 |  0   0  0  0   3   0 |  *   *   *   *   *  *  * 192   *   * |  0  0  0   0   0   0   1   0   0   0  0  1  1   0   2   0 | 0  0   0  1  0  1   0   0   2  0 1   1  2  2 |  0  0 1  3   1  2  0  1 2 |  0 3  1 1
.xo. .... .... .... ....    ....&#x  & |  0  3 |  0   0  0  1   0   2 |  *   *   *   *   *  *  *   * 192   * |  0  0  0   0   0   0   0   1   1   0  0  0  0   3   0   0 | 0  0   0  0  0  0   3   3   0  1 0   3  0  0 |  0  0 0  3   3  0  3  1 0 |  0 1  1 3
.... .... .ox. .... ....    ....&#x  & |  0  3 |  0   0  0  0   1   2 |  *   *   *   *   *  *  *   *   * 576 |  0  0  0   0   0   0   0   0   0   1  0  0  0   1   2   1 | 0  0   0  0  0  0   2   1   2  0 0   2  2  1 |  0  0 0  4   2  1  1  1 1 |  0 2  1 2
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x...3o...3o...    ....     &   4  0 |  6   0  0  0   0   0 |  4   0   0   0   0  0  0   0   0   0 | 16  *  *   *   *   *   *   *   *   *  *  *  *   *   *   *  1  0   0  3  0  0   0   0   0  0 0   0  0  0 |  0  0 3  3   0  0  0  0 0 |  0 3  0 1
.... .... x...3o... .... *d3o...     &   4  0 |  6   0  0  0   0   0 |  4   0   0   0   0  0  0   0   0   0 |  * 16  *   *   *   *   *   *   *   *  *  *  *   *   *   * | 1  0   0  0  3  0   0   0   0  0 0   0  0  0 |  0  3 3  0   0  0  0  0 0 |  1 3  0 0
ox..3oo.. .... .... ....    ....&#x  &   1  3 |  0   3  0  3   0   0 |  0   3   0   0   0  0  1   0   0   0 |  *  * 64   *   *   *   *   *   *   *  *  *  *   *   *   * | 0  3   0  0  0  0   0   0   0  1 0   0  0  0 |  3  0 0  0   0  0  3  0 0 |  1 0  0 3
ox.. .... xo.. .... ....    ....&#x  &   2  2 |  1   4  0  1   0   0 |  0   2   2   0   0  0  0   0   0   0 |  *  *  * 288   *   *   *   *   *   *  *  *  *   *   *   * | 0  1   2  0  0  0   1   0   0  0 0   0  0  0 |  2  1 0  2   0  0  1  0 0 |  1 1  0 2
.... .... xo..3oo.. ....    ....&#x  &   3  1 |  3   3  0  0   0   0 |  1   0   3   0   0  0  0   0   0   0 |  *  *  *   * 192   *   *   *   *   *  *  *  *   *   *   * | 0  0   2  1  1  0   0   0   0  0 0   0  0  0 |  1  2 1  2   0  0  0  0 0 |  1 2  0 1
.... .... xo.. .... ox..    ....&#x  &   2  2 |  1   4  0  0   1   0 |  0   0   2   2   0  0  0   0   0   0 |  *  *  *   *   * 144   *   *   *   *  *  *  *   *   *   *  0  0   0  2  0  0   2   0   0  0 0   0  0  0 |  0  0 1  4   0  0  1  0 0 |  0 2  0 2
.... .... .... oo..3ox..    ....&#x  &   1  3 |  0   3  0  0   3   0 |  0   0   0   3   0  0  0   1   0   0 |  *  *  *   *   *   * 192   *   *   *  *  *  *   *   *   * | 0  0   0  1  0  1   0   0   2  0 0   0  0  0 |  0  0 1  2   1  2  0  0 0 |  0 2  1 1
oxo. .... .... .... ....    ....&#x  &   1  3 |  0   2  1  1   0   2 |  0   1   0   0   2  0  0   0   1   0 |  *  *  *   *   *   *   * 192   *   *  *  *  *   *   *   *  0  0   0  0  0  0   3   0   0  1 0   0  0  0 |  0  0 0  3   0  0  3  0 0 |  0 1  0 3
