Acronym ico
Name icositetrachoron,
24-cell,
xylochoron,
rectified hexadecachoron,
birectified tesseract,
vertex figure of hext,
Voronoi cell of lattice F4,
Voronoi cell of lattice D4*,
surtegmated tesseract
 
 ©
(edge-skeleton, readily
visualizing oct || pseudo co || oct)
 
Cross sections
 ©
Circumradius 1
Edge radius sqrt(3)/2 = 0.866025
Face radius sqrt(2/3) = 0.816497
Inradius 1/sqrt(2) = 0.707107
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o4o3o o3o4o . o3o . o o . o3o . o4o3o
1x3o4o3o x3o4o .
oct first
x3o . o
{3} first
x . o3o
edge first
. o4o3o
vertex first
2 o3x4o . o3x . q o . q3o . x4o3o
vertex figure
3 x3o4o .
opposite oct
x3x . o x . o3q . o4o3q
4   x3o . q u . o3o . x4o3o
5 o3x . o
opposite {3}
x . q3o . o4o3o
opposite vertex
6   o . o3q  
7 x . o3o
opposite edge
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1o3x3o4o o3x3o .
oct first
o3x . o
{3} first
o . o4o
vertex first
. x3o4o
oct first
2 x3o3x . x3o . q x . x4o
vertex figure
. o3x4o
3a o3x3o .
opposite oct
x3x . o u . o4o . x3o4o
opposite oct
3b o . o4q
4   o3x . q x . x4o  
5 x3o . o
opposite {3}
o . o4o
opposite vertex
 o3o3o *b3o o3o3o    . o3o . *b3o o . o    o . o3o *b3o
1o3x3o *b3o o3x3o    .
oct first
o3x . *b3o
oct first
o . o    o
vertex first
. x3o *b3o
oct first
2 x3o3x    . x3o . *b3x x . x    x
vertex figure
. o3x *b3x
3a o3x3o    .
opposite oct
o3x . *b3o
opposite oct
u . o    o . x3o *b3o
opposite oct
3b o . u    o
3c o . o    u
4     x . x    x  
5 o . o    o
opposite vertex
Lace city
in approx. ASCII-art
 ©  
         o3o         
                     
o3o   q3o   o3q   o3o
                     
   o3q         q3o   
                     
o3o   q3o   o3q   o3o
                     
         o3o         
 ©  
   o3x   x3o   
               
x3o   x3x   o3x
               
   o3x   x3o   
 ©  
o4o  x4o  o4o
             
x4o  o4q  x4o
             
o4o  x4o  o4o
Coordinates
    1. (1, 0, 0, 0)                & all permutations, all changes of sign
      (vertex inscribed q-hex)
    2. (1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
      (vertex inscribed tes)
  • or just   (1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
    (in dual positioning)
  • (the compound of those 2 such oriented icositetrachora is stoc)
General of army (is itself convex)
Colonel of regiment (is itself locally convex
by cells: cho co cube oct oho thah
hoh honho 8400024
hohoh 8008016
huhoh 8000016
dod honho 4400416
hodho 4001648
odho 400048
ihi 01200024
ohuhoh 0808016
ghahoh 0800016
doh honho 040888
ratho 040808
gico (compound) 0024000
ico 0002400
shahoh 0001680
oh 000880
)
Dual (selfdual, in different orientation)
Dihedral angles
  • at {3} between oct and oct:   120°
Confer
Grünbaumian relatives:
2ico   2ico+48{4}+128{3}   2ico+2gico   ico+gico+72{4}   ico+gico+24co  
compounds:
stoc   chi   dox  
segmentochora:
oct || co   {6} || oct   cubpy  
related CRFs:
pabdico   pexic   bicyte ausodip   pacsrit   poxic   pocsric   cytau tes   ecubedpy   ecubpy  
uniform relative:
hex   tes  
decompositions:
icopy  
general polytopal classes:
regular   noble polytopes   bistratic lace towers   partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   mathworld   quickfur

Considering its cells, i.e. the octs, more as trigonal antiprisms, then always 6 build a closed ring each, 4 of witch thus are swirling around each other.

As can be seen from what is mentioned above (at coordinates): the hex-diminished ico is nothing but the tes. Conversely, the 8-diminished ico (corresponding to the vertex directions of tes) is nothing but the hex.

Note that ico can be thought of as the external blend of 24 octpies. This decomposition is described as the degenerate segmentoteron ox3oo4oo3oo&#x.

The desmic configuration of the vertices of the projective compound of 3 tetrahedra (mentioned here) can, by doubling each point into antipodal pairs, transfered into elliptical space of the next dimension, then becoming the points of this icositetrachoron. In fact, the former vertex sets of the 3 tetrahedra here become the vertices of the 3 inscribed hexes. Projective lines of the former setup here would become great circles for sure.


