Acronym hin
Name hemipenteract,
demipenteract,
hemitesseractic gyroprism,
tetrahedral altersquarism,
vertex figure of jak,
Gosset polytope 12,1
Field of sections 
 ©
Circumradius sqrt(5/8) = 0.790569
Inradius
wrt. pen 		3/sqrt(40) = 0.474342
Inradius
wrt. hex 		1/sqrt(8) = 0.353553
Vertex figure 
 ©    ©
Lace city
in approx. ASCII-art 
o   O   o	-- x3o3o *b3o (hex)
         
  t   T  	-- o3o3x *b3o (alt. hex)

    \   \   \
     \   \   +-- o3o3o3o (point)
      \   +----- o3x3o3o (rap)
       +-------- o3o3o3x (inv pen)

where:
o = o3o3o (point)
O = o3x3o (oct)
t = x3o3o (tet)
T = o3o3x (dual tet)

t   T		-- x3o3o *b3o (hex)
     
T   t		-- o3o3x *b3o (alt. hex)

   \   \   \
     \   \   +-- o x3o3o (tet)
       \   +---- x o3o3x (inv tepe)
         +------ o x3o3o (tet)

where:
t = x3o3o (tet)
T = o3o3x (dual tet)

+-------- x o o3o (line)
| +------ o x x3o (perp trip)
| | +---- x o o3x (para trip)
| | | +-- o x o3o (perp line)

o   3  		-- o x3o3o (tet)
  P   l		-- x o3o3x (inv tepe)
o   3  		-- o x3o3o (tet)

   \   \   \
     \   \   +-- o3o3o3x (pen)
       \   +---- o3x3o3o (inv rap)
         +------ o3o3o3o (point)

where:
o = o o3o (point)
l = x o3o (line)
3 = o o3x (triangle)
P = x x3o (gyro trip)

 ©  

    x2o    o2x     		-- x3o3o o (tet)
                  
                  
                  
o2x  xo2ox&#x  x2o		-- o3o3x x (inv tepe)
                  
                  
                  
    x2o    o2x     		-- x3o3o o (tet)
Lace hyper city
in approx. ASCII-art 
      o o      
               
               
o o   x x   o o
               
               
      o o      

               
   x o   o x   
               
               
               
   o x   x o
(hex || alternate hex)
Coordinates (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all permutations, all even changes of sign
Volume 13 sqrt(2)/120 = 0.153206
Surface [10+sqrt(5)]/6 = 2.039345
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: firp hex pen pinnip rap
rinah 1610000
radah 1601600
hin 0101600
han 0100016
dah 0016016
hit 000160
)
Dihedral angles
(at margins)
  • at tet between hex and pen:   arccos[-1/sqrt(5)] = 116.565051°
  • at tet between hex and hex:   90°
Face vector 16, 80, 160, 120, 26
Confer
segmentotera:
dihin   bidhin   tedhin   squasquasc   rappy   trafpy   tetaf   triddaf   trippasc  
ambification:
nit  
general polytopal classes:
Wythoffian polytera   partial Stott expansions   segmentotera   fundamental lace prisms   lace simplices   Coxeter-Elte-Gosset polytopes  
analogs:
demihypercube Dn   Gossetic n2,1   Gossetic 1n,2  
External
links 		hedrondude   wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

x3o3o *b3o3o

. . .    . . | 16 ♦ 10 |  30 | 10 20 |  5  5
-------------+----+----+-----+-------+------
x . .    . . |  2 | 80 ♦   6 |  3  6 |  3  2
-------------+----+----+-----+-------+------
x3o .    . . |  3 |  3 | 160 |  1  2 |  2  1
-------------+----+----+-----+-------+------
x3o3o    . . ♦  4 |  6 |   4 | 40  * |  2  0
x3o . *b3o . ♦  4 |  6 |   4 |  * 80 |  1  1
-------------+----+----+-----+-------+------
x3o3o *b3o . ♦  8 | 24 |  32 |  8  8 | 10  *
x3o . *b3o3o ♦  5 | 10 |  10 |  0  5 |  * 16


x3/2o3o *b3o3o

.   . .    . . | 16 ♦ 10 |  30 | 10 20 |  5  5
---------------+----+----+-----+-------+------
x   . .    . . |  2 | 80 ♦   6 |  3  6 |  3  2
---------------+----+----+-----+-------+------
x3/2o .    . . |  3 |  3 | 160 |  1  2 |  2  1
---------------+----+----+-----+-------+------
x3/2o3o    . . ♦  4 |  6 |   4 | 40  * |  2  0
x3/2o . *b3o . ♦  4 |  6 |   4 |  * 80 |  1  1
---------------+----+----+-----+-------+------
x3/2o3o *b3o . ♦  8 | 24 |  32 |  8  8 | 10  *
x3/2o . *b3o3o ♦  5 | 10 |  10 |  0  5 |  * 16


x3o3/2o *b3o3o

. .   .    . . | 16 ♦ 10 |  30 | 10 20 |  5  5
---------------+----+----+-----+-------+------
x .   .    . . |  2 | 80 ♦   6 |  3  6 |  3  2
---------------+----+----+-----+-------+------
x3o   .    . . |  3 |  3 | 160 |  1  2 |  2  1
---------------+----+----+-----+-------+------
x3o3/2o    . . ♦  4 |  6 |   4 | 40  * |  2  0
x3o   . *b3o . ♦  4 |  6 |   4 |  * 80 |  1  1
---------------+----+----+-----+-------+------
x3o3/2o *b3o . ♦  8 | 24 |  32 |  8  8 | 10  *
x3o   . *b3o3o ♦  5 | 10 |  10 |  0  5 |  * 16


x3o3o *b3/2o3o

. . .      . . | 16 ♦ 10 |  30 | 10 20 |  5  5
---------------+----+----+-----+-------+------
x . .      . . |  2 | 80 ♦   6 |  3  6 |  3  2
---------------+----+----+-----+-------+------
x3o .      . . |  3 |  3 | 160 |  1  2 |  2  1
---------------+----+----+-----+-------+------
x3o3o      . . ♦  4 |  6 |   4 | 40  * |  2  0
x3o . *b3/2o . ♦  4 |  6 |   4 |  * 80 |  1  1
---------------+----+----+-----+-------+------
x3o3o *b3/2o . ♦  8 | 24 |  32 |  8  8 | 10  *
x3o . *b3/2o3o ♦  5 | 10 |  10 |  0  5 |  * 16


x3o3o *b3o3/2o

. . .    .   . | 16 ♦ 10 |  30 | 10 20 |  5  5
---------------+----+----+-----+-------+------
x . .    .   . |  2 | 80 ♦   6 |  3  6 |  3  2
---------------+----+----+-----+-------+------
x3o .    .   . |  3 |  3 | 160 |  1  2 |  2  1
---------------+----+----+-----+-------+------
x3o3o    .   . ♦  4 |  6 |   4 | 40  * |  2  0
x3o . *b3o   . ♦  4 |  6 |   4 |  * 80 |  1  1
---------------+----+----+-----+-------+------
x3o3o *b3o   . ♦  8 | 24 |  32 |  8  8 | 10  *
x3o . *b3o3/2o ♦  5 | 10 |  10 |  0  5 |  * 16


o3o3o3o4s

demi( . . . . . ) | 16 ♦ 10 |  30 | 10 20 |  5  5
------------------+----+----+-----+-------+------
      . . . o4s   |  2 | 80 ♦   6 |  3  6 |  3  1
------------------+----+----+-----+-------+------
sefa( . . o3o4s ) |  3 |  3 | 160 |  1  2 |  2  1
------------------+----+----+-----+-------+------
      . . o3o4s   ♦  4 |  6 |   4 | 40  * |  2  0
sefa( . o3o3o4s ) ♦  4 |  6 |   4 |  * 80 |  1  1
------------------+----+----+-----+-------+------
      . o3o3o4s   ♦  8 | 24 |  32 |  8  8 | 10  *
sefa( o3o3o3o4s ) ♦  5 | 10 |  10 |  0  5 |  * 16

starting figure: o3o3o3o4x


s2o3o3o4s

demi( . . . . . ) | 16 ♦  4  6 | 18 12 |  6  4 16  4 | 4 1  5
------------------+----+-------+-------+-------------+-------
      s . 2 . s   |  2 | 32  * ♦  6  0 |  3  0  6  0 | 3 0  2
      . . . o4s   |  2 |  * 48 ♦  2  4 |  1  2  4  2 | 2 1  2
------------------+----+-------+-------+-------------+-------
sefa( s 2 . o4s ) |  3 |  2  1 | 96  * |  1  0  2  0 | 2 0  1
sefa( . . o3o4s ) |  3 |  0  3 |  * 64 |  0  1  1  1 | 1 1  1
------------------+----+-------+-------+-------------+-------
      s 2 . o4s   ♦  4 |  4  2 |  4  0 | 24  *  *  * | 2 0  0
      . . o3o4s   ♦  4 |  0  6 |  0  4 |  * 16  *  * | 1 1  0
sefa( s 2 o3o4s ) ♦  4 |  3  3 |  3  1 |  *  * 64  * | 1 0  1
sefa( . o3o3o4s ) ♦  4 |  0  6 |  0  4 |  *  *  * 16 | 0 1  1
------------------+----+-------+-------+-------------+-------
      s 2 o3o4s   ♦  8 | 12 12 | 24  8 |  6  2  8  0 | 8 *  *
      . o3o3o4s   ♦  8 |  0 24 |  0 32 |  0  8  0  8 | * 2  *
sefa( s2o3o3o4s ) ♦  5 |  4  6 |  6  4 |  0  0  4  1 | * * 16