.... oox. .... .... ....    ....&#x  &   1  3 |  0   1  2  1   0   2 |  0   0   0   0   2  1  0   0   1   0 |  *  *  *   *   *   *   *   * 192   *  *  *  *   *   *   * | 0  0   0  0  0  0   0   3   0  1 0   0  0  0 |  0  0 0  0   3  0  3  0 0 |  0 0  1 3
.... .... .... .... oxo.    ....&#x  &   1  3 |  0   2  1  0   1   2 |  0   0   0   1   2  0  0   0   0   1 |  *  *  *   *   *   *   *   *   * 576  *  *  *   *   *   * | 0  0   0  0  0  0   1   1   2  0 0   0  0  0 |  0  0 0  2   2  1  1  0 0 |  0 1  1 2
o.o.3o.x. .... .... ....    ....&#x  &   1  3 |  0   0  3  3   0   0 |  0   0   0   0   0  3  1   0   0   0 |  *  *  *   *   *   *   *   *   *   * 16  *  *   *   *   *  0  0   0  0  0  0   0   0   0  4 0   0  0  0 |  0  0 0  0   0  0  6  0 0 |  0 0  0 4
.... .... .o..3.o..3.x..    ....     &   0  4 |  0   0  0  0   6   0 |  0   0   0   0   0  0  0   4   0   0 |  *  *  *   *   *   *   *   *   *   *  * 48  *   *   *   *  0  0   0  1  0  0   0   0   0  0 1   0  2  0 |  0  0 1  3   0  0  0  0 2 |  0 3  0 1
.... .... .... .o..3.x.. *d3.o..     &   0  4 |  0   0  0  0   6   0 |  0   0   0   0   0  0  0   4   0   0 |  *  *  *   *   *   *   *   *   *   *  *  * 48   *   *   * | 0  0   0  0  0  1   0   0   0  0 1   0  0  2 |  0  0 1  0   0  2  0  1 2 |  0 3  1 0
.xo. .... .ox. .... ....    ....&#x  &   0  4 |  0   0  0  1   1   4 |  0   0   0   0   0  0  0   0   2   2 |  *  *  *   *   *   *   *   *   *   *  *  *  * 288   *   * | 0  0   0  0  0  0   1   1   0  0 0   2  0  0 |  0  0 0  2   2  0  1  1 0 |  0 1  1 2
.... .... .ox.3.oo. ....    ....&#x  &   0  4 |  0   0  0  0   3   3 |  0   0   0   0   0  0  0   1   0   3 |  *  *  *   *   *   *   *   *   *   *  *  *  *   * 384   * | 0  0   0  0  0  0   0   0   1  0 0   1  1  1 |  0  0 0  2   1  1  0  1 1 |  0 2  1 1
.... .... .ox. .... .xo.    ....&#x      0  4 |  0   0  0  0   2   4 |  0   0   0   0   0  0  0   0   0   4 |  *  *  *   *   *   *   *   *   *   *  *  *  *   *   * 144  0  0   0  0  0  0   2   0   0  0 0   0  2  0 |  0  0 0  4   0  0  1  0 1 |  0 2  0 2
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
.... .... x...3o...3o... *d3o...     &   8  0 | 24   0  0  0   0   0 | 32   0   0   0   0  0  0   0   0   0 |  8  8  0   0   0   0   0   0   0   0  0  0  0   0   0   0 | 2  *   *  *  *  *   *   *   *  * *   *  *  * |  0  0 3  0   0  0  0  0 0 |  0 3  0 0
ox..3oo.. xo.. .... ....    ....&#x  &   2  3 |  1   6  0  3   0   0 |  0   6   3   0   0  0  1   0   0   0 |  0  0  2   3   0   0   0   0   0   0  0  0  0   0   0   0 | * 96   *  *  *  *   *   *   *  * *   *  *  * |  2  0 0  0   0  0  1  0 0 |  1 0  0 2
ox.. .... xo..3oo.. ....    ....&#x  &   3  2 |  3   6  0  1   0   0 |  1   3   6   0   0  0  0   0   0   0 |  0  0  0   3   2   0   0   0   0   0  0  0  0   0   0   0 | *  * 192  *  *  *   *   *   *  * *   *  *  * |  1  1 0  1   0  0  0  0 0 |  1 1  0 1
