Acronym rix
Name rectified hexateron,
vertex figure of hax,
Gosset polytope 03,1,
equatorial cross-section of hix-first jak
Field of sections 
 ©
Circumradius sqrt(2/3) = 0.816497
Inradius
wrt. pen 		2/sqrt(15) = 0.516398
Inradius
wrt. rap 		1/sqrt(15) = 0.258199
Vertex figure 
 ©    ©
Lace city
in approx. ASCII-art 
o3o3o   x3o3o  		- x3o3o3o (pen)
               
               
               
  x3o3o   o3x3o		- o3x3o3o (rap)

            +-------------- x3o o3o ({3})
           /      +-------- o3x o3x (bidual triddip)
          /      /      +-- o3o x3o (perp {3})
         /      /      /

    x o3o   o o3x    		- x3o3o3o (pen)
                     
                     
                     
o o3o   x o3x   o x3o		- o3x3o3o (rap)

    \       \       \
     \       \       +-- o o3x3o (oct)
      \       +--------- x o3o3x (tepe)
       +---------------- o o3o3o (point)

o o o   x x o   o o o		-- o o3x3o (oct)
B       A       F    
                     
                     
    x o x   o x x    		-- x o3o3x (tepe)
    C       E        
                     
                     
        o o o        		-- o o3o3o (point)
        D
Lace hyper city
in approx. ASCII-art 
 ©  


where:
o  – point within plane of display
+  – point 1/sqrt(12) above plane of display
#  – point 1/sqrt(3) above plane of display
-  – point 1/sqrt(12) below plane of display
=  – point 1/sqrt(3) below plane of display


    
    
    
    
    

    o    
         
         
         
    o
x o3o layer of pen 
         
         
+   =   +
o o3x layer of pen 
    
    
    
    
    

         
         
    o
o o3o layer of rap 
+   =   +
         
         
         
+   =   +
x o3x layer of rap 
         
         
-   #   -
o x3o layer of rap 
 ©  

           
           
    x3o
{3} 
  o3x      
           
        o3x
           
  o3x
bidual triddip 
      o3o  
           
o3o        
           
      o3o
perp {3}
or 
    
    
    
    
    

         
         
    x
x o3o layer of pen 
  o      
         
        o
         
  o
o o3x layer of pen 
    
    
    
    
    

         
         
    o
o o3o layer of rap 
  x      
         
        x
         
  x
x o3x layer of rap 
      o  
         
o        
         
      o
o x3o layer of rap
Volume 13 sqrt(3)/240 = 0.093819
Surface 3 sqrt(5)/4 = 1.677051
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: pen rap tepe triddip
rix 6600
firx 601510
& others)
Dihedral angles
(at margins)
  • at tet between pen and rap:   arccos(-1/5) = 101.536959°
  • at oct between rap and rap:   arccos(1/5) = 78.463041°
Face vector 15, 60, 80, 45, 12
Confer
related segmentotera:
tepepy   octatepe   bidrix   tedrix   trial triddip  
ambification:
sarx  
ambification pre-image:
hix  
general polytopal classes:
Wythoffian polytera   segmentotera   fundamental lace prisms   lace simplices   Coxeter-Elte-Gosset polytopes  
analogs:
rectified simplex rSn  
External
links 		hedrondude   wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

o3x3o3o3o

. . . . . | 15 ♦  8 |  4 12 |  6  8 | 4 2
----------+----+----+-------+-------+----
. x . . . |  2 | 60 |  1  3 |  3  3 | 3 1
----------+----+----+-------+-------+----
o3x . . . |  3 |  3 | 20  * |  3  0 | 3 0
. x3o . . |  3 |  3 |  * 60 |  1  2 | 2 1
----------+----+----+-------+-------+----
o3x3o . . ♦  6 | 12 |  4  4 | 15  * | 2 0
. x3o3o . ♦  4 |  6 |  0  4 |  * 30 | 1 1
----------+----+----+-------+-------+----
o3x3o3o . ♦ 10 | 30 | 10 20 |  5  5 | 6 *
. x3o3o3o ♦  5 | 10 |  0 10 |  0  5 | * 6


o3/2x3o3o3o

.   . . . . | 15 ♦  8 |  4 12 |  6  8 | 4 2
------------+----+----+-------+-------+----
.   x . . . |  2 | 60 |  1  3 |  3  3 | 3 1
------------+----+----+-------+-------+----
o3/2x . . . |  3 |  3 | 20  * |  3  0 | 3 0
.   x3o . . |  3 |  3 |  * 60 |  1  2 | 2 1
------------+----+----+-------+-------+----
o3/2x3o . . ♦  6 | 12 |  4  4 | 15  * | 2 0
.   x3o3o . ♦  4 |  6 |  0  4 |  * 30 | 1 1
------------+----+----+-------+-------+----
o3/2x3o3o . ♦ 10 | 30 | 10 20 |  5  5 | 6 *
.   x3o3o3o ♦  5 | 10 |  0 10 |  0  5 | * 6


o3x3o3o3/2o

. . . .   . | 15 ♦  8 |  4 12 |  6  8 | 4 2
------------+----+----+-------+-------+----
. x . .   . |  2 | 60 |  1  3 |  3  3 | 3 1
------------+----+----+-------+-------+----
o3x . .   . |  3 |  3 | 20  * |  3  0 | 3 0
. x3o .   . |  3 |  3 |  * 60 |  1  2 | 2 1
------------+----+----+-------+-------+----
o3x3o .   . ♦  6 | 12 |  4  4 | 15  * | 2 0
. x3o3o   . ♦  4 |  6 |  0  4 |  * 30 | 1 1
------------+----+----+-------+-------+----
o3x3o3o   . ♦ 10 | 30 | 10 20 |  5  5 | 6 *
. x3o3o3/2o ♦  5 | 10 |  0 10 |  0  5 | * 6


xo3ox3oo3oo&#x   → height = sqrt(3/5) = 0.774597
(pen || rap)