starting figure: x o3o3o4x


s4o2o3o4s

demi( . . . . . ) | 16 ♦ 1  6  3 |  9 18  3 |  3  6 1 12  8 | 3 2  5
------------------+----+---------+----------+---------------+-------
      s4o . . .   |  2 | 8  *  * ♦  6  0  0 |  3  0 0  6  0 | 3 0  2
      s . 2 . s   |  2 | * 48  * ♦  2  4  0 |  1  2 0  4  2 | 2 1  2
      . . . o4s   |  2 | *  * 24 ♦  0  4  2 |  0  2 1  2  4 | 1 2  2
------------------+----+---------+----------+---------------+-------
sefa( s4o 2 . s ) |  3 | 1  2  0 | 48  *  * |  1  0 0  2  0 | 2 0  1
sefa( s . 2 o4s ) |  3 | 0  2  1 |  * 96  * |  0  1 0  1  1 | 1 1  1
sefa( . . o3o4s ) |  3 | 0  0  3 |  *  * 16 |  0  0 1  0  2 | 0 2  1
------------------+----+---------+----------+---------------+-------
      s4o 2 . s   ♦  4 | 2  4  0 |  4  0  0 | 12  * *  *  * | 2 0  0
      s . 2 o4s   ♦  4 | 0  4  2 |  0  4  0 |  * 24 *  *  * | 1 1  0
      . . o3o4s   ♦  4 | 0  0  6 |  0  0  4 |  *  * 4  *  * | 0 2  0
sefa( s4o 2 o4s ) ♦  4 | 1  4  1 |  2  2  0 |  *  * * 48  * | 1 0  1
sefa( s 2 o3o4s ) ♦  4 | 0  3  3 |  0  3  1 |  *  * *  * 32 | 0 1  1
------------------+----+---------+----------+---------------+-------
      s4o 2 o4s   ♦  8 | 4 16  4 | 16 16  0 |  4  4 0  8  0 | 6 *  *
      s 2 o3o4s   ♦  8 | 0 12 12 |  0 24  8 |  0  6 2  0  8 | * 4  *
sefa( s4o2o3o4s ) ♦  5 | 1  6  3 |  3  6  1 |  0  0 0  3  2 | * * 16

starting figure: x4o o3o4x


xo3oo3ox *b3oo&#x   → height = 1/sqrt(2) = 0.707107
(hex || alternate hex)

o.3o.3o. *b3o.    | 8 * ♦  6  4  0 | 12 12  6  0 | 4 4 12  6  4 0 0 | 1 4 4 1 0
.o3.o3.o *b3.o    | * 8 ♦  0  4  6 |  0  6 12 12 | 0 0  4  6 12 4 4 | 0 4 1 4 1
------------------+-----+----------+-------------+------------------+----------
x. .. ..    ..    | 2 0 | 24  *  * ♦  4  2  0  0 | 2 2  4  1  0 0 0 | 1 2 2 0 0
oo3oo3oo *b3oo&#x | 1 1 |  * 32  * ♦  0  3  3  0 | 0 0  3  3  3 0 0 | 0 3 1 1 0
.. .. .x    ..    | 0 2 |  *  * 24 ♦  0  0  2  4 | 0 0  0  1  4 2 2 | 0 2 0 2 1
------------------+-----+----------+-------------+------------------+----------
x.3o. ..    ..    | 3 0 |  3  0  0 | 32  *  *  * | 1 1  1  0  0 0 0 | 1 1 1 0 0
xo .. ..    ..&#x | 2 1 |  1  2  0 |  * 48  *  * | 0 0  2  1  0 0 0 | 0 2 1 0 0
.. .. ox    ..&#x | 1 2 |  0  2  1 |  *  * 48  * | 0 0  0  1  2 0 0 | 0 2 0 1 0
.. .o3.x    ..    | 0 3 |  0  0  3 |  *  *  * 32 | 0 0  0  0  1 1 1 | 0 1 0 1 1
------------------+-----+----------+-------------+------------------+----------
x.3o.3o.    ..    ♦ 4 0 |  6  0  0 |  4  0  0  0 | 8 *  *  *  * * * | 1 1 0 0 0
x.3o. .. *b3o.    ♦ 4 0 |  6  0  0 |  4  0  0  0 | * 8  *  *  * * * | 1 0 1 0 0
xo3oo ..    ..&#x ♦ 3 1 |  3  3  0 |  1  3  0  0 | * * 32  *  * * * | 0 1 1 0 0
xo .. ox    ..&#x ♦ 2 2 |  1  4  1 |  0  2  2  0 | * *  * 24  * * * | 0 2 0 0 0
.. oo3ox    ..&#x ♦ 1 3 |  0  3  3 |  0  0  3  1 | * *  *  * 32 * * | 0 1 0 1 0
.o3.o3.x    ..    ♦ 0 4 |  0  0  6 |  0  0  0  4 | * *  *  *  * 8 * | 0 1 0 0 1
.. .o3.x *b3.o    ♦ 0 4 |  0  0  6 |  0  0  0  4 | * *  *  *  * * 8 | 0 0 0 1 1
------------------+-----+----------+-------------+------------------+----------
x.3o.3o. *b3o.    ♦ 8 0 | 24  0  0 | 32  0  0  0 | 8 8  0  0  0 0 0 | 1 * * * *
xo3oo3ox    ..&#x ♦ 4 4 |  6 12  6 |  4 12 12  4 | 1 0  4  6  4 1 0 | * 8 * * *
xo3oo .. *b3oo&#x ♦ 4 1 |  6  4  0 |  4  6  0  0 | 0 1  4  0  0 0 0 | * * 8 * *
.. oo3ox *b3oo&#x ♦ 1 4 |  0  4  6 |  0  0  6  4 | 0 0  0  0  4 0 1 | * * * 8 *
.o3.o3.x *b3.o    ♦ 0 8 |  0  0 24 |  0  0  0 32 | 0 0  0  0  0 8 8 | * * * * 1

or
o.3o.3o. *b3o.    & | 16 ♦  6  4 | 12 18 |  4  4 16  6 | 1 4  5
--------------------+----+-------+-------+-------------+-------
x. .. ..    ..      |  2 | 48  * ♦  4  2 |  2  2  4  1 | 1 2  2
oo3oo3oo *b3oo&#x   |  2 |  * 32 ♦  0  6 |  0  0  6  3 | 0 3  2
--------------------+----+-------+-------+-------------+-------
x.3o. ..    ..    & |  3 |  3  0 | 64  * |  1  1  1  0 | 1 1  1
xo .. ..    ..&#x & |  3 |  1  2 |  * 96 |  0  0  2  1 | 0 2  1
--------------------+----+-------+-------+-------------+-------
x.3o.3o.    ..    & ♦  4 |  6  0 |  4  0 | 16  *  *  * | 1 1  0
x.3o. .. *b3o.    & ♦  4 |  6  0 |  4  0 |  * 16  *  * | 1 0  1
xo3oo ..    ..&#x & ♦  4 |  3  3 |  1  3 |  *  * 64  * | 0 1  1
xo .. ox    ..&#x   ♦  4 |  2  4 |  0  4 |  *  *  * 24 | 0 2  0
--------------------+----+-------+-------+-------------+-------
x.3o.3o. *b3o.    & ♦  8 | 24  0 | 32  0 |  8  8  0  0 | 2 *  *
xo3oo3ox    ..&#x   ♦  8 | 12 12 |  8 24 |  2  0  8  6 | * 8  *
xo3oo .. *b3oo&#x & ♦  5 |  6  4 |  4  6 |  0  1  4  0 | * * 16


ooo3oxo3ooo3oox&#xt   → both heights = sqrt(2/5) = 0.632456
(pt || pseudo rap || inv pen)