.... .... xo..3oo..3ox..    ....&#x  &   4  4 |  6  12  0  0   6   0 |  4   0  12  12   0  0  0   4   0   0 |  1  0  0   0   4   6   4   0   0   0  0  1  0   0   0   0 | *  *   * 48  *  *   *   *   *  * *   *  *  * |  0  0 1  2   0  0  0  0 0 |  0 2  0 1
.... .... xo..3oo.. .... *d3oo..&#x  &   4  1 |  6   4  0  0   0   0 |  4   0   6   0   0  0  0   0   0   0 |  0  1  0   0   4   0   0   0   0   0  0  0  0   0   0   0 | *  *   *  * 48  *   *   *   *  * *   *  *  * |  0  2 1  0   0  0  0  0 0 |  1 2  0 0
.... .... .... oo..3ox.. *d3oo..&#x  &   1  4 |  0   4  0  0   6   0 |  0   0   0   6   0  0  0   4   0   0 |  0  0  0   0   0   0   4   0   0   0  0  0  1   0   0   0 | *  *   *  *  * 48   *   *   *  * *   *  *  * |  0  0 1  0   0  2  0  0 0 |  0 2  1 0
oxo. .... xox. .... oxo.    ....&#xt &   2  6 |  1   8  2  2   3   8 |  0   4   4   4   8  0  0   0   4   8 |  0  0  0   2   0   2   0   4   0   4  0  0  0   2   0   2 | *  *   *  *  *  * 144   *   *  * *   *  *  * |  0  0 0  2   0  0  1  0 0 |  0 1  0 2
.... oox. .... .... oxo.    ....&#x  &   1  4 |  0   2  2  1   1   4 |  0   0   0   1   4  1  0   0   2   2 |  0  0  0   0   0   0   0   0   2   2  0  0  0   1   0   0 | *  *   *  *  *  *   * 288   *  * *   *  *  * |  0  0 0  0   2  0  1  0 0 |  0 0  1 2
.... .... .... ooo.3oxo.    ....&#x  &   1  4 |  0   3  1  0   3   3 |  0   0   0   3   3  0  0   1   0   3 |  0  0  0   0   0   0   1   0   0   3  0  0  0   0   1   0 | *  *   *  *  *  *   *   * 384  * *   *  *  * |  0  0 0  1   1  1  0  0 0 |  0 1  1 1
oxoo3ooxo .... .... ....    ....&#xr     2  6 |  0   6  6  6   0   6 |  0   6   0   0  12  6  2   0   6   0 |  0  0  2   0   0   0   0   6   6   0  2  0  0   0   0   0 | *  *   *  *  *  *   *   *   * 32 *   *  *  * |  0  0 0  0   0  0  3  0 0 |  0 0  0 3  cycle: (ABDC)
.... .... .o..3.o..3.x.. *d3.o..     &   0  8 |  0   0  0  0  24   0 |  0   0   0   0   0  0  0  32   0   0 |  0  0  0   0   0   0   0   0   0   0  0  8  8   0   0   0 | *  *   *  *  *  *   *   *   *  * 6   *  *  * |  0  0 1  0   0  0  0  0 2 |  0 3  0 0
.xo. .... .ox.3.oo. ....    ....&#x  &   0  5 |  0   0  0  1   3   6 |  0   0   0   0   0  0  0   1   3   6 |  0  0  0   0   0   0   0   0   0   0  0  0  0   3   2   0 | *  *   *  *  *  *   *   *   *  * * 192  *  * |  0  0 0  1   1  0  0  1 0 |  0 1  1 1
.... .... .ox.3.oo.3.xo.    ....&#x      0  8 |  0   0  0  0  12  12 |  0   0   0   0   0  0  0   8   0  24 |  0  0  0   0   0   0   0   0   0   0  0  2  0   0   8   6 | *  *   *  *  *  *   *   *   *  * *   * 48  * |  0  0 0  2   0  0  0  0 1 |  0 2  0 1
.... .... .ox.3.oo. .... *d3.oo.&#x  &   0  5 |  0   0  0  0   6   4 |  0   0   0   0   0  0  0   4   0   6 |  0  0  0   0   0   0   0   0   0   0  0  0  1   0   4   0 | *  *   *  *  *  *   *   *   *  * *   *  * 96 |  0  0 0  0   0  1  0  1 1 |  0 2  1 0
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
ox..3oo.. xo..3oo.. ....    ....&#x  &   3  3 |  3   9  0  3   0   0 |  1   9   9   0   0  0  1   0   0   0 |  0  0  3   9   3   0   0   0   0   0  0  0  0   0   0   0 | 0  3   3  0  0  0   0   0   0  0 0   0  0  0 | 64  * *  *   *  *  *  * * |  1 0  0 1