o.3o.3o.3o.    | 5  * ♦  4  4  0 |  6  4  6  0  0 | 4  6  4 0 0 | 1 4 1 0
.o3.o3.o3.o    | * 10 ♦  0  2  6 |  0  1  6  3  6 | 0  3  6 3 2 | 0 3 2 1
---------------+------+----------+----------------+-------------+--------
x. .. .. ..    | 2  0 | 10  *  * |  3  1  0  0  0 | 3  3  0 0 0 | 1 3 0 0
oo3oo3oo3oo&#x | 1  1 |  * 20  * |  0  1  3  0  0 | 0  3  3 0 0 | 0 3 1 0
.. .x .. ..    | 0  2 |  *  * 30 |  0  0  1  1  2 | 0  1  2 2 1 | 0 2 1 1
---------------+------+----------+----------------+-------------+--------
x.3o. .. ..    | 3  0 |  3  0  0 | 10  *  *  *  * | 2  1  0 0 0 | 1 2 0 0
xo .. .. ..&#x | 2  1 |  1  2  0 |  * 10  *  *  * | 0  3  0 0 0 | 0 3 0 0
.. ox .. ..&#x | 1  2 |  0  2  1 |  *  * 30  *  * | 0  1  2 0 0 | 0 2 1 0
.o3.x .. ..    | 0  3 |  0  0  3 |  *  *  * 10  * | 0  1  0 2 0 | 0 2 0 1
.. .x3.o ..    | 0  3 |  0  0  3 |  *  *  *  * 20 | 0  0  1 1 1 | 0 1 1 1
---------------+------+----------+----------------+-------------+--------
x.3o.3o. ..    ♦ 4  0 |  6  0  0 |  4  0  0  0  0 | 5  *  * * * | 1 1 0 0
xo3ox .. ..&#x ♦ 3  3 |  3  6  3 |  1  3  3  1  0 | * 10  * * * | 0 2 0 0
.. ox3oo ..&#x ♦ 1  3 |  0  3  3 |  0  0  3  0  1 | *  * 20 * * | 0 1 1 0
.o3.x3.o ..    ♦ 0  6 |  0  0 12 |  0  0  0  4  4 | *  *  * 5 * | 0 1 0 1
.. .x3.o3.o    ♦ 0  4 |  0  0  6 |  0  0  0  0  4 | *  *  * * 5 | 0 0 1 1
---------------+------+----------+----------------+-------------+--------
x.3o.3o.3o.    ♦ 5  0 | 10  0  0 | 10  0  0  0  0 | 5  0  0 0 0 | 1 * * *
xo3ox3oo ..&#x ♦ 4  6 |  6 12 12 |  4  6 12  4  4 | 1  4  4 1 0 | * 5 * *
.. ox3oo3oo&#x ♦ 1  4 |  0  4  6 |  0  0  6  0  4 | 0  0  4 0 1 | * * 5 *
.o3.x3.o3.o    ♦ 0 10 |  0  0 30 |  0  0  0 10 20 | 0  0  0 5 5 | * * * 1


oxo oxo3oox3ooo&#xt   → both heights = sqrt(3/8) = 0.612372
(pt || pseudo tepe || oct)

o.. o..3o..3o..     | 1 * * ♦ 8 0  0  0  0 | 4 12 0  0  0  0 0 0 | 6 8 0  0 0 0 0 | 4 2 0 0
.o. .o.3.o.3.o.     | * 8 * ♦ 1 1  3  3  0 | 1  3 3  3  3  3 0 0 | 3 3 1  3 3 1 0 | 3 1 1 1
..o ..o3..o3..o     | * * 6 ♦ 0 0  0  4  4 | 0  0 0  2  2  8 2 2 | 1 0 0  4 4 4 1 | 2 0 2 2
--------------------+-------+--------------+---------------------+----------------+--------
oo. oo.3oo.3oo.&#x  | 1 1 0 | 8 *  *  *  * | 1  3 0  0  0  0 0 0 | 3 3 0  0 0 0 0 | 3 1 0 0
.x. ... ... ...     | 0 2 0 | * 4  *  *  * | 1  0 0  3  0  0 0 0 | 3 0 0  3 0 0 0 | 3 0 1 0
... .x. ... ...     | 0 2 0 | * * 12  *  * | 0  1 2  0  1  0 0 0 | 1 2 1  0 2 0 0 | 2 1 0 1
.oo .oo3.oo3.oo&#x  | 0 1 1 | * *  * 24  * | 0  0 0  1  1  2 0 0 | 1 0 0  2 2 1 0 | 2 0 1 1
... ... ..x ...     | 0 0 2 | * *  *  * 12 | 0  0 0  0  0  2 1 1 | 0 0 0  1 2 2 1 | 1 0 1 2
--------------------+-------+--------------+---------------------+----------------+--------
ox. ... ... ...&#x  | 1 2 0 | 2 1  0  0  0 | 4  * *  *  *  * * * | 3 0 0  0 0 0 0 | 3 0 0 0
... ox. ... ...&#x  | 1 2 0 | 2 0  1  0  0 | * 12 *  *  *  * * * | 1 2 0  0 0 0 0 | 2 1 0 0
... .x.3.o. ...     | 0 3 0 | 0 0  3  0  0 | *  * 8  *  *  * * * | 0 1 1  0 1 0 0 | 1 1 0 1
.xo ... ... ...&#x  | 0 2 1 | 0 1  0  2  0 | *  * * 12  *  * * * | 1 0 0  2 0 0 0 | 2 0 1 0
... .xo ... ...&#x  | 0 2 1 | 0 0  1  2  0 | *  * *  * 12  * * * | 1 0 0  0 2 0 0 | 2 0 0 1
... ... .ox ...&#x  | 0 1 2 | 0 0  0  2  1 | *  * *  *  * 24 * * | 0 0 0  1 1 1 0 | 1 0 1 1
... ..o3..x ...     | 0 0 3 | 0 0  0  0  3 | *  * *  *  *  * 4 * | 0 0 0  0 2 0 1 | 1 0 0 2
... ... ..x3..o     | 0 0 3 | 0 0  0  0  3 | *  * *  *  *  * * 4 | 0 0 0  0 0 2 1 | 0 0 1 2
--------------------+-------+--------------+---------------------+----------------+--------
oxo oxo ... ...&#xt ♦ 1 4 1 | 4 2  2  4  0 | 2  2 0  2  2  0 0 0 | 6 * *  * * * * | 2 0 0 0
... ox.3oo. ...&#x  ♦ 1 3 0 | 3 0  3  0  0 | 0  3 1  0  0  0 0 0 | * 8 *  * * * * | 1 1 0 0
... .x.3.o.3.o.     ♦ 0 4 0 | 0 0  6  0  0 | 0  0 4  0  0  0 0 0 | * * 2  * * * * | 0 1 0 1
.xo ... .ox ...&#x  ♦ 0 2 2 | 0 1  0  4  1 | 0  0 0  2  0  2 0 0 | * * * 12 * * * | 1 0 1 0
... .xo3.ox ...&#x  ♦ 0 3 3 | 0 0  3  6  3 | 0  0 1  0  3  3 1 0 | * * *  * 8 * * | 1 0 0 1
... ... .ox3.oo&#x  ♦ 0 1 3 | 0 0  0  3  3 | 0  0 0  0  0  3 0 1 | * * *  * * 8 * | 0 0 1 1
... ..o3..x3..o     ♦ 0 0 6 | 0 0  0  0 12 | 0  0 0  0  0  0 4 4 | * * *  * * * 1 | 0 0 0 2
--------------------+-------+--------------+---------------------+----------------+--------
oxo oxo3oox ...&#xt ♦ 1 6 3 | 6 3  6 12  3 | 3  6 2  6  6  6 1 0 | 3 2 0  3 2 0 0 | 4 * * *
... ox.3oo.3oo.&#x  ♦ 1 4 0 | 4 0  6  0  0 | 0  6 4  0  0  0 0 0 | 0 4 1  0 0 0 0 | * 2 * *
.xo ... .ox3.oo&#x  ♦ 0 2 3 | 0 1  0  6  3 | 0  0 0  3  0  6 0 1 | 0 0 0  3 0 2 0 | * * 4 *
... .xo3.ox3.oo&#x  ♦ 0 4 6 | 0 0  6 12 12 | 0  0 4  0  6 12 4 4 | 0 0 1  0 4 4 1 | * * * 2