o..3o..3o..3o..     | 1  * * ♦ 10  0  0  0 | 30  0  0  0  0  0 | 10 20 0  0  0  0  0 0 | 5 5  0 0 0
.o.3.o.3.o.3.o.     | * 10 * ♦  1  6  3  0 |  6  3  6 12  3  0 |  3  6 2  6  6  6  1 0 | 3 2  3 2 0
..o3..o3..o3..o     | *  * 5 ♦  0  0  6  4 |  0  0  0 12 12  6 |  0  0 0  4  4 12  6 4 | 1 0  4 4 1
--------------------+--------+-------------+-------------------+-----------------------+-----------
oo.3oo.3oo.3oo.&#x  | 1  1 0 | 10  *  *  * ♦  6  0  0  0  0  0 |  3  6 0  0  0  0  0 0 | 3 2  0 0 0
... .x. ... ...     | 0  2 0 |  * 30  *  * ♦  1  1  2  2  0  0 |  1  2 1  2  2  1  0 0 | 2 1  1 1 0
.oo3.oo3.oo3.oo&#x  | 0  1 1 |  *  * 30  * ♦  0  0  0  4  2  0 |  0  0 0  2  2  4  1 0 | 1 0  2 2 0
... ... ... ..x     | 0  0 2 |  *  *  * 10 ♦  0  0  0  0  3  3 |  0  0 0  0  0  3  3 3 | 0 0  1 3 1
--------------------+--------+-------------+-------------------+-----------------------+-----------
... ox. ... ...&#x  | 1  2 0 |  2  1  0  0 | 30  *  *  *  *  * |  1  2 0  0  0  0  0 0 | 2 1  0 0 0
.o.3.x. ... ...     | 0  3 0 |  0  3  0  0 |  * 10  *  *  *  * |  1  0 2  0  0  0  0 0 | 2 0  1 0 0
... .x.3.o. ...     | 0  3 0 |  0  3  0  0 |  *  * 20  *  *  * |  0  1 1  0  1  0  0 0 | 1 1  0 1 0
... .xo ... ...&#x  | 0  2 1 |  0  1  2  0 |  *  *  * 60  *  * |  0  0 0  1  1  1  0 0 | 1 0  1 1 0
... ... ... .ox&#x  | 0  1 2 |  0  0  2  1 |  *  *  *  * 30  * |  0  0 0  0  0  2  1 0 | 0 0  1 2 0
... ... ..o3..x     | 0  0 3 |  0  0  0  3 |  *  *  *  *  * 10 |  0  0 0  0  0  0  1 2 | 0 0  0 2 1
--------------------+--------+-------------+-------------------+-----------------------+-----------
oo.3ox. ... ...&#x  ♦ 1  3 0 |  3  3  0  0 |  3  1  0  0  0  0 | 10  * *  *  *  *  * * | 2 0  0 0 0
... ox.3oo. ...&#x  ♦ 1  3 0 |  3  3  0  0 |  3  0  1  0  0  0 |  * 20 *  *  *  *  * * | 1 1  0 0 0
... .x.3.o.3.o.     ♦ 0  4 0 |  0  6  0  0 |  0  0  4  0  0  0 |  *  * 5  *  *  *  * * | 0 1  0 1 0
.oo3.xo ... ...&#x  ♦ 0  3 1 |  0  3  3  0 |  0  1  0  3  0  0 |  *  * * 20  *  *  * * | 1 0  1 0 0
... .xo3.oo ...&#x  ♦ 0  3 1 |  0  3  3  0 |  0  0  1  3  0  0 |  *  * *  * 20  *  * * | 1 0  0 1 0
... .xo ... .ox&#x  ♦ 0  2 2 |  0  1  4  1 |  0  0  0  2  2  0 |  *  * *  *  * 30  * * | 0 0  1 1 0
... ... .oo3.ox&#x  ♦ 0  1 3 |  0  0  3  3 |  0  0  0  0  3  1 |  *  * *  *  *  * 10 * | 0 0  0 2 0
... ..o3..o3..x     ♦ 0  0 4 |  0  0  0  6 |  0  0  0  0  0  4 |  *  * *  *  *  *  * 5 | 0 0  0 1 1
--------------------+--------+-------------+-------------------+-----------------------+-----------
ooo3oxo3ooo ...&#xt ♦ 1  6 1 |  6 12  6  0 | 12  4  4 12  0  0 |  4  4 0  4  4  0  0 0 | 5 *  * * *
... ox.3oo.3oo.&#x  ♦ 1  4 0 |  4  6  0  0 |  6  0  4  0  0  0 |  0  4 1  0  0  0  0 0 | * 5  * * *
.oo3.xo ... .ox&#x  ♦ 0  3 2 |  0  3  6  1 |  0  1  0  6  3  0 |  0  0 0  2  0  3  0 0 | * * 10 * *
... .xo3.oo3.ox&#x  ♦ 0  4 4 |  0  6 12  6 |  0  0  4 12 12  4 |  0  0 1  0  4  6  4 1 | * *  * 5 *
..o3..o3..o3..x     ♦ 0  0 5 |  0  0  0 10 |  0  0  0  0  0 10 |  0  0 0  0  0  0  0 5 | * *  * * 1


xox3ooo3oxo oxo&#xt   → both heights = 1/2
(tet || inv pseudo tepe || tet)

o..3o..3o.. o..     | 4 * * ♦ 3  6 1  0 0  0 0 | 3 12  6  3  6 0  0  0  0 0 | 1 6  6  6 2  6  3 0 0  0  0 0 0 | 2 3 3 2 0 0
.o.3.o.3.o. .o.     | * 8 * ♦ 0  3 0  3 1  3 0 | 0  3  6  3  3 3  3  6  3 0 | 0 1  3  3 3  6  3 1 1  3  3 3 0 | 1 1 3 3 1 1
..o3..o3..o ..o     | * * 4 ♦ 0  0 1  0 0  6 3 | 0  0  0  0  6 0 12  6  3 3 | 0 0  0  0 0  6  3 0 6  6  6 2 1 | 0 0 3 2 2 3
--------------------+-------+------------------+----------------------------+---------------------------------+------------
x.. ... ... ...     | 2 0 0 | 6  * *  * *  * * ♦ 2  4  0  0  0 0  0  0  0 0 | 1 4  2  2 0  0  0 0 0  0  0 0 0 | 2 2 1 0 0 0
oo.3oo.3oo. oo.&#x  | 1 1 0 | * 24 *  * *  * * ♦ 0  2  2  1  1 0  0  0  0 0 | 0 1  2  2 1  2  1 0 0  0  0 0 0 | 1 1 2 1 0 0
o.o3o.o3o.o o.o&#x  | 1 0 1 | *  * 4  * *  * * ♦ 0  0  0  0  6 0  0  0  0 0 | 0 0  0  0 0  6  3 0 0  0  0 0 0 | 0 0 3 2 0 0
... ... .x. ...     | 0 2 0 | *  * * 12 *  * * ♦ 0  0  2  0  0 2  0  2  0 0 | 0 0  1  0 2  2  0 1 0  1  0 2 0 | 1 0 1 2 1 0
... ... ... .x.     | 0 2 0 | *  * *  * 4  * * ♦ 0  0  0  3  0 0  0  0  3 0 | 0 0  0  3 0  0  3 0 0  0  3 0 0 | 0 1 3 0 0 1
.oo3.oo3.oo .oo&#x  | 0 1 1 | *  * *  * * 24 * ♦ 0  0  0  0  1 0  2  2  1 0 | 0 0  0  0 0  2  1 0 1  2  2 1 0 | 0 0 2 1 1 1
..x ... ... ...     | 0 0 2 | *  * *  * *  * 6 ♦ 0  0  0  0  0 0  4  0  0 2 | 0 0  0  0 0  0  0 0 4  2  2 0 1 | 0 0 1 0 2 2
--------------------+-------+------------------+----------------------------+---------------------------------+------------
x..3o.. ... ...     | 3 0 0 | 3  0 0  0 0  0 0 | 4  *  *  *  * *  *  *  * * | 1 2  0  0 0  0  0 0 0  0  0 0 0 | 2 1 0 0 0 0
xo. ... ... ...&#x  | 2 1 0 | 1  2 0  0 0  0 0 | * 24  *  *  * *  *  *  * * | 0 1  1  1 0  0  0 0 0  0  0 0 0 | 1 1 1 0 0 0
... ... ox. ...&#x  | 1 2 0 | 0  2 0  1 0  0 0 | *  * 24  *  * *  *  *  * * | 0 0  1  0 1  1  0 0 0  0  0 0 0 | 1 0 1 1 0 0
... ... ... ox.&#x  | 1 2 0 | 0  2 0  0 1  0 0 | *  *  * 12  * *  *  *  * * | 0 0  0  2 0  0  1 0 0  0  0 0 0 | 0 1 2 0 0 0
ooo3ooo3ooo ooo&#x  | 1 1 1 | 0  1 1  0 0  1 0 | *  *  *  * 24 *  *  *  * * | 0 0  0  0 0  2  1 0 0  0  0 0 0 | 0 0 2 1 0 0
... .o.3.x. ...     | 0 3 0 | 0  0 0  3 0  0 0 | *  *  *  *  * 8  *  *  * * | 0 0  0  0 1  0  0 1 0  0  0 1 0 | 1 0 0 1 1 0
.ox ... ... ...&#x  | 0 1 2 | 0  0 0  0 0  2 1 | *  *  *  *  * * 24  *  * * | 0 0  0  0 0  0  0 0 1  1  1 0 0 | 0 0 1 0 1 1
... ... .xo ...&#x  | 0 2 1 | 0  0 0  1 0  2 0 | *  *  *  *  * *  * 24  * * | 0 0  0  0 0  1  0 0 0  1  0 1 0 | 0 0 1 1 1 0
... ... ... .xo&#x  | 0 2 1 | 0  0 0  0 1  2 0 | *  *  *  *  * *  *  * 12 * | 0 0  0  0 0  0  1 0 0  0  2 0 0 | 0 0 2 0 0 1
..x3..o ... ...     | 0 0 3 | 0  0 0  0 0  0 3 | *  *  *  *  * *  *  *  * 4 | 0 0  0  0 0  0  0 0 2  0  0 0 1 | 0 0 0 0 2 1
--------------------+-------+------------------+----------------------------+---------------------------------+------------
x..3o..3o.. ...     ♦ 4 0 0 | 6  0 0  0 0  0 0 | 4  0  0  0  0 0  0  0  0 0 | 1 *  *  * *  *  * * *  *  * * * | 2 0 0 0 0 0
xo.3oo. ... ...&#x  ♦ 3 1 0 | 3  3 0  0 0  0 0 | 1  3  0  0  0 0  0  0  0 0 | * 8  *  * *  *  * * *  *  * * * | 1 1 0 0 0 0
xo. ... ox. ...&#x  ♦ 2 2 0 | 1  4 0  1 0  0 0 | 0  2  2  0  0 0  0  0  0 0 | * * 12  * *  *  * * *  *  * * * | 1 0 1 0 0 0
xo. ... ... ox.&#x  ♦ 2 2 0 | 1  4 0  0 1  0 0 | 0  2  0  2  0 0  0  0  0 0 | * *  * 12 *  *  * * *  *  * * * | 0 1 1 0 0 0
... oo.3ox. ...&#x  ♦ 1 3 0 | 0  3 0  3 0  0 0 | 0  0  3  0  0 1  0  0  0 0 | * *  *  * 8  *  * * *  *  * * * | 1 0 0 1 0 0
... ... oxo ...&#x  ♦ 1 2 1 | 0  2 1  1 0  2 0 | 0  0  1  0  2 0  0  1  0 0 | * *  *  * * 24  * * *  *  * * * | 0 0 1 1 0 0
... ... ... oxo&#x  ♦ 1 2 1 | 0  2 1  0 1  2 0 | 0  0  0  1  2 0  0  0  1 0 | * *  *  * *  * 12 * *  *  * * * | 0 0 2 0 0 0
.o.3.o.3.x. ...     ♦ 0 4 0 | 0  0 0  6 0  0 0 | 0  0  0  0  0 4  0  0  0 0 | * *  *  * *  *  * 2 *  *  * * * | 1 0 0 0 1 0
.ox3.oo ... ...&#x  ♦ 0 1 3 | 0  0 0  0 0  3 3 | 0  0  0  0  0 0  3  0  0 1 | * *  *  * *  *  * * 8  *  * * * | 0 0 0 0 1 1
.ox ... .xo ...&#x  ♦ 0 2 2 | 0  0 0  1 0  4 1 | 0  0  0  0  0 0  2  2  0 0 | * *  *  * *  *  * * * 12  * * * | 0 0 1 0 1 0
.ox ... ... .xo&#x  ♦ 0 2 2 | 0  0 0  0 1  4 1 | 0  0  0  0  0 0  2  0  2 0 | * *  *  * *  *  * * *  * 12 * * | 0 0 1 0 0 1
... .oo3.xo ...&#x  ♦ 0 3 1 | 0  0 0  3 0  3 0 | 0  0  0  0  0 1  0  3  0 0 | * *  *  * *  *  * * *  *  * 8 * | 0 0 0 1 1 0
..x3..o3..o ...     ♦ 0 0 4 | 0  0 0  0 0  0 6 | 0  0  0  0  0 0  0  0  0 4 | * *  *  * *  *  * * *  *  * * 1 | 0 0 0 0 2 0
--------------------+-------+------------------+----------------------------+---------------------------------+------------
xo.3oo.3ox. ...&#x  ♦ 4 4 0 | 6 12 0  6 0  0 0 | 4 12 12  0  0 4  0  0  0 0 | 1 4  6  0 4  0  0 1 0  0  0 0 0 | 2 * * * * *
xo.3oo. ... ox.&#x  ♦ 3 2 0 | 3  6 0  0 1  0 0 | 1  6  0  3  0 0  0  0  0 0 | 0 2  0  3 0  0  0 0 0  0  0 0 0 | * 4 * * * *
xox ... oxo oxo&#xt ♦ 2 4 2 | 1  8 2  2 2  8 1 | 0  4  4  4  8 0  4  4  4 0 | 0 0  2  2 0  4  4 0 0  2  2 0 0 | * * 6 * * *
... ooo3oxo ...&#x  ♦ 1 3 1 | 0  3 1  3 0  3 0 | 0  0  3  0  3 1  0  3  0 0 | 0 0  0  0 1  3  0 0 0  0  0 1 0 | * * * 8 * *
.ox3.oo3.xo ...&#x  ♦ 0 4 4 | 0  0 0  6 0 12 6 | 0  0  0  0  0 4 12 12  0 4 | 0 0  0  0 0  0  0 1 4  6  0 4 1 | * * * * 2 *
.ox3.oo ... .xo&#x  ♦ 0 2 3 | 0  0 0  0 1  6 3 | 0  0  0  0  0 0  6  0  3 1 | 0 0  0  0 0  0  0 0 2  0  3 0 0 | * * * * * 4