ox.. .... xo..3oo.. .... *d3oo..&#x  &   4  2 |  6   8  0  1   0   0 |  4   4  12   0   0  0  0   0   0   0 |  0  1  0   6   8   0   0   0   0   0  0  0  0   0   0   0 | 0  0   4  0  2  0   0   0   0  0 0   0  0  0 |  * 48 *  *   *  *  *  * * |  1 1  0 0
.... .... xo..3oo..3ox.. *d3oo..&#x  &   8  8 | 24  32  0  0  24   0 | 32   0  48  48   0  0  0  32   0   0 |  8  8  0   0  32  24  32   0   0   0  0  8  8   0   0   0 | 1  0   0  8  8  8   0   0   0  0 1   0  0  0 |  *  * 6  *   *  *  *  * * |  0 2  0 0
oxo. .... xox.3ooo.3oxo.    ....&#xt &   4 12 |  6  24  4  4  18  24 |  4  12  24  24  24  0  0  12  12  48 |  1  0  0  12   8  12   8  12   0  24  0  3  0  12  16  12 | 0  0   4  2  0  0   6   0   8  0 0   4  2  0 |  *  * * 48   *  *  *  * * |  0 1  0 1
.... oox. .... ooo.3oxo.    ....&#xt &   1  5 |  0   3  2  1   3   6 |  0   0   0   3   6  1  0   1   3   6 |  0  0  0   0   0   0   1   0   3   6  0  0  0   3   2   0 | 0  0   0  0  0  0   0   3   2  0 0   1  0  0 |  *  * *  * 192  *  *  * * |  0 0  1 1
.... .... .... ooo.3oxo. *d3ooo.&#x  &   1  5 |  0   4  1  0   6   4 |  0   0   0   6   4  0  0   4   0   6 |  0  0  0   0   0   0   4   0   0   6  0  0  1   0   4   0 | 0  0   0  0  0  1   0   0   4  0 0   0  0  1 |  *  * *  *   * 96  *  * * |  0 1  1 0
oxoo3ooxo xoxo .... oxox    ....&#xt &   4 12 |  2  24 12 12   6  24 |  0  24  12  12  48 12  4   0  24  24 |  0  0  8  12   0   6   0  24  24  24  4  0  0  12   0   6 | 0  4   0  0  0  0   6  12   0  4 0   0  0  0 |  *  * *  *   *  * 24  * * |  0 0  0 2
.xo. .... .ox.3.oo. .... *d3.oo.&#x  &   0  6 |  0   0  0  1   6   8 |  0   0   0   0   0  0  0   4   4  12 |  0  0  0   0   0   0   0   0   0   0  0  0  1   6   8   0 | 0  0   0  0  0  0   0   0   0  0 0   4  0  2 |  *  * *  *   *  *  * 48 * |  0 1  1 0
.... .... .ox.3.oo.3.xo. *d3.oo.&#x      0 16 |  0   0  0  0  48  32 |  0   0   0   0   0  0  0  64   0  96 |  0  0  0   0   0   0   0   0   0   0  0 16 16   0  64  24 | 0  0   0  0  0  0   0   0   0  0 2   0  8 16 |  *  * *  *   *  *  *  * 6 |  0 2  0 0
---------------------------------------+-------+----------------------+--------------------------------------+-----------------------------------------------------------+----------------------------------------------+---------------------------+----------
ox..3oo.. xo..3oo.. .... *d3oo..&#x  &   4  3 |  6  12  0  3   0   0 |  4  12  18   0   0  0  1   0   0   0 |  0  1  4  18  12   0   0   0   0   0  0  0  0   0   0   0 | 0  6  12  0  3  0   0   0   0  0 0   0  0  0 |  4  3 0  0   0  0  0  0 0 | 16 *  * *
oxo. .... xox.3ooo.3oxo. *d3ooo.&#xt &   8 24 | 24  64  8  8  72  64 | 32  32  96  96  64  0  0  96  32 192 |  8  8  0  48  64  48  64  32   0  96  0 24 24  48 128  48 | 1  0  32 16 16 16  24   0  64  0 3  32 16 32 |  0  8 2  8   0 16  0  8 2 |  * 6  * *