x(oo)x3o(ox)o3o(oo)o&#xt   → height(1,23) = height(23,4) = 1/2
                             height(2,3) = sqrt(3/2) = 1.224745
(tet || pseudo ( pt || oct ) || tet)

o(..).3o(..).3o(..).     | 4 * * * ♦ 3 1  3 1 0  0  0 0 | 3 3 3  3 1  3 0 0 0 0  0 0 | 1 3 3 1 3  3 0 0 0 0 0 | 1 1 3 1 0 0
.(o.).3.(o.).3.(o.).     | * 1 * * ♦ 0 4  0 0 4  0  0 0 | 0 6 0  0 4  0 6 0 0 0  0 0 | 0 4 0 0 6  0 4 0 0 0 0 | 1 0 4 0 1 0
.(.o).3.(.o).3.(.o).     | * * 6 * ♦ 0 0  2 0 0  4  2 0 | 0 0 1  4 0  2 0 2 2 1  4 0 | 0 0 2 2 1  4 0 1 2 2 0 | 0 1 2 2 0 1
.(..)o3.(..)o3.(..)o     | * * * 4 ♦ 0 0  0 1 1  0  3 3 | 0 0 0  0 1  3 3 0 0 3  3 3 | 0 0 0 0 3  3 3 0 3 1 1 | 0 0 3 1 1 1
-------------------------+---------+--------------------+----------------------------+------------------------+------------
x(..). .(..). .(..).     | 2 0 0 0 | 6 *  * * *  *  * * | 2 1 1  0 0  0 0 0 0 0  0 0 | 1 2 2 0 1  0 0 0 0 0 0 | 1 1 2 0 0 0
o(o.).3o(o.).3o(o.).&#x  | 1 1 0 0 | * 4  * * *  *  * * | 0 3 0  0 1  0 0 0 0 0  0 0 | 0 3 0 0 3  0 0 0 0 0 0 | 1 0 3 0 0 0
o(.o).3o(.o).3o(.o).&#x  | 1 0 1 0 | * * 12 * *  *  * * | 0 0 1  2 0  1 0 0 0 0  0 0 | 0 0 2 1 1  2 0 0 0 0 0 | 0 1 2 1 0 0
o(..)o3o(..)o3o(..)o&#x  | 1 0 0 1 | * *  * 4 *  *  * * | 0 0 0  0 1  3 0 0 0 0  0 0 | 0 0 0 0 3  3 0 0 0 0 0 | 0 0 3 1 0 0
.(o.)o3.(o.)o3.(o.)o&#x  | 0 1 0 1 | * *  * * 4  *  * * | 0 0 0  0 1  0 3 0 0 0  0 0 | 0 0 0 0 3  0 3 0 0 0 0 | 0 0 3 0 1 0
.(..). .(.x). .(..).     | 0 0 2 0 | * *  * * * 12  * * | 0 0 0  1 0  0 0 1 1 0  1 0 | 0 0 1 1 0  1 0 1 1 1 0 | 0 1 1 1 0 1
.(.o)o3.(.o)o3.(.o)o&#x  | 0 0 1 1 | * *  * * *  * 12 * | 0 0 0  0 0  1 0 0 0 1  2 0 | 0 0 0 0 1  2 0 0 2 1 0 | 0 0 2 1 0 1
.(..)x .(..). .(..).     | 0 0 0 2 | * *  * * *  *  * 6 | 0 0 0  0 0  0 1 0 0 1  0 2 | 0 0 0 0 1  0 2 0 2 0 1 | 0 0 2 0 1 1
-------------------------+---------+--------------------+----------------------------+------------------------+------------
x(..).3o(..). .(..).     | 3 0 0 0 | 3 0  0 0 0  0  0 0 | 4 * *  * *  * * * * *  * * | 1 1 1 0 0  0 0 0 0 0 0 | 1 1 1 0 0 0
x(o.). .(..). .(..).&#x  | 2 1 0 0 | 1 2  0 0 0  0  0 0 | * 6 *  * *  * * * * *  * * | 0 2 0 0 1  0 0 0 0 0 0 | 1 0 2 0 0 0
x(.o). .(..). .(..).&#x  | 2 0 1 0 | 1 0  2 0 0  0  0 0 | * * 6  * *  * * * * *  * * | 0 0 2 0 1  0 0 0 0 0 0 | 0 1 2 0 0 0
.(..). o(.x). .(..).&#x  | 1 0 2 0 | 0 0  2 0 0  1  0 0 | * * * 12 *  * * * * *  * * | 0 0 1 1 0  1 0 0 0 0 0 | 0 1 1 1 0 0
o(o.)o3o(o.)o3o(o.)o&#x  | 1 1 0 1 | 0 1  0 1 1  0  0 0 | * * *  * 4  * * * * *  * * | 0 0 0 0 3  0 0 0 0 0 0 | 0 0 3 0 0 0
o(.o)o3o(.o)o3o(.o)o&#x  | 1 0 1 1 | 0 0  1 1 0  0  1 0 | * * *  * * 12 * * * *  * * | 0 0 0 0 1  2 0 0 0 0 0 | 0 0 2 1 0 0
.(o.)x .(..). .(..).&#x  | 0 1 0 2 | 0 0  0 0 2  0  0 1 | * * *  * *  * 6 * * *  * * | 0 0 0 0 1  0 2 0 0 0 0 | 0 0 2 0 1 0
.(.o).3.(.x). .(..).     | 0 0 3 0 | 0 0  0 0 0  3  0 0 | * * *  * *  * * 4 * *  * * | 0 0 1 0 0  0 0 1 1 0 0 | 0 1 1 0 0 1
.(..). .(.x).3.(.o).     | 0 0 3 0 | 0 0  0 0 0  3  0 0 | * * *  * *  * * * 4 *  * * | 0 0 0 1 0  0 0 1 0 1 0 | 0 1 0 1 0 1