or
o..3o..3o.. o..     & | 8 * ♦  3  6 1  0 0 | 3 12  6  3  6 0 | 1  6  6  6  2  6  3 0 | 2 3 3 2
.o.3.o.3.o. .o.       | * 8 ♦  0  6 0  3 1 | 0  6 12  6  3 3 | 0  2  6  6  6  6  3 1 | 2 2 3 3
----------------------+-----+--------------+-----------------+-----------------------+--------
x.. ... ... ...     & | 2 0 | 12  * *  * * ♦ 2  4  0  0  0 0 | 1  4  2  2  0  0  0 0 | 2 2 1 0
oo.3oo.3oo. oo.&#x  & | 1 1 |  * 48 *  * * ♦ 0  2  2  1  1 0 | 0  1  2  2  1  2  1 0 | 1 1 2 1
o.o3o.o3o.o o.o&#x    | 2 0 |  *  * 4  * * ♦ 0  0  0  0  6 0 | 0  0  0  0  0  6  3 0 | 0 0 3 2
... ... .x. ...       | 0 2 |  *  * * 12 * ♦ 0  0  4  0  0 2 | 0  0  2  0  4  2  0 1 | 2 0 1 2
... ... ... .x.       | 0 2 |  *  * *  * 4 ♦ 0  0  0  6  0 0 | 0  0  0  6  0  0  3 0 | 0 2 3 0
----------------------+-----+--------------+-----------------+-----------------------+--------
x..3o.. ... ...     & | 3 0 |  3  0 0  0 0 | 8  *  *  *  * * | 1  2  0  0  0  0  0 0 | 2 1 0 0
xo. ... ... ...&#x  & | 2 1 |  1  2 0  0 0 | * 48  *  *  * * | 0  1  1  1  0  0  0 0 | 1 1 1 0
... ... ox. ...&#x  & | 1 2 |  0  2 0  1 0 | *  * 48  *  * * | 0  0  1  0  1  1  0 0 | 1 0 1 1
... ... ... ox.&#x  & | 1 2 |  0  2 0  0 1 | *  *  * 24  * * | 0  0  0  2  0  0  1 0 | 0 1 2 0
ooo3ooo3ooo ooo&#x    | 2 1 |  0  2 1  0 0 | *  *  *  * 24 * | 0  0  0  0  0  2  1 0 | 0 0 2 1
... .o.3.x. ...       | 0 3 |  0  0 0  3 0 | *  *  *  *  * 8 | 0  0  0  0  2  0  0 1 | 2 0 0 1
----------------------+-----+--------------+-----------------+-----------------------+--------
x..3o..3o.. ...     & ♦ 4 0 |  6  0 0  0 0 | 4  0  0  0  0 0 | 2  *  *  *  *  *  * * | 2 0 0 0
xo.3oo. ... ...&#x  & ♦ 3 1 |  3  3 0  0 0 | 1  3  0  0  0 0 | * 16  *  *  *  *  * * | 1 1 0 0
xo. ... ox. ...&#x  & ♦ 2 2 |  1  4 0  1 0 | 0  2  2  0  0 0 | *  * 24  *  *  *  * * | 1 0 1 0
xo. ... ... ox.&#x  & ♦ 2 2 |  1  4 0  0 1 | 0  2  0  2  0 0 | *  *  * 24  *  *  * * | 0 1 1 0
... oo.3ox. ...&#x  & ♦ 1 3 |  0  3 0  3 0 | 0  0  3  0  0 1 | *  *  *  * 16  *  * * | 1 0 0 1
... ... oxo ...&#x    ♦ 2 2 |  0  4 1  1 0 | 0  0  2  0  2 0 | *  *  *  *  * 24  * * | 0 0 1 1
... ... ... oxo&#x    ♦ 2 2 |  0  4 1  0 1 | 0  0  0  2  2 0 | *  *  *  *  *  * 12 * | 0 0 2 0
.o.3.o.3.x. ...       ♦ 0 4 |  0  0 0  6 0 | 0  0  0  0  0 4 | *  *  *  *  *  *  * 2 | 2 0 0 0
----------------------+-----+--------------+-----------------+-----------------------+--------
xo.3oo.3ox. ...&#x  & ♦ 4 4 |  6 12 0  6 0 | 4 12 12  0  0 4 | 1  4  6  0  4  0  0 1 | 4 * * *
xo.3oo. ... ox.&#x  & ♦ 3 2 |  3  6 0  0 1 | 1  6  0  3  0 0 | 0  2  0  3  0  0  0 0 | * 8 * *
xox ... oxo oxo&#xt   ♦ 4 4 |  2 16 2  2 2 | 0  8  8  8  8 0 | 0  0  4  4  0  4  4 0 | * * 6 *
... ooo3oxo ...&#x    ♦ 2 3 |  0  6 1  3 0 | 0  0  6  0  3 1 | 0  0  0  0  2  3  0 0 | * * * 8