.... oox. .... ooo.3oxo. *d3ooo.&#x  &   1  6 |  0   4  2  1   6   8 |  0   0   0   6   8  1  0   4   4  12 |  0  0  0   0   0   0   4   0   4  12  0  0  1   6   8   0 | 0  0   0  0  0  1   0   6   8  0 0   4  0  2 |  0  0 0  0   4  2  0  1 0 |  * * 48 *
oxoo3ooxo xoxo3oooo3oxox    ....&#xt     8 24 | 12  72 24 24  36  72 |  8  72  72  72 144 24  8  24  72 144 |  2  0 24  72  24  36  24  72  72 144  8  6  0  72  48  36 | 0 24  24  6  0  0  36  72  48 12 0  24  6  0 |  8  0 0  6  24  0  6  0 0 |  * *  * 8

xo3oo3ox *b3oo xo3oo3ox&#zx   → height = 0
(tegum sum of 2 mutually gyro-dual tethexes)

o.3o.3o. *b3o. o.3o.3o.     & | 64    6  3  12 |  12  3   54  36 |  4  4  1  48  18   72  16  12 | 1 12  15  60  18  30  4 |  3 12  18  24  6 | 3 4  7
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x. .. ..    .. .. .. ..     & |  2 | 192  *   *    4  0    6   0 |  2  2  0  12   3    6   0   0 | 1  6   6  12   3   2  0 |  3  6   6   4  1 | 3 2  2
.. .. ..    .. x. .. ..     & |  2 |   * 96   *    0  2    0   8 |  0  0  1   0   0   12   8   4 | 0  0   0   8   6  12  4 |  0  4   2   8  6 | 1 4  2
oo3oo3oo *b3oo oo3oo3oo&#x    |  2 |   *  * 384    0  0    6   4 |  0  0  0   6   3   12   2   2 | 0  3   2  12   6   6  1 |  1  6   4   6  3 | 2 3  2
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x.3o. ..    .. .. .. ..     & |  3 |   3  0   0 | 256  *    *   * |  1  1  0   3   0    0   0   0 | 1  3   3   3   0   0  0 |  3  3   3   1  0 | 3 1  1
.. .. ..    .. x.3o....     & |  3 |   0  3   0 |   * 64    *   * |  0  0  1   0   0    0   4   0 | 0  0   0   0   0   6  4 |  0  0   0   4  6 | 0 4  1
xo .. ..    .. .. .. ..&#x  & |  3 |   1  0   2 |   *  * 1152   * |  0  0  0   2   1    2   0   0 | 0  2   1   4   2   1  0 |  1  4   2   2  1 | 2 2  1
.. .. ..    .. xo .. ..&#x  & |  3 |   0  1   2 |   *  *    * 768 |  0  0  0   0   0    3   1   1 | 0  0   0   3   3   3  1 |  0  3   1   3  3 | 1 3  1
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x.3o.3o.    .. .. .. ..     &   4 |   6  0   0 |   4  0    0   0 | 64  *  *   *   *    *   *   *  1  3   0   0   0   0  0 |  3  3   0   0  0 | 3 1  0
x.3o. .. *b3o. .. .. ..     &   4 |   6  0   0 |   4  0    0   0 |  * 64  *   *   *    *   *   * | 1  0   3   0   0   0  0 |  3  0   3   0  0 | 3 0  1
.. .. ..    .. x.3o.3o.     &   4 |   0  6   0 |   0  4    0   0 |  *  * 16   *   *    *   *   *  0  0   0   0   0   0  4 |  0  0   0   0  6 | 0 4  0
xo3oo ..    .. .. .. ..&#x  &   4 |   3  0   3 |   1  0    3   0 |  *  *  * 768   *    *   *   * | 0  1   1   2   0   0  0 |  1  2   2   1  0 | 2 1  1
xo .. ox    .. .. .. ..&#x      4 |   2  0   4 |   0  0    4   0 |  *  *  *   * 288    *   *   *  0  2   0   0   2   0  0 |  1  4   0   0  1 | 2 2  0
xo .. ..    .. .. .. ox&#x  &   4 |   1  1   4 |   0  0    2   2 |  *  *  *   *   * 1152   *   * | 0  0   0   2   1   1  0 |  0  2   1   2  1 | 1 2  1