.(.o)x .(..). .(..).&#x  | 0 0 1 2 | 0 0  0 0 0  0  2 1 | * * *  * *  * * * * 6  * * | 0 0 0 0 1  0 0 0 2 0 0 | 0 0 2 0 0 1
.(..). .(.x)o .(..).&#x  | 0 0 2 1 | 0 0  0 0 0  1  2 0 | * * *  * *  * * * * * 12 * | 0 0 0 0 0  1 0 0 1 1 0 | 0 0 1 1 0 1
.(..)x3.(..)o .(..).     | 0 0 0 3 | 0 0  0 0 0  0  0 3 | * * *  * *  * * * * *  * 4 | 0 0 0 0 0  0 1 0 1 0 1 | 0 0 1 0 1 1
-------------------------+---------+--------------------+----------------------------+------------------------+------------
x(..).3o(..).3o(..).     ♦ 4 0 0 0 | 6 0  0 0 0  0  0 0 | 4 0 0  0 0  0 0 0 0 0  0 0 | 1 * * * *  * * * * * * | 1 1 0 0 0 0
x(o.).3o(o.). .(..).&#x  ♦ 3 1 0 0 | 3 3  0 0 0  0  0 0 | 1 3 0  0 0  0 0 0 0 0  0 0 | * 4 * * *  * * * * * * | 1 0 1 0 0 0
x(.o).3o(.x). .(..).&#x  ♦ 3 0 3 0 | 3 0  6 0 0  3  0 0 | 1 0 3  3 0  0 0 1 0 0  0 0 | * * 4 * *  * * * * * * | 0 1 1 0 0 0
.(..). o(.x).3o(.o).&#x  ♦ 1 0 3 0 | 0 0  3 0 0  3  0 0 | 0 0 0  3 0  0 0 0 1 0  0 0 | * * * 4 *  * * * * * * | 0 1 0 1 0 0
x(oo)x .(..). .(..).&#xt ♦ 2 1 1 2 | 1 2  2 2 2  0  2 1 | 0 1 1  0 2  2 1 0 0 1  0 0 | * * * * 6  * * * * * * | 0 0 2 0 0 0
.(..). o(.x)o .(..).&#xt ♦ 1 0 2 1 | 0 0  2 1 0  1  2 0 | 0 0 0  1 0  2 0 0 0 0  1 0 | * * * * * 12 * * * * * | 0 0 1 1 0 0
.(o.)x3.(o.)o .(..).&#x  ♦ 0 1 0 3 | 0 0  0 0 3  0  0 3 | 0 0 0  0 0  0 3 0 0 0  0 1 | * * * * *  * 4 * * * * | 0 0 1 0 1 0
.(.o).3.(.x).3.(.o).     ♦ 0 0 6 0 | 0 0  0 0 0 12  0 0 | 0 0 0  0 0  0 0 4 4 0  0 0 | * * * * *  * * 1 * * * | 0 1 0 0 0 1
.(.o)x3.(.x)o .(..).&#x  ♦ 0 0 3 3 | 0 0  0 0 0  3  6 3 | 0 0 0  0 0  0 0 1 0 3  3 1 | * * * * *  * * * 4 * * | 0 0 1 0 0 1
.(..). .(.x)o3.(.o)o&#x  ♦ 0 0 3 1 | 0 0  0 0 0  3  3 0 | 0 0 0  0 0  0 0 0 1 0  3 0 | * * * * *  * * * * 4 * | 0 0 0 1 0 1
.(..)x3.(..)o3.(..)o     ♦ 0 0 0 4 | 0 0  0 0 0  0  0 6 | 0 0 0  0 0  0 0 0 0 0  0 4 | * * * * *  * * * * * 1 | 0 0 0 0 1 1
-------------------------+---------+--------------------+----------------------------+------------------------+------------
x(o.).3o(o.).3o(o.).&#x  ♦ 4 1 0 0 | 6 4  0 0 0  0  0 0 | 4 6 0  0 0  0 0 0 0 0  0 0 | 1 4 0 0 0  0 0 0 0 0 0 | 1 * * * * *
x(.o).3o(.x).3o(.o).&#x  ♦ 4 0 6 0 | 6 0 12 0 0 12  0 0 | 4 0 6 12 0  0 0 4 4 0  0 0 | 1 0 4 4 0  0 0 1 0 0 0 | * 1 * * * *
x(oo)x3o(ox)o .(..).&#xt ♦ 3 1 3 3 | 3 3  6 3 3  3  6 3 | 1 3 3  3 3  6 3 1 0 3  3 1 | 0 1 1 0 3  3 1 0 1 0 0 | * * 4 * * *
.(..). o(.x)o3o(.o)o&#xt ♦ 1 0 3 1 | 0 0  3 1 0  3  3 0 | 0 0 0  3 0  3 0 0 1 0  3 0 | 0 0 0 1 0  3 0 0 0 1 0 | * * * 4 * *
.(o.)x3.(o.)o3.(o.)o&#x  ♦ 0 1 0 4 | 0 0  0 0 4  0  0 6 | 0 0 0  0 0  0 6 0 0 0  0 4 | 0 0 0 0 0  0 4 0 0 0 1 | * * * * 1 *
.(.o)o3.(.x)o3.(.o)o&#x  ♦ 0 0 6 4 | 0 0  0 0 0 12 12 6 | 0 0 0  0 0  0 0 4 4 6 12 4 | 0 0 0 0 0  0 0 1 4 4 1 | * * * * * 1


oooo3ooxo3oxox&#xr   → all heights = sqrt(5/8) = 0.790569

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


xoo3oxo oxo3oox&#xt   → both heights = 1/sqrt(3) = 0.577350
({3} || pseudo bidual triddip || perp {3})