xo3oo3ox xo ox&#zx   → height = 0
(tegum sum of 2 mutually inverted, lacings-orthogonal tepes)

o.3o.3o. o. o.     | 8 * ♦  3 1  6  0 0 | 3 12  6  6  3 0 | 1  6  6  6  2  6  3 0 | 2 3 3 2
.o3.o3.o .o .o     | * 8 ♦  0 0  6  3 1 | 0  6 12  3  6 3 | 0  2  6  6  6  6  3 1 | 2 2 3 3
-------------------+-----+--------------+-----------------+-----------------------+--------
x. .. .. .. ..     | 2 0 | 12 *  *  * * ♦ 2  4  0  0  0 0 | 1  4  2  2  0  0  0 0 | 2 2 1 0
.. .. .. x. ..     | 2 0 |  * 4  *  * * ♦ 0  0  0  6  0 0 | 0  0  0  0  0  6  3 0 | 0 0 3 2
oo3oo3oo oo oo&#x  | 1 1 |  * * 48  * * ♦ 0  2  2  1  1 0 | 0  1  2  2  1  2  1 0 | 1 1 2 1
.. .. .x .. ..     | 0 2 |  * *  * 12 * ♦ 0  0  4  0  0 2 | 0  0  2  0  4  2  0 1 | 2 0 1 2
.. .. .. .. .x     | 0 2 |  * *  *  * 4 ♦ 0  0  0  0  6 0 | 0  0  0  6  0  0  3 0 | 0 2 3 0
-------------------+-----+--------------+-----------------+-----------------------+--------
x.3o. .. .. ..     | 3 0 |  3 0  0  0 0 | 8  *  *  *  * * | 1  2  0  0  0  0  0 0 | 2 1 0 0
xo .. .. .. ..&#x  | 2 1 |  1 0  2  0 0 | * 48  *  *  * * | 0  1  1  1  0  0  0 0 | 1 1 1 0
.. .. ox .. ..&#x  | 1 2 |  0 0  2  1 0 | *  * 48  *  * * | 0  0  1  0  1  1  0 0 | 1 0 1 1
.. .. .. xo ..&#x  | 2 1 |  0 1  2  0 0 | *  *  * 24  * * | 0  0  0  0  0  2  1 0 | 0 0 2 1
.. .. .. .. ox&#x  | 1 2 |  0 0  2  0 1 | *  *  *  * 24 * | 0  0  0  2  0  0  1 0 | 0 1 2 0
.. .o3.x .. ..     | 0 3 |  0 0  0  3 0 | *  *  *  *  * 8 | 0  0  0  0  2  0  0 1 | 2 0 0 1
-------------------+-----+--------------+-----------------+-----------------------+--------
x.3o.3o. .. ..     ♦ 4 0 |  6 0  0  0 0 | 4  0  0  0  0 0 | 2  *  *  *  *  *  * * | 2 0 0 0
xo3oo .. .. ..&#x  ♦ 3 1 |  3 0  3  0 0 | 1  3  0  0  0 0 | * 16  *  *  *  *  * * | 1 1 0 0
xo .. ox .. ..&#x  ♦ 2 2 |  1 0  4  1 0 | 0  2  2  0  0 0 | *  * 24  *  *  *  * * | 1 0 1 0
xo .. .. .. ox&#x  ♦ 2 2 |  1 0  4  0 1 | 0  2  0  0  2 0 | *  *  * 24  *  *  * * | 0 1 1 0
.. oo3ox .. ..&#x  ♦ 1 3 |  0 0  3  3 0 | 0  0  3  0  0 1 | *  *  *  * 16  *  * * | 1 0 0 1
.. .. ox xo ..&#x  ♦ 2 2 |  0 1  4  1 0 | 0  0  2  2  0 0 | *  *  *  *  * 24  * * | 0 0 1 1
.. .. .. xo ox&#x  ♦ 2 2 |  0 1  4  0 1 | 0  0  0  2  2 0 | *  *  *  *  *  * 12 * | 0 0 2 0
.o3.o3.x .. ..     ♦ 0 4 |  0 0  0  6 0 | 0  0  0  0  0 4 | *  *  *  *  *  *  * 2 | 2 0 0 0
-------------------+-----+--------------+-----------------+-----------------------+--------
xo3oo3ox .. ..&#x  ♦ 4 4 |  6 0 12  6 0 | 4 12 12  0  0 4 | 1  4  6  0  4  0  0 1 | 4 * * *
xo3oo .. .. ox&#x  ♦ 3 2 |  3 0  6  0 1 | 1  6  0  0  3 0 | 0  2  0  3  0  0  0 0 | * 8 * *
xo .. ox xo ox&#zx ♦ 4 4 |  2 2 16  2 2 | 0  8  8  8  8 0 | 0  0  4  4  0  4  4 0 | * * 6 *
.. oo3ox xo ..&#x  ♦ 2 3 |  0 1  6  3 0 | 0  0  6  3  0 1 | 0  0  0  0  2  3  0 0 | * * * 8

or
o.3o.3o. o. o.     & | 16 ♦  3 1  6 |  3 18  9 | 1  8  6 12  3 | 2  5 3
---------------------+----+---------+----------+---------------+-------
x. .. .. .. ..     & |  2 | 24 *  * ♦  2  4  0 | 1  4  2  2  0 | 2  2 1
.. .. .. x. ..     & |  2 |  * 8  * ♦  0  0  6 | 0  0  0  6  3 | 0  2 3
oo3oo3oo oo oo&#x    |  2 |  * * 48 ♦  0  4  2 | 0  2  2  4  1 | 1  2 2
---------------------+----+---------+----------+---------------+-------
x.3o. .. .. ..     & |  3 |  3 0  0 | 16  *  * | 1  2  0  0  0 | 2  1 0
xo .. .. .. ..&#x  & |  3 |  1 0  2 |  * 96  * | 0  1  1  1  0 | 1  1 1
.. .. .. xo ..&#x  & |  3 |  0 1  2 |  *  * 48 | 0  0  0  2  1 | 0  1 2
---------------------+----+---------+----------+---------------+-------
x.3o.3o. .. ..     & ♦  4 |  6 0  0 |  4  0  0 | 4  *  *  *  * | 2  0 0
xo3oo .. .. ..&#x  & ♦  4 |  3 0  3 |  1  3  0 | * 32  *  *  * | 1  1 0
xo .. ox .. ..&#x    ♦  4 |  2 0  4 |  0  4  0 | *  * 24  *  * | 1  0 1
xo .. .. .. ox&#x  & ♦  4 |  1 1  4 |  0  2  2 | *  *  * 48  * | 0  1 1
.. .. .. xo ox&#x    ♦  4 |  0 2  4 |  0  0  4 | *  *  *  * 12 | 0  0 2
---------------------+----+---------+----------+---------------+-------
xo3oo3ox .. ..&#x    ♦  8 | 12 0 12 |  8 24  0 | 2  8  6  0  0 | 4  * *
xo3oo .. .. ox&#x  & ♦  5 |  3 1  6 |  1  6  3 | 0  2  0  3  0 | * 16 *
xo .. ox xo ox&#zx   ♦  8 |  4 4 16 |  0 16 16 | 0  0  4  8  4 | *  * 6


xoxo oxox oxoo3ooxo&#xt   → all heights = 1/sqrt(6) = 0.408248
(line || pseudo perp trip || pseudo para trip || perp line)