.. .. ..    .. xo3oo ..&#x  &   4 |   0  3   3 |   0  1    0   3 |  *  *  *   *   *    * 256   * | 0  0   0   0   0   3  1 |  0  0   0   3  3 | 0 3  1
.. .. ..    .. xo .. ox&#x      4 |   0  2   4 |   0  0    0   4 |  *  *  *   *   *    *   * 192  0  0   0   0   3   0  1 |  0  3   0   0  3 | 1 3  0
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
x.3o.3o. *b3o. .. .. ..     &   8 |  24  0   0 |  32  0    0   0 |  8  8  0   0   0    0   0   0 | 8  *   *   *   *   *  * |  3  0   0   0  0 | 3 0  0
xo3oo3ox    .. .. .. ..&#x      8 |  12  0  12 |   8  0   24   0 |  2  0  0   8   6    0   0   0 | * 96   *   *   *   *  * |  1  2   0   0  0 | 2 1  0
xo3oo .. *b3oo .. .. ..&#x  &   5 |   6  0   4 |   4  0    6   0 |  0  1  0   4   0    0   0   0 | *  * 192   *   *   *  * |  1  0   2   0  0 | 2 0  1
xo3oo ..    .. .. .. ox&#x  &   5 |   3  1   6 |   1  0    6   3 |  0  0  0   2   0    3   0   0 | *  *   * 768   *   *  * |  0  1   1   1  0 | 1 1  1
xo .. ox    .. xo .. ox&#zx     8 |   4  4  16 |   0  0   16  16 |  0  0  0   0   4    8   0   4 | *  *   *   * 144   *  * |  0  2   0   0  1 | 1 2  0
xo .. ..    .. .. oo3ox&#x  &   5 |   1  3   6 |   0  1    3   6 |  0  0  0   0   0    3   2   0 | *  *   *   *   * 384  * |  0  0   0   2  1 | 0 2  1
.. .. ..    .. xo3oo3ox&#x      8 |   0 12  12 |   0  8    0  24 |  0  0  2   0   0    0   8   6 | *  *   *   *   *   * 32 |  0  0   0   0  3 | 0 3  0
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
xo3oo3ox *b3oo .. .. ..&#x     16 |  48  0  32 |  64  0   96   0 | 16 16  0  64  24    0   0   0 | 2  8  16   0   0   0  0 | 12  *   *   *  * | 2 0  0
xo3oo3ox    .. xo .. ox&#zx    16 |  24  8  48 |  16  0   96  48 |  4  0  0  32  24   48   0  12 | 0  4   0  16   6   0  0 |  * 48   *   *  * | 1 1  0
xo3oo .. *b3oo .. .. ox&#x  &   6 |   6  1   8 |   4  0   12   4 |  0  1  0   8   0    6   0   0 | 0  0   2   4   0   0  0 |  *  * 192   *  * | 1 0  1
xo3oo ..    .. .. oo3ox&#x  &   6 |   3  3   9 |   1  1    9   9 |  0  0  0   3   0    9   3   0 | 0  0   0   3   0   3  0 |  *  *   * 256  * | 0 1  1
xo .. ox    .. xo3oo3ox&#zx    16 |   8 24  48 |   0 16   48  96 |  0  0  4   0  12   48  32  24 | 0  0   0   0   6  16  4 |  *  *   *   * 24 | 0 2  0
------------------------------+----+------------+-----------------+-------------------------------+-------------------------+------------------+-------
xo3oo3ox *b3oo xo .. ox&#zx    32 |  96 16 128 | 128  0  384 128 | 32 32  0 256  96  192   0  32 | 4 32  64 128  24   0  0 |  4  8  32   0  0 | 6 *  *
xo3oo3ox    .. xo3oo3ox&#zx    32 |  48 48 144 |  32 32  288 288 |  8  0  8  96  72  288  96  72 | 0 12   0  96  36  96 12 |  0  6   0  32  6 | * 8  *
xo3oo .. *b3oo .. oo3ox&#x  &   7 |   6  3  12 |   4  1   18  12 |  0  1  0  12   0   18   4   0 | 0  0   3  12   0   6  0 |  0  0   3   4  0 | * * 64

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