o..3o.. o..3o..     | 3 * * ♦ 2  6 0 0  0 0 | 1 6 3  6 0 0  0 0 0 0 | 3 6 3 2 0 0 0 | 3 2 1 0
.o.3.o. .o.3.o.     | * 9 * ♦ 0  2 2 2  2 0 | 0 1 2  4 1 1  4 2 1 0 | 1 2 4 2 2 2 1 | 2 1 2 1
..o3..o ..o3..o     | * * 3 ♦ 0  0 0 0  6 2 | 0 0 0  0 0 0  6 3 6 1 | 0 0 3 0 2 6 3 | 1 0 3 2
--------------------+-------+---------------+-----------------------+---------------+--------
x.. ... ... ...     | 2 0 0 | 3  * * *  * * | 1 3 0  0 0 0  0 0 0 0 | 3 3 0 0 0 0 0 | 3 1 0 0
oo.3oo. oo.3oo.&#x  | 1 1 0 | * 18 * *  * * | 0 1 1  2 0 0  0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
... .x. ... ...     | 0 2 0 | *  * 9 *  * * | 0 0 1  0 1 0  2 0 0 0 | 1 0 2 0 2 1 0 | 2 0 1 1
... ... .x. ...     | 0 2 0 | *  * * 9  * * | 0 0 0  2 0 1  0 1 0 0 | 0 1 2 2 0 0 1 | 1 1 2 0
.oo3.oo .oo3.oo&#x  | 0 1 1 | *  * * * 18 * | 0 0 0  0 0 0  2 1 1 0 | 0 0 2 0 1 2 1 | 1 0 2 1
... ... ... ..x     | 0 0 2 | *  * * *  * 3 | 0 0 0  0 0 0  0 0 3 1 | 0 0 0 0 0 3 3 | 0 0 3 1
--------------------+-------+---------------+-----------------------+---------------+--------
x..3o.. ... ...     | 3 0 0 | 3  0 0 0  0 0 | 1 * *  * * *  * * * * | 3 0 0 0 0 0 0 | 3 0 0 0
xo. ... ... ...&#x  | 2 1 0 | 1  2 0 0  0 0 | * 9 *  * * *  * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
... ox. ... ...&#x  | 1 2 0 | 0  2 1 0  0 0 | * * 9  * * *  * * * * | 1 0 2 0 0 0 0 | 2 0 1 0
... ... ox. ...&#x  | 1 2 0 | 0  2 0 1  0 0 | * * * 18 * *  * * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.o.3.x. ... ...     | 0 3 0 | 0  0 3 0  0 0 | * * *  * 3 *  * * * * | 1 0 0 0 2 0 0 | 2 0 0 1
... ... .x.3.o.     | 0 3 0 | 0  0 0 3  0 0 | * * *  * * 3  * * * * | 0 0 0 2 0 0 1 | 0 1 2 0
... .xo ... ...&#x  | 0 2 1 | 0  0 1 0  2 0 | * * *  * * * 18 * * * | 0 0 1 0 1 1 0 | 1 0 1 1
... ... .xo ...&#x  | 0 2 1 | 0  0 0 1  2 0 | * * *  * * *  * 9 * * | 0 0 2 0 0 0 1 | 1 0 2 0
... ... ... .ox&#x  | 0 1 2 | 0  0 0 0  2 1 | * * *  * * *  * * 9 * | 0 0 0 0 0 2 1 | 0 0 2 1
... ... ..o3..x     | 0 0 3 | 0  0 0 0  0 3 | * * *  * * *  * * * 1 | 0 0 0 0 0 0 3 | 0 0 3 0
--------------------+-------+---------------+-----------------------+---------------+--------
xo.3ox. ... ...&#x  ♦ 3 3 0 | 3  6 3 0  0 0 | 1 3 3  0 1 0  0 0 0 0 | 3 * * * * * * | 2 0 0 0
xo. ... ox. ...&#x  ♦ 2 2 0 | 1  4 0 1  0 0 | 0 2 0  2 0 0  0 0 0 0 | * 9 * * * * * | 1 1 0 0
... oxo oxo ...&#x  ♦ 1 4 1 | 0  4 2 2  4 0 | 0 0 2  2 0 0  2 2 0 0 | * * 9 * * * * | 1 0 1 0
... ... ox.3oo.&#x  ♦ 1 3 0 | 0  3 0 3  0 0 | 0 0 0  3 0 1  0 0 0 0 | * * * 6 * * * | 0 1 1 0
.oo3.xo ... ...&#x  ♦ 0 3 1 | 0  0 3 0  3 0 | 0 0 0  0 1 0  3 0 0 0 | * * * * 6 * * | 1 0 0 1
... .xo ... .ox&#x  ♦ 0 2 2 | 0  0 1 0  4 1 | 0 0 0  0 0 0  2 0 2 0 | * * * * * 9 * | 0 0 1 1
... ... .xo3.ox&#x  ♦ 0 3 3 | 0  0 0 3  6 3 | 0 0 0  0 0 1  0 3 3 1 | * * * * * * 3 | 0 0 2 0
--------------------+-------+---------------+-----------------------+---------------+--------
xoo3oxo oxo ...&#xt ♦ 3 6 1 | 3 12 6 3  6 0 | 1 6 6  6 2 0  6 3 0 0 | 2 3 3 0 2 0 0 | 3 * * *
xo. ... ox.3oo.&#x  ♦ 2 3 0 | 1  6 0 3  0 0 | 0 3 0  6 0 1  0 0 0 0 | 0 3 0 2 0 0 0 | * 3 * *
... oxo oxo3oox&#xt ♦ 1 6 3 | 0  6 3 6 12 3 | 0 0 3  6 0 2  6 6 6 1 | 0 0 3 2 0 3 2 | * * 3 *
.oo3.xo ... .ox&#x  ♦ 0 3 2 | 0  0 3 0  6 1 | 0 0 0  0 1 0  6 0 3 0 | 0 0 0 0 2 3 0 | * * * 3

or
o..3o.. o..3o..     & | 6 * ♦ 2  6  0 | 1  6  3  6 0 | 3  6 3  2 | 4 2
.o.3.o. .o.3.o.       | * 9 ♦ 0  4  4 | 0  2  4  8 2 | 2  4 4  4 | 4 2
----------------------+-----+---------+--------------+-----------+----
x.. ... ... ...     & | 2 0 | 6  *  * | 1  3  0  0 0 | 3  3 0  0 | 3 1
oo.3oo. oo.3oo.&#x  & | 1 1 | * 36  * | 0  1  1  2 0 | 1  2 2  1 | 3 1
... .x. ... ...     & | 0 2 | *  * 18 | 0  0  1  2 1 | 1  1 2  2 | 3 1
----------------------+-----+---------+--------------+-----------+----
x..3o.. ... ...     & | 3 0 | 3  0  0 | 2  *  *  * * | 3  0 0  0 | 3 0
xo. ... ... ...&#x  & | 2 1 | 1  2  0 | * 18  *  * * | 1  2 0  0 | 2 1
... ox. ... ...&#x  & | 1 2 | 0  2  1 | *  * 18  * * | 1  0 2  0 | 3 0
... ... ox. ...&#x  & | 1 2 | 0  2  1 | *  *  * 36 * | 0  1 1  1 | 2 1
.o.3.x. ... ...     & | 0 3 | 0  0  3 | *  *  *  * 6 | 1  0 0  2 | 2 1
----------------------+-----+---------+--------------+-----------+----
xo.3ox. ... ...&#x  & ♦ 3 3 | 3  6  3 | 1  3  3  0 1 | 6  * *  * | 2 0
xo. ... ox. ...&#x  & ♦ 2 2 | 1  4  1 | 0  2  0  2 0 | * 18 *  * | 1 1
... oxo oxo ...&#x    ♦ 2 4 | 0  8  4 | 0  0  4  4 0 | *  * 9  * | 2 0
... ... ox.3oo.&#x  & ♦ 1 3 | 0  3  3 | 0  0  0  3 1 | *  * * 12 | 1 1
----------------------+-----+---------+--------------+-----------+----
xoo3oxo oxo ...&#xt & ♦ 4 6 | 3 18  9 | 1  6  9 12 2 | 2  3 3  2 | 6 *
xo. ... ox.3oo.&#x  & ♦ 2 3 | 1  6  3 | 0  3  0  6 1 | 0  3 0  2 | * 6