o... o... o...3o...     | 2 * * * ♦ 1  6 3 0 0  0 0 0 0  0 0 | 6 3  6 12 3 0  0  0  0  0  0 0 0 0 0  0 | 3 6 2  6  6  6 1 0 0 0  0  0  0 0 0 0 0 | 2 3 3 2 0 0 0
.o.. .o.. .o..3.o..     | * 6 * * ♦ 0  2 0 1 2  4 1 0 0  0 0 | 1 2  4  4 0 1  2  4  4  2  4 2 0 0 0  0 | 1 2 2  4  4  2 0 2 2 2  2  4  2 1 0 0 0 | 1 2 2 2 2 1 0
..o. ..o. ..o.3..o.     | * * 6 * ♦ 0  0 1 0 0  4 0 1 2  2 0 | 0 0  0  4 2 0  4  2  2  4  4 0 1 2 1  4 | 0 0 0  2  2  4 1 2 2 2  4  2  4 0 1 2 2 | 0 2 1 2 2 2 1
...o ...o ...o3...o     | * * * 2 ♦ 0  0 0 0 0  0 3 0 0  6 1 | 0 0  0  0 0 0  0  0  0  0 12 3 0 3 6  6 | 0 0 0  0  0  0 0 0 0 0  6  6  6 1 3 6 2 | 0 0 0 2 3 3 2
------------------------+---------+--------------------------+-----------------------------------------+-----------------------------------------+--------------
x... .... .... ....     | 2 0 0 0 | 1  * * * *  * * * *  * * ♦ 6 0  0  0 0 0  0  0  0  0  0 0 0 0 0  0 | 3 6 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0 | 2 0 3 0 0 0 0
oo.. oo.. oo..3oo..&#x  | 1 1 0 0 | * 12 * * *  * * * *  * * ♦ 1 1  2  2 0 0  0  0  0  0  0 0 0 0 0  0 | 1 2 1  2  2  1 0 0 0 0  0  0  0 0 0 0 0 | 1 1 2 1 0 0 0
o.o. o.o. o.o.3o.o.&#x  | 1 0 1 0 | *  * 6 * *  * * * *  * * ♦ 0 0  0  4 2 0  0  0  0  0  0 0 0 0 0  0 | 0 0 0  2  2  4 1 0 0 0  0  0  0 0 0 0 0 | 0 2 1 2 0 0 0
.... .x.. .... ....     | 0 2 0 0 | *  * * 3 *  * * * *  * * ♦ 0 2  0  0 0 0  0  4  0  0  0 0 0 0 0  0 | 1 0 0  4  0  0 0 2 0 2  0  0  0 0 0 0 0 | 0 2 2 0 0 1 0
.... .... .x.. ....     | 0 2 0 0 | *  * * * 6  * * * *  * * ♦ 0 0  2  0 0 1  0  0  2  0  0 1 0 0 0  0 | 0 1 2  0  2  0 0 0 1 0  0  2  0 1 0 0 0 | 1 0 1 2 1 0 0
.oo. .oo. .oo.3.oo.&#x  | 0 1 1 0 | *  * * * * 24 * * *  * * ♦ 0 0  0  1 0 0  1  1  1  1  1 0 0 0 0  0 | 0 0 0  1  1  1 0 1 1 1  1  1  1 0 0 0 0 | 0 1 1 1 1 1 0
.o.o .o.o .o.o3.o.o&#x  | 0 1 0 1 | *  * * * *  * 6 * *  * * ♦ 0 0  0  0 0 0  0  0  0  0  4 2 0 0 0  0 | 0 0 0  0  0  0 0 0 0 0  2  4  2 1 0 0 0 | 0 0 0 2 2 1 0
..x. .... .... ....     | 0 0 2 0 | *  * * * *  * * 3 *  * * ♦ 0 0  0  0 0 0  4  0  0  0  0 0 0 2 0  0 | 0 0 0  0  0  0 0 2 2 0  4  0  0 0 1 0 0 | 0 0 1 0 2 2 0
.... .... .... ..x.     | 0 0 2 0 | *  * * * *  * * * 6  * * ♦ 0 0  0  0 1 0  0  0  0  2  0 0 1 0 0  2 | 0 0 0  0  0  2 1 0 0 1  0  0  2 0 0 1 2 | 0 1 0 2 0 1 1
..oo ..oo ..oo3..oo&#x  | 0 0 1 1 | *  * * * *  * * * * 12 * ♦ 0 0  0  0 0 0  0  0  0  0  2 0 0 1 1  2 | 0 0 0  0  0  0 0 0 0 0  2  1  2 0 1 2 1 | 0 0 0 1 1 2 1
.... ...x .... ....     | 0 0 0 2 | *  * * * *  * * * *  * 1 ♦ 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 0  0  0  0 0 3 6 0 | 0 0 0 0 0 3 2
------------------------+---------+--------------------------+-----------------------------------------+-----------------------------------------+--------------
xo.. .... .... ....&#x  | 2 1 0 0 | 1  2 0 0 0  0 0 0 0  0 0 | 6 *  *  * * *  *  *  *  *  * * * * *  * | 1 2 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0 | 1 0 2 0 0 0 0
.... ox.. .... ....&#x  | 1 2 0 0 | 0  2 0 1 0  0 0 0 0  0 0 | * 6  *  * * *  *  *  *  *  * * * * *  * | 1 0 0  2  0  0 0 0 0 0  0  0  0 0 0 0 0 | 0 1 2 0 0 0 0
.... .... ox.. ....&#x  | 1 2 0 0 | 0  2 0 0 1  0 0 0 0  0 0 | * * 12  * * *  *  *  *  *  * * * * *  * | 0 1 1  0  1  0 0 0 0 0  0  0  0 0 0 0 0 | 1 0 1 1 0 0 0
ooo. ooo. ooo.3ooo.&#x  | 1 1 1 0 | 0  1 1 0 0  1 0 0 0  0 0 | * *  * 24 * *  *  *  *  *  * * * * *  * | 0 0 0  1  1  1 0 0 0 0  0  0  0 0 0 0 0 | 0 1 1 1 0 0 0
.... .... .... o.x.&#x  | 1 0 2 0 | 0  0 2 0 0  0 0 0 1  0 0 | * *  *  * 6 *  *  *  *  *  * * * * *  * | 0 0 0  0  0  2 1 0 0 0  0  0  0 0 0 0 0 | 0 1 0 2 0 0 0
.... .... .x..3.o..     | 0 3 0 0 | 0  0 0 0 3  0 0 0 0  0 0 | * *  *  * * 2  *  *  *  *  * * * * *  * | 0 0 2  0  0  0 0 0 0 0  0  0  0 1 0 0 0 | 1 0 0 2 0 0 0
.ox. .... .... ....&#x  | 0 1 2 0 | 0  0 0 0 0  2 0 1 0  0 0 | * *  *  * * * 12  *  *  *  * * * * *  * | 0 0 0  0  0  0 0 1 1 0  1  0  0 0 0 0 0 | 0 0 1 0 1 1 0
.... .xo. .... ....&#x  | 0 2 1 0 | 0  0 0 1 0  2 0 0 0  0 0 | * *  *  * * *  * 12  *  *  * * * * *  * | 0 0 0  1  0  0 0 1 0 1  0  0  0 0 0 0 0 | 0 1 1 0 0 1 0
.... .... .xo. ....&#x  | 0 2 1 0 | 0  0 0 0 1  2 0 0 0  0 0 | * *  *  * * *  *  * 12  *  * * * * *  * | 0 0 0  0  1  0 0 0 1 0  0  1  0 0 0 0 0 | 0 0 1 1 1 0 0
.... .... .... .ox.&#x  | 0 1 2 0 | 0  0 0 0 0  2 0 0 1  0 0 | * *  *  * * *  *  *  * 12  * * * * *  * | 0 0 0  0  0  1 0 0 0 1  0  0  1 0 0 0 0 | 0 1 0 1 0 1 0
.ooo .ooo .ooo3.ooo&#x  | 0 1 1 1 | 0  0 0 0 0  1 1 0 0  1 0 | * *  *  * * *  *  *  *  * 24 * * * *  * | 0 0 0  0  0  0 0 0 0 0  1  1  1 0 0 0 0 | 0 0 0 1 1 1 0
.... .... .x.o ....&#x  | 0 2 0 1 | 0  0 0 0 1  0 2 0 0  0 0 | * *  *  * * *  *  *  *  *  * 6 * * *  * | 0 0 0  0  0  0 0 0 0 0  0  2  0 1 0 0 0 | 0 0 0 2 1 0 0
.... .... ..o.3..x.     | 0 0 3 0 | 0  0 0 0 0  0 0 0 3  0 0 | * *  *  * * *  *  *  *  *  * * 2 * *  * | 0 0 0  0  0  0 1 0 0 0  0  0  0 0 0 0 2 | 0 0 0 2 0 0 1
..xo .... .... ....&#x  | 0 0 2 1 | 0  0 0 0 0  0 0 1 0  2 0 | * *  *  * * *  *  *  *  *  * * * 6 *  * | 0 0 0  0  0  0 0 0 0 0  2  0  0 0 1 0 0 | 0 0 0 0 1 2 0
.... ..ox .... ....&#x  | 0 0 1 2 | 0  0 0 0 0  0 0 0 0  2 1 | * *  *  * * *  *  *  *  *  * * * * 6  * | 0 0 0  0  0  0 0 0 0 0  0  0  0 0 1 2 0 | 0 0 0 0 0 2 1
.... .... .... ..xo&#x  | 0 0 2 1 | 0  0 0 0 0  0 0 0 1  2 0 | * *  *  * * *  *  *  *  *  * * * * * 12 | 0 0 0  0  0  0 0 0 0 0  0  0  1 0 0 1 1 | 0 0 0 1 0 1 1
------------------------+---------+--------------------------+-----------------------------------------+-----------------------------------------+--------------
xo.. ox.. .... ....&#x  ♦ 2 2 0 0 | 1  4 0 1 0  0 0 0 0  0 0 | 2 2  0  0 0 0  0  0  0  0  0 0 0 0 0  0 | 3 * *  *  *  * * * * *  *  *  * * * * * | 0 0 2 0 0 0 0
xo.. .... ox.. ....&#x  ♦ 2 2 0 0 | 1  4 0 0 1  0 0 0 0  0 0 | 2 0  2  0 0 0  0  0  0  0  0 0 0 0 0  0 | * 6 *  *  *  * * * * *  *  *  * * * * * | 1 0 1 0 0 0 0
.... .... ox..3oo..&#x  ♦ 1 3 0 0 | 0  3 0 0 3  0 0 0 0  0 0 | 0 0  3  0 0 1  0  0  0  0  0 0 0 0 0  0 | * * 4  *  *  * * * * *  *  *  * * * * * | 1 0 0 1 0 0 0
.... oxo. .... ....&#x  ♦ 1 2 1 0 | 0  2 1 1 0  2 0 0 0  0 0 | 0 1  0  2 0 0  0  1  0  0  0 0 0 0 0  0 | * * * 12  *  * * * * *  *  *  * * * * * | 0 1 1 0 0 0 0
.... .... oxo. ....&#x  ♦ 1 2 1 0 | 0  2 1 0 1  2 0 0 0  0 0 | 0 0  1  2 0 0  0  0  1  0  0 0 0 0 0  0 | * * *  * 12  * * * * *  *  *  * * * * * | 0 0 1 1 0 0 0
.... .... .... oox.&#x  ♦ 1 1 2 0 | 0  1 2 0 0  2 0 0 1  0 0 | 0 0  0  2 1 0  0  0  0  1  0 0 0 0 0  0 | * * *  *  * 12 * * * *  *  *  * * * * * | 0 1 0 1 0 0 0
.... .... o.o.3o.x.&#x  ♦ 1 0 3 0 | 0  0 3 0 0  0 0 0 3  0 0 | 0 0  0  0 3 0  0  0  0  0  0 0 1 0 0  0 | * * *  *  *  * 2 * * *  *  *  * * * * * | 0 0 0 2 0 0 0
.ox. .xo. .... ....&#x  ♦ 0 2 2 0 | 0  0 0 1 0  4 0 1 0  0 0 | 0 0  0  0 0 0  2  2  0  0  0 0 0 0 0  0 | * * *  *  *  * * 6 * *  *  *  * * * * * | 0 0 1 0 0 1 0
.ox. .... .xo. ....&#x  ♦ 0 2 2 0 | 0  0 0 0 1  4 0 1 0  0 0 | 0 0  0  0 0 0  2  0  2  0  0 0 0 0 0  0 | * * *  *  *  * * * 6 *  *  *  * * * * * | 0 0 1 0 1 0 0
.... .xo. .... .ox.&#x  ♦ 0 2 2 0 | 0  0 0 1 0  4 0 0 1  0 0 | 0 0  0  0 0 0  0  2  0  2  0 0 0 0 0  0 | * * *  *  *  * * * * 6  *  *  * * * * * | 0 1 0 0 0 1 0
.oxo .... .... ....&#x  ♦ 0 1 2 1 | 0  0 0 0 0  2 1 1 0  2 0 | 0 0  0  0 0 0  1  0  0  0  2 0 0 1 0  0 | * * *  *  *  * * * * * 12  *  * * * * * | 0 0 0 0 1 1 0
.... .... .xoo ....&#x  ♦ 0 2 1 1 | 0  0 0 0 1  2 2 0 0  1 0 | 0 0  0  0 0 0  0  0  1  0  2 1 0 0 0  0 | * * *  *  *  * * * * *  * 12  * * * * * | 0 0 0 1 1 0 0
.... .... .... .oxo&#x  ♦ 0 1 2 1 | 0  0 0 0 0  2 1 0 1  2 0 | 0 0  0  0 0 0  0  0  0  1  2 0 0 0 0  1 | * * *  *  *  * * * * *  *  * 12 * * * * | 0 0 0 1 0 1 0
.... .... .x.o3.o.o&#x  ♦ 0 3 0 1 | 0  0 0 0 3  0 3 0 0  0 0 | 0 0  0  0 0 1  0  0  0  0  0 3 0 0 0  0 | * * *  *  *  * * * * *  *  *  * 2 * * * | 0 0 0 2 0 0 0
..xo ..ox .... ....&#x  ♦ 0 0 2 2 | 0  0 0 0 0  0 0 1 0  4 1 | 0 0  0  0 0 0  0  0  0  0  0 0 0 2 2  0 | * * *  *  *  * * * * *  *  *  * * 3 * * | 0 0 0 0 0 2 0
.... ..ox .... ..xo&#x  ♦ 0 0 2 2 | 0  0 0 0 0  0 0 0 1  4 1 | 0 0  0  0 0 0  0  0  0  0  0 0 0 0 2  2 | * * *  *  *  * * * * *  *  *  * * * 6 * | 0 0 0 0 0 1 1
.... .... ..oo3..xo&#x  ♦ 0 0 3 1 | 0  0 0 0 0  0 0 0 3  3 0 | 0 0  0  0 0 0  0  0  0  0  0 0 1 0 0  3 | * * *  *  *  * * * * *  *  *  * * * * 4 | 0 0 0 1 0 0 1
------------------------+---------+--------------------------+-----------------------------------------+-----------------------------------------+--------------
xo.. .... ox..3oo..&#x  ♦ 2 3 0 0 | 1  6 0 0 3  0 0 0 0  0 0 | 3 0  6  0 0 1  0  0  0  0  0 0 0 0 0  0 | 0 3 2  0  0  0 0 0 0 0  0  0  0 0 0 0 0 | 2 * * * * * *
.... oxo. .... oox.&#x  ♦ 1 2 2 0 | 0  2 2 1 0  4 0 0 1  0 0 | 0 1  0  4 1 0  0  2  0  2  0 0 0 0 0  0 | 0 0 0  2  0  2 0 0 0 1  0  0  0 0 0 0 0 | * 6 * * * * *
xox. oxo. oxo. ....&#xt ♦ 2 4 2 0 | 1  8 2 2 2  8 0 1 0  0 0 | 4 4  4  8 0 0  4  4  4  0  0 0 0 0 0  0 | 2 2 0  4  4  0 0 2 2 0  0  0  0 0 0 0 0 | * * 3 * * * *
.... .... oxoo3ooxo&#xr ♦ 1 3 3 1 | 0  3 3 0 3  6 3 0 3  3 0 | 0 0  3  6 3 1  0  0  3  3  6 3 1 0 0  3 | 0 0 1  0  3  3 1 0 0 0  0  3  3 1 0 0 1 | * * * 4 * * * cycle: (ABDC)
.oxo .... .xoo ....&#x  ♦ 0 2 2 1 | 0  0 0 0 1  4 2 1 0  2 0 | 0 0  0  0 0 0  2  0  2  0  4 1 0 1 0  0 | 0 0 0  0  0  0 0 0 1 0  2  2  0 0 0 0 0 | * * * * 6 * *
.oxo .xox .... .oxo&#xt ♦ 0 2 4 2 | 0  0 0 1 0  8 2 2 2  8 1 | 0 0  0  0 0 0  4  4  0  4  8 0 0 4 4  4 | 0 0 0  0  0  0 0 2 0 2  4  0  4 0 2 2 0 | * * * * * 3 *
.... ..ox ..oo3..xo&#x  ♦ 0 0 3 2 | 0  0 0 0 0  0 0 0 3  6 1 | 0 0  0  0 0 0  0  0  0  0  0 0 1 0 3  6 | 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 3 2 | * * * * * * 2