oxoox ooxoo3oxoxo&#xr   → height(1,2) = height(2,3) = height(4,5) = sqrt(5/12) = 0.645497
                          height(3,4) = sqrt(2/3) = 0.816497
                          height(1,5) = sqrt(3)/2 = 0.866025

o.... o....3o....     | 1 * * * * ♦ 6 2 0 0  0 0 0 0 0 0 0 0 | 3 6 1 6 0 0 0 0 0 0  0 0 0 0 0 0 0 0 | 2 3 3 6 0 0 0 0 0 0 0 0 0 | 1 3 2 0 0 0
.o... .o...3.o...     | * 6 * * * ♦ 1 0 1 2  2 1 1 0 0 0 0 0 | 1 2 0 1 1 2 1 2 1 2  2 1 0 0 0 0 0 0 | 1 2 1 2 1 1 2 1 1 2 0 0 0 | 1 2 1 1 1 0
..o.. ..o..3..o..     | * * 3 * * ♦ 0 0 0 0  4 0 0 2 2 0 0 0 | 0 0 0 0 0 2 4 2 0 0  4 0 1 2 1 0 0 0 | 0 1 0 0 2 2 2 0 4 2 1 0 0 | 1 1 0 2 2 0
...o. ...o.3...o.     | * * * 3 * ♦ 0 0 0 0  0 2 0 0 2 2 2 0 | 0 0 0 0 0 0 0 0 1 0  4 2 0 1 2 1 1 4 | 0 0 1 0 0 0 2 0 2 4 1 2 2 | 0 2 0 1 2 1
....o ....o3....o     | * * * * 2 ♦ 0 1 0 0  0 0 3 0 0 0 3 1 | 0 0 1 3 0 0 0 0 0 3  0 3 0 0 0 0 3 3 | 0 0 3 3 0 0 0 1 0 3 0 3 1 | 0 3 1 0 1 1
----------------------+-----------+--------------------------+--------------------------------------+---------------------------+------------
oo... oo...3oo...&#x  | 1 1 0 0 0 | 6 * * *  * * * * * * * * | 1 2 0 1 0 0 0 0 0 0  0 0 0 0 0 0 0 0 | 1 2 1 2 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0
o...o o...o3o...o&#x  | 1 0 0 0 1 | * 2 * *  * * * * * * * * | 0 0 1 3 0 0 0 0 0 0  0 0 0 0 0 0 0 0 | 0 0 3 3 0 0 0 0 0 0 0 0 0 | 0 3 1 0 0 0
.x... ..... .....     | 0 2 0 0 0 | * * 3 *  * * * * * * * * | 1 0 0 0 0 2 0 0 1 0  0 0 0 0 0 0 0 0 | 0 2 1 0 1 0 2 0 0 0 0 0 0 | 1 2 0 1 0 0
..... ..... .x...     | 0 2 0 0 0 | * * * 6  * * * * * * * * | 0 1 0 0 1 0 0 1 0 1  0 0 0 0 0 0 0 0 | 1 1 0 1 0 1 0 1 0 1 0 0 0 | 1 1 1 0 1 0
.oo.. .oo..3.oo..&#x  | 0 1 1 0 0 | * * * * 12 * * * * * * * | 0 0 0 0 0 1 1 1 0 0  1 0 0 0 0 0 0 0 | 0 1 0 0 1 1 1 0 1 1 0 0 0 | 1 1 0 1 1 0
.o.o. .o.o.3.o.o.&#x  | 0 1 0 1 0 | * * * *  * 6 * * * * * * | 0 0 0 0 0 0 0 0 1 0  2 1 0 0 0 0 0 0 | 0 0 1 0 0 0 2 0 1 2 0 0 0 | 0 2 0 1 1 0
.o..o .o..o3.o..o&#x  | 0 1 0 0 1 | * * * *  * * 6 * * * * * | 0 0 0 1 0 0 0 0 0 2  0 1 0 0 0 0 0 0 | 0 0 1 2 0 0 0 1 0 2 0 0 0 | 0 2 1 0 1 0
..... ..x.. .....     | 0 0 2 0 0 | * * * *  * * * 3 * * * * | 0 0 0 0 0 0 2 0 0 0  0 0 1 1 0 0 0 0 | 0 0 0 0 1 2 0 0 2 0 1 0 0 | 1 0 0 1 2 0
..oo. ..oo.3..oo.&#x  | 0 0 1 1 0 | * * * *  * * * * 6 * * * | 0 0 0 0 0 0 0 0 0 0  2 0 0 1 1 0 0 0 | 0 0 0 0 0 0 1 0 2 2 1 0 0 | 0 1 0 1 2 0
..... ..... ...x.     | 0 0 0 2 0 | * * * *  * * * * * 3 * * | 0 0 0 0 0 0 0 0 0 0  0 0 0 0 1 1 0 2 | 0 0 0 0 0 0 0 0 0 2 1 1 2 | 0 1 0 0 2 1
...oo ...oo3...oo&#x  | 0 0 0 1 1 | * * * *  * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 0  0 1 0 0 0 0 1 2 | 0 0 1 0 0 0 0 0 0 2 0 2 1 | 0 2 0 0 1 1
....x ..... .....     | 0 0 0 0 2 | * * * *  * * * * * * * 1 | 0 0 1 0 0 0 0 0 0 0  0 0 0 0 0 0 3 0 | 0 0 3 0 0 0 0 0 0 0 0 3 0 | 0 3 0 0 0 1
----------------------+-----------+--------------------------+--------------------------------------+---------------------------+------------
ox... ..... .....&#x  | 1 2 0 0 0 | 2 0 1 0  0 0 0 0 0 0 0 0 | 3 * * * * * * * * *  * * * * * * * * | 0 2 1 0 0 0 0 0 0 0 0 0 0 | 1 2 0 0 0 0
..... ..... ox...&#x  | 1 2 0 0 0 | 2 0 0 1  0 0 0 0 0 0 0 0 | * 6 * * * * * * * *  * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
o...x ..... .....&#x  | 1 0 0 0 2 | 0 2 0 0  0 0 0 0 0 0 0 1 | * * 1 * * * * * * *  * * * * * * * * | 0 0 3 0 0 0 0 0 0 0 0 0 0 | 0 3 0 0 0 0
oo..o oo..o3oo..o&#x  | 1 1 0 0 1 | 1 1 0 0  0 0 1 0 0 0 0 0 | * * * 6 * * * * * *  * * * * * * * * | 0 0 1 2 0 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0
..... .o...3.x...     | 0 3 0 0 0 | 0 0 0 3  0 0 0 0 0 0 0 0 | * * * * 2 * * * * *  * * * * * * * * | 1 0 0 0 0 1 0 1 0 0 0 0 0 | 1 0 1 0 1 0
.xo.. ..... .....&#x  | 0 2 1 0 0 | 0 0 1 0  2 0 0 0 0 0 0 0 | * * * * * 6 * * * *  * * * * * * * * | 0 1 0 0 1 0 1 0 0 0 0 0 0 | 1 1 0 1 0 0
..... .ox.. .....&#x  | 0 1 2 0 0 | 0 0 0 0  2 0 0 1 0 0 0 0 | * * * * * * 6 * * *  * * * * * * * * | 0 0 0 0 1 1 0 0 1 0 0 0 0 | 1 0 0 1 1 0
..... ..... .xo..&#x  | 0 2 1 0 0 | 0 0 0 1  2 0 0 0 0 0 0 0 | * * * * * * * 6 * *  * * * * * * * * | 0 1 0 0 0 1 0 0 0 1 0 0 0 | 1 1 0 0 1 0
.x.o. ..... .....&#x  | 0 2 0 1 0 | 0 0 1 0  0 2 0 0 0 0 0 0 | * * * * * * * * 3 *  * * * * * * * * | 0 0 1 0 0 0 2 0 0 0 0 0 0 | 0 2 0 1 0 0
..... ..... .x..o&#x  | 0 2 0 0 1 | 0 0 0 1  0 0 2 0 0 0 0 0 | * * * * * * * * * 6  * * * * * * * * | 0 0 0 1 0 0 0 1 0 1 0 0 0 | 0 1 1 0 1 0
.ooo. .ooo.3.ooo.&#x  | 0 1 1 1 0 | 0 0 0 0  1 1 0 0 1 0 0 0 | * * * * * * * * * * 12 * * * * * * * | 0 0 0 0 0 0 1 0 1 1 0 0 0 | 0 1 0 1 1 0
.o.oo .o.oo3.o.oo&#x  | 0 1 0 1 1 | 0 0 0 0  0 1 1 0 0 0 1 0 | * * * * * * * * * *  * 6 * * * * * * | 0 0 1 0 0 0 0 0 0 2 0 0 0 | 0 2 0 0 1 0
..... ..x..3..o..     | 0 0 3 0 0 | 0 0 0 0  0 0 0 3 0 0 0 0 | * * * * * * * * * *  * * 1 * * * * * | 0 0 0 0 0 2 0 0 0 0 1 0 0 | 1 0 0 0 2 0
..... ..xo. .....&#x  | 0 0 2 1 0 | 0 0 0 0  0 0 0 1 2 0 0 0 | * * * * * * * * * *  * * * 3 * * * * | 0 0 0 0 0 0 0 0 2 0 1 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 0 0 | * * * * * * * * * *  * * * * 3 * * * | 0 0 0 0 0 0 0 0 0 2 1 0 0 | 0 1 0 0 2 0
..... ...o.3...x.     | 0 0 0 3 0 | 0 0 0 0  0 0 0 0 0 3 0 0 | * * * * * * * * * *  * * * * * 1 * * | 0 0 0 0 0 0 0 0 0 0 1 0 2 | 0 0 0 0 2 1
...ox ..... .....&#x  | 0 0 0 1 2 | 0 0 0 0  0 0 0 0 0 0 2 1 | * * * * * * * * * *  * * * * * * 3 * | 0 0 1 0 0 0 0 0 0 0 0 2 0 | 0 2 0 0 0 1
..... ..... ...xo&#x  | 0 0 0 2 1 | 0 0 0 0  0 0 0 0 0 1 2 0 | * * * * * * * * * *  * * * * * * * 6 | 0 0 0 0 0 0 0 0 0 1 0 1 1 | 0 1 0 0 1 1
----------------------+-----------+--------------------------+--------------------------------------+---------------------------+------------
..... oo...3ox...&#x  ♦ 1 3 0 0 0 | 3 0 0 3  0 0 0 0 0 0 0 0 | 0 3 0 0 1 0 0 0 0 0  0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * | 1 0 1 0 0 0
oxo.. ..... oxo..&#xt ♦ 1 4 1 0 0 | 4 0 2 2  4 0 0 0 0 0 0 0 | 2 2 0 0 0 2 0 2 0 0  0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * | 1 1 0 0 0 0
ox.ox ..... .....&#xr ♦ 1 2 0 1 2 | 2 2 1 0  0 2 2 0 0 0 2 1 | 1 0 1 2 0 0 0 0 1 0  0 2 0 0 0 0 1 0 | * * 3 * * * * * * * * * * | 0 2 0 0 0 0
..... ..... ox..o&#x  ♦ 1 2 0 0 1 | 2 1 0 1  0 0 2 0 0 0 0 0 | 0 1 0 2 0 0 0 0 0 1  0 0 0 0 0 0 0 0 | * * * 6 * * * * * * * * * | 0 1 1 0 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 2 0 0 0  0 0 0 0 0 0 0 0 | * * * * 3 * * * * * * * * | 1 0 0 1 0 0
..... .ox..3.xo..&#x  ♦ 0 3 3 0 0 | 0 0 0 3  6 0 0 3 0 0 0 0 | 0 0 0 0 1 0 3 3 0 0  0 0 1 0 0 0 0 0 | * * * * * 2 * * * * * * * | 1 0 0 0 1 0
.xoo. ..... .....&#x  ♦ 0 2 1 1 0 | 0 0 1 0  2 2 0 0 1 0 0 0 | 0 0 0 0 0 1 0 0 1 0  2 0 0 0 0 0 0 0 | * * * * * * 6 * * * * * * | 0 1 0 1 0 0
..... .o..o3.x..o&#x  ♦ 0 3 0 0 1 | 0 0 0 3  0 0 3 0 0 0 0 0 | 0 0 0 0 1 0 0 0 0 3  0 0 0 0 0 0 0 0 | * * * * * * * 2 * * * * * | 0 0 1 0 1 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 1 0 0 0  2 0 0 1 0 0 0 0 | * * * * * * * * 6 * * * * | 0 0 0 1 1 0
..... ..... .xoxo&#xr ♦ 0 2 1 2 1 | 0 0 0 1  2 2 2 0 2 1 2 0 | 0 0 0 0 0 0 0 1 0 1  2 2 0 0 1 0 0 1 | * * * * * * * * * 6 * * * | 0 1 0 0 1 0
..... ..xo.3..ox.&#x  ♦ 0 0 3 3 0 | 0 0 0 0  0 0 0 3 6 3 0 0 | 0 0 0 0 0 0 0 0 0 0  0 0 1 3 3 1 0 0 | * * * * * * * * * * 1 * * | 0 0 0 0 2 0
...ox ..... ...xo&#x  ♦ 0 0 0 2 2 | 0 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 0 0 2 2 | * * * * * * * * * * * 3 * | 0 1 0 0 0 1
..... ...oo3...xo&#x  ♦ 0 0 0 3 1 | 0 0 0 0  0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 1 0 3 | * * * * * * * * * * * * 2 | 0 0 0 0 1 1
----------------------+-----------+--------------------------+--------------------------------------+---------------------------+------------
oxo.. oox..3oxo..&#xt ♦ 1 6 3 0 0 | 6 0 3 6 12 0 0 3 0 0 0 0 | 3 6 0 0 2 6 6 6 0 0  0 0 1 0 0 0 0 0 | 2 3 0 0 3 2 0 0 0 0 0 0 0 | 1 * * * * *
oxoox ..... oxoxo&#xr ♦ 1 4 1 2 2 | 4 2 2 2  4 4 4 0 2 1 4 1 | 2 2 1 4 0 2 0 2 2 2  4 4 0 0 1 0 2 2 | 0 1 2 2 0 0 2 0 0 2 0 1 0 | * 3 * * * *
..... oo..o3ox..o&#x  ♦ 1 3 0 0 1 | 3 1 0 3  0 0 3 0 0 0 0 0 | 0 3 0 3 1 0 0 0 0 3  0 0 0 0 0 0 0 0 | 1 0 0 3 0 0 0 1 0 0 0 0 0 | * * 2 * * *
.xoo. .oxo. .....&#x  ♦ 0 2 2 1 0 | 0 0 1 0  4 2 0 1 2 0 0 0 | 0 0 0 0 0 2 2 0 1 0  4 0 0 1 0 0 0 0 | 0 0 0 0 1 0 2 0 2 0 0 0 0 | * * * 3 * *
..... .oxoo3.xoxo&#xr ♦ 0 3 3 3 1 | 0 0 0 3  6 3 3 3 6 3 3 0 | 0 0 0 0 1 0 3 3 0 3  6 3 1 3 3 1 0 3 | 0 0 0 0 0 1 0 1 3 3 1 0 1 | * * * * 2 *
...ox ...oo3...xo&#x  ♦ 0 0 0 3 2 | 0 0 0 0  0 0 0 0 0 3 6 1 | 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 1 3 6 | 0 0 0 0 0 0 0 0 0 0 0 3 2 | * * * * * 1