or
o... o... o...3o...     & | 4  * ♦ 1  6  3 0  0  0 |  6  3  6 12  3 0  0  0 | 3  6 2  6  6  6 1 0  0 | 2  3 3 2
.o.. .o.. .o..3.o..     & | * 12 ♦ 0  2  1 1  2  4 |  1  2  4  8  2 1  6  6 | 1  2 2  6  6  6 1 2  4 | 1  4 3 2
--------------------------+------+-----------------+------------------------+------------------------+---------
x... .... .... ....     & | 2  0 | 2  *  * *  *  * ♦  6  0  0  0  0 0  0  0 | 3  6 0  0  0  0 0 0  0 | 2  0 3 0
oo.. oo.. oo..3oo..&#x  & | 1  1 | * 24  * *  *  * ♦  1  1  2  2  0 0  0  0 | 1  2 1  2  2  1 0 0  0 | 1  1 2 1
o.o. o.o. o.o.3o.o.&#x  & | 1  1 | *  * 12 *  *  * ♦  0  0  0  4  2 0  0  0 | 0  0 0  2  2  4 1 0  0 | 0  2 1 2
.... .x.. .... ....     & | 0  2 | *  *  * 6  *  * ♦  0  2  0  0  0 0  4  0 | 1  0 0  4  0  0 0 2  2 | 0  2 3 0
.... .... .x.. ....     & | 0  2 | *  *  * * 12  * ♦  0  0  2  0  1 1  0  2 | 0  1 2  0  2  2 1 0  1 | 1  1 1 2
.oo. .oo. .oo.3.oo.&#x    | 0  2 | *  *  * *  * 24 ♦  0  0  0  2  0 0  2  2 | 0  0 0  2  2  2 0 1  2 | 0  2 2 1
--------------------------+------+-----------------+------------------------+------------------------+---------
xo.. .... .... ....&#x  & | 2  1 | 1  2  0 0  0  0 | 12  *  *  *  * *  *  * | 1  2 0  0  0  0 0 0  0 | 1  0 2 0
.... ox.. .... ....&#x  & | 1  2 | 0  2  0 1  0  0 |  * 12  *  *  * *  *  * | 1  0 0  2  0  0 0 0  0 | 0  1 2 0
.... .... ox.. ....&#x  & | 1  2 | 0  2  0 0  1  0 |  *  * 24  *  * *  *  * | 0  1 1  0  1  0 0 0  0 | 1  0 1 1
ooo. ooo. ooo.3ooo.&#x  & | 1  2 | 0  1  1 0  0  1 |  *  *  * 48  * *  *  * | 0  0 0  1  1  1 0 0  0 | 0  1 1 1
.... .... .... o.x.&#x  & | 1  2 | 0  0  2 0  1  0 |  *  *  *  * 12 *  *  * | 0  0 0  0  0  2 1 0  0 | 0  1 0 2
.... .... .x..3.o..     & | 0  3 | 0  0  0 0  3  0 |  *  *  *  *  * 4  *  * | 0  0 2  0  0  0 1 0  0 | 1  0 0 2
.ox. .... .... ....&#x  & | 0  3 | 0  0  0 1  0  2 |  *  *  *  *  * * 24  * | 0  0 0  1  0  0 0 1  1 | 0  1 2 0
.... .... .xo. ....&#x  & | 0  3 | 0  0  0 0  1  2 |  *  *  *  *  * *  * 24 | 0  0 0  0  1  1 0 0  1 | 0  1 1 1
--------------------------+------+-----------------+------------------------+------------------------+---------
xo.. ox.. .... ....&#x  & ♦ 2  2 | 1  4  0 1  0  0 |  2  2  0  0  0 0  0  0 | 6  * *  *  *  * * *  * | 0  0 2 0
xo.. .... ox.. ....&#x  & ♦ 2  2 | 1  4  0 0  1  0 |  2  0  2  0  0 0  0  0 | * 12 *  *  *  * * *  * | 1  0 1 0
.... .... ox..3oo..&#x  & ♦ 1  3 | 0  3  0 0  3  0 |  0  0  3  0  0 1  0  0 | *  * 8  *  *  * * *  * | 1  0 0 1
.... oxo. .... ....&#x  & ♦ 1  3 | 0  2  1 1  0  2 |  0  1  0  2  0 0  1  0 | *  * * 24  *  * * *  * | 0  1 1 0
.... .... oxo. ....&#x  & ♦ 1  3 | 0  2  1 0  1  2 |  0  0  1  2  0 0  0  1 | *  * *  * 24  * * *  * | 0  0 1 1
.... .... .... oox.&#x  & ♦ 1  3 | 0  1  2 0  1  2 |  0  0  0  2  1 0  0  1 | *  * *  *  * 24 * *  * | 0  1 0 1
.... .... o.o.3o.x.&#x  & ♦ 1  3 | 0  0  3 0  3  0 |  0  0  0  0  3 1  0  0 | *  * *  *  *  * 4 *  * | 0  0 0 2
.ox. .xo. .... ....&#x    ♦ 0  4 | 0  0  0 2  0  4 |  0  0  0  0  0 0  4  0 | *  * *  *  *  * * 6  * | 0  0 2 0
.ox. .... .xo. ....&#x  & ♦ 0  4 | 0  0  0 1  1  4 |  0  0  0  0  0 0  2  2 | *  * *  *  *  * * * 12 | 0  1 1 0
--------------------------+------+-----------------+------------------------+------------------------+---------
xo.. .... ox..3oo..&#x  & ♦ 2  3 | 1  6  0 0  3  0 |  3  0  6  0  0 1  0  0 | 0  3 2  0  0  0 0 0  0 | 4  * * *
.... oxo. .... oox.&#x  & ♦ 1  4 | 0  2  2 1  1  4 |  0  1  0  4  1 0  2  2 | 0  0 0  2  0  2 0 0  1 | * 12 * *
xox. oxo. oxo. ....&#xt & ♦ 2  6 | 1  8  2 3  2  8 |  4  4  4  8  0 0  8  4 | 2  2 0  4  4  0 0 2  2 | *  * 6 *
.... .... oxoo3ooxo&#xr   ♦ 2  6 | 0  6  6 0  6  6 |  0  0  6 12  6 2  0  6 | 0  0 2  0  6  6 2 0  0 | *  * * 4 cycle: (ABDC)