xoxooo xoooxo ooxoxo&#xr   → all cyclical heights = 1/sqrt(2) = 0.707107
ABCDEF

o..... o..... o.....     & | 12 * ♦ 1 1  1  1  4 |  2  2  4  3  3 2 |  3  3  5 1 2 | 2 4  A,C,E
.o.... .o.... .o....     & |  * 3 ♦ 0 0  4  4  0 |  4  4  8  0  0 0 |  4  4  4 2 0 | 2 4  B,D,F
---------------------------+------+--------------+------------------+--------------+----
x..... ...... ......     & |  2 0 | 6 *  *  *  * |  2  0  0  0  2 0 |  0  2  2 1 1 | 1 3
...... x..... ......     & |  2 0 | * 6  *  *  * |  0  2  0  2  0 0 |  2  0  2 1 1 | 1 3
oo.... oo.... oo....&#x  & |  1 1 | * * 12  *  * |  1  1  2  0  0 0 |  2  1  2 1 0 | 1 3
oo.... oo.... oo....&#x  & |  1 1 | * *  * 12  * |  1  1  2  0  0 0 |  1  2  2 1 0 | 1 3
o.o... o.o... o.o...&#x  & |  2 0 | * *  *  * 24 |  0  0  1  1  1 1 |  1  1  2 0 1 | 1 3
---------------------------+------+--------------+------------------+--------------+----
xo.... ...... ......&#x  & |  2 1 | 1 0  1  1  0 | 12  *  *  *  * * |  0  1  1 1 0 | 0 3
...... xo.... ......&#x  & |  2 1 | 0 1  1  1  0 |  * 12  *  *  * * |  1  0  1 1 0 | 1 2
ooo... ooo... ooo...&#x  & |  2 1 | 0 0  1  1  1 |  *  * 24  *  * * |  1  1  1 0 0 | 1 2
...... x.o... ......&#x  & |  3 0 | 0 1  0  0  2 |  *  *  * 12  * * |  1  1  0 0 1 | 1 2
...... ...... o.x...&#x  & |  3 0 | 1 0  0  0  2 |  *  *  *  * 12 * |  0  0  2 0 1 | 1 2
o.o.o. o.o.o. o.o.o.&#x    |  3 0 | 0 0  0  0  3 |  *  *  *  *  * 8 |  0  0  3 0 0 | 0 3
---------------------------+------+--------------+------------------+--------------+----
...... xoo... ......&#x  & ♦  3 1 | 0 1  2  1  2 |  0  1  2  1  0 0 | 12  *  * * * | 1 1
...... ...... oox...&#x  & ♦  3 1 | 1 0  1  2  2 |  1  0  2  1  0 0 |  * 12  * * * | 1 1
xox.o. ...... ......&#xr & ♦  5 1 | 1 1  2  2  4 |  1  1  2  0  2 2 |  *  * 12 * * | 0 2
xo...o xo...o ......&#xt & ♦  4 2 | 2 2  4  4  0 |  4  4  0  0  0 0 |  *  *  * 3 * | 0 2  tower F-A-B
...... x.o... o.x...&#x  & ♦  4 0 | 1 1  0  0  4 |  0  0  0  2  2 0 |  *  *  * * 6 | 1 1
---------------------------+------+--------------+------------------+--------------+----
...... xoo... oox...&#x  & ♦  4 1 | 1 1  2  2  4 |  0  2  4  2  2 0 |  2  2  0 0 1 | 6 *
xoxoo. ...... ooxox.&#xr & ♦  8 2 | 3 3  6  6 12 |  6  4  8  4  4 4 |  2  2  4 1 1 | * 6

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