(xo)(ox) (xo)(xo) (ox)(xo) (ox)(ox)&#x   → height(12,34) = 1/sqrt(2) = 0.707107
(hex || alt. hex)

(o.)(..) (o.)(..) (o.)(..) (o.)(..)     & | 16 ♦  2  4  4 | 12  6 12 |  4  4 2 16  4 | 1  5 4
------------------------------------------+----+----------+----------+---------------+-------
(x.)(..) (..)(..) (..)(..) (..)(..)     & |  2 | 16  *  * ♦  4  2  0 |  2  2 1  4  0 | 1  2 2
(oo)(..) (oo)(..) (oo)(..) (oo)(..)&#x  & |  2 |  * 32  * ♦  4  0  2 |  2  2 0  4  1 | 1  2 2
(o.)(o.) (o.)(o.) (o.)(o.) (o.)(o.)&#x  & |  2 |  *  * 32 ♦  0  2  4 |  0  0 1  6  2 | 0  2 3
------------------------------------------+----+----------+----------+---------------+-------
(xo)(..) (..)(..) (..)(..) (..)(..)&#x  & |  3 |  1  2  0 | 64  *  * |  1  1 0  1  0 | 1  1 1
(x.)(o.) (..)(..) (..)(..) (..)(..)&#x  & |  3 |  1  0  2 |  * 32  * |  0  0 1  2  0 | 0  1 2
(oo)(o.) (oo)(o.) (oo)(o.) (oo)(o.)&#x  & |  3 |  0  1  2 |  *  * 64 |  0  0 0  2  1 | 0  1 2
------------------------------------------+----+----------+----------+---------------+-------
(xo)(..) (..)(..) (ox)(..) (..)(..)&#x  & ♦  4 |  2  4  0 |  4  0  0 | 16  * *  *  * | 1  0 1
(xo)(..) (..)(..) (..)(..) (ox)(..)&#x  & ♦  4 |  2  4  0 |  4  0  0 |  * 16 *  *  * | 1  1 0
(x.)(o.) (..)(..) (o.)(x.) (..)(..)&#x  & ♦  4 |  2  0  4 |  0  4  0 |  *  * 8  *  * | 0  0 2
(xo)(o.) (..)(..) (..)(..) (..)(..)&#x  & ♦  4 |  1  2  3 |  1  1  2 |  *  * * 64  * | 0  1 1
(oo)(oo) (oo)(oo) (oo)(oo) (oo)(oo)&#x    ♦  4 |  0  2  4 |  0  0  4 |  *  * *  * 16 | 0  0 2
------------------------------------------+----+----------+----------+---------------+-------
(xo)(..) (xo)(..) (ox)(..) (ox)(..)&#zx & ♦  8 |  8 16  0 | 32  0  0 |  8  8 0  0  0 | 2  * *
(xo)(o.) (..)(..) (..)(..) (ox)(o.)&#x  & ♦  5 |  2  4  4 |  4  2  4 |  0  1 0  4  0 | * 16 *
(xo)(ox) (..)(..) (ox)(xo) (..)(..)&#xr & ♦  8 |  4  8 12 |  8  8 16 |  2  0 2  8  4 | *  * 8


xoxo3oooo3oxox&#xr   → cyclical heights = 1/sqrt(2) = 0.707107
(hex || alt. hex)
(tet altersquarism)

o...3o...3o...     & | 16 ♦  3  6 1 |  3 18  9 | 1  8  6 12  3 | 2  5 3
---------------------+----+---------+----------+---------------+-------
x... .... ....     & |  2 | 24  * * ♦  2  4  0 | 1  4  2  2  0 | 2  2 1
oo..3oo..3oo..&#x  & |  2 |  * 48 * ♦  0  4  2 | 0  2  2  4  1 | 1  2 2
o.o.3o.o.3o.o.&#x  & |  2 |  *  * 8 ♦  0  0  6 | 0  0  0  6  3 | 0  2 3
---------------------+----+---------+----------+---------------+-------
x...3o... ....     & |  3 |  3  0 0 | 16  *  * | 1  2  0  0  0 | 2  1 0
xo.. .... ....&#x  & |  3 |  1  2 0 |  * 96  * | 0  1  1  1  0 | 1  1 1
ooo.3ooo.3ooo.&#x  & |  3 |  0  2 1 |  *  * 48 | 0  0  0  2  1 | 0  1 2
---------------------+----+---------+----------+---------------+-------
x...3o...3o...     & ♦  4 |  6  0 0 |  4  0  0 | 4  *  *  *  * | 2  0 0
xo..3oo.. ....&#x  & ♦  4 |  3  3 0 |  1  3  0 | * 32  *  *  * | 1  1 0
xo.. .... ox..&#x  & ♦  4 |  2  4 0 |  0  4  0 | *  * 24  *  * | 1  0 1
.... .... oxo.&#x  & ♦  4 |  1  4 1 |  0  2  2 | *  *  * 48  * | 0  1 1
oooo3oooo3oooo&#x    ♦  4 |  0  4 2 |  0  0  4 | *  *  *  * 12 | 0  0 2
---------------------+----+---------+----------+---------------+-------
xo..3oo..3ox..&#x  & ♦  8 | 12 12 0 |  8 24  0 | 2  8  6  0  0 | 4  * *
.... ooo.3oxo.&#x  & ♦  5 |  3  6 1 |  1  6  3 | 0  2  0  3  0 | * 16 *
xoxo .... oxox&#xr   ♦  8 |  4 16 4 |  0 16 16 | 0  0  4  8  4 | *  * 6

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