Incidence matrix according to Dynkin symbol

x3o4o3o

. . . . | 24   8 | 12 |  6
--------+----+----+----+---
x . . . |  2 | 96 |  3 |  3
--------+----+----+----+---
x3o . . |  3 |  3 | 96 |  2
--------+----+----+----+---
x3o4o .   6 | 12 |  8 | 24

snubbed forms: β3o4o3o

x3o4o3/2o

. . .   . | 24   8 | 12 |  6
----------+----+----+----+---
x . .   . |  2 | 96 |  3 |  3
----------+----+----+----+---
x3o .   . |  3 |  3 | 96 |  2
----------+----+----+----+---
x3o4o   .   6 | 12 |  8 | 24

x3o4/3o3o

. .   . . | 24   8 | 12 |  6
----------+----+----+----+---
x .   . . |  2 | 96 |  3 |  3
----------+----+----+----+---
x3o   . . |  3 |  3 | 96 |  2
----------+----+----+----+---
x3o4/3o .   6 | 12 |  8 | 24

x3o4/3o3/2o

. .   .   . | 24   8 | 12 |  6
------------+----+----+----+---
x .   .   . |  2 | 96 |  3 |  3
------------+----+----+----+---
x3o   .   . |  3 |  3 | 96 |  2
------------+----+----+----+---
x3o4/3o   .   6 | 12 |  8 | 24

x3/2o4o3o

.   . . . | 24   8 | 12 |  6
----------+----+----+----+---
x   . . . |  2 | 96 |  3 |  3
----------+----+----+----+---
x3/2o . . |  3 |  3 | 96 |  2
----------+----+----+----+---
x3/2o4o .   6 | 12 |  8 | 24

x3/2o4o3/2o

.   . .   . | 24   8 | 12 |  6
------------+----+----+----+---
x   . .   . |  2 | 96 |  3 |  3
------------+----+----+----+---
x3/2o .   . |  3 |  3 | 96 |  2
------------+----+----+----+---
x3/2o4o   .   6 | 12 |  8 | 24

x3/2o4/3o3o

.   .   . . | 24   8 | 12 |  6
------------+----+----+----+---
x   .   . . |  2 | 96 |  3 |  3
------------+----+----+----+---
x3/2o   . . |  3 |  3 | 96 |  2
------------+----+----+----+---
x3/2o4/3o .   6 | 12 |  8 | 24

x3/2o4/3o3/2o

.   .   .   . | 24   8 | 12 |  6
--------------+----+----+----+---
x   .   .   . |  2 | 96 |  3 |  3
--------------+----+----+----+---
x3/2o   .   . |  3 |  3 | 96 |  2
--------------+----+----+----+---
x3/2o4/3o   .   6 | 12 |  8 | 24

o3x3o4o

. . . . | 24   8 |  4  8 |  4 2
--------+----+----+-------+-----
. x . . |  2 | 96 |  1  2 |  2 1
--------+----+----+-------+-----
o3x . . |  3 |  3 | 32  * |  2 0
. x3o . |  3 |  3 |  * 64 |  1 1
--------+----+----+-------+-----
o3x3o .   6 | 12 |  4  4 | 16 *
. x3o4o   6 | 12 |  0  8 |  * 8

snubbed forms: o3β3o4o

o3x3o4/3o

. . .   . | 24   8 |  4  8 |  4 2
----------+----+----+-------+-----
. x .   . |  2 | 96 |  1  2 |  2 1
----------+----+----+-------+-----
o3x .   . |  3 |  3 | 32  * |  2 0
. x3o   . |  3 |  3 |  * 64 |  1 1
----------+----+----+-------+-----
o3x3o   .   6 | 12 |  4  4 | 16 *
. x3o4/3o   6 | 12 |  0  8 |  * 8

o3x3/2o4o

. .   . . | 24   8 |  4  8 |  4 2
----------+----+----+-------+-----
. x   . . |  2 | 96 |  1  2 |  2 1
----------+----+----+-------+-----
o3x   . . |  3 |  3 | 32  * |  2 0
. x3/2o . |  3 |  3 |  * 64 |  1 1
----------+----+----+-------+-----
o3x3/2o .   6 | 12 |  4  4 | 16 *
. x3/2o4o   6 | 12 |  0  8 |  * 8

o3x3/2o4/3o

. .   .   . | 24   8 |  4  8 |  4 2
------------+----+----+-------+-----
. x   .   . |  2 | 96 |  1  2 |  2 1
------------+----+----+-------+-----
o3x   .   . |  3 |  3 | 32  * |  2 0
. x3/2o   . |  3 |  3 |  * 64 |  1 1
------------+----+----+-------+-----
o3x3/2o   .   6 | 12 |  4  4 | 16 *
. x3/2o4/3o   6 | 12 |  0  8 |  * 8

o3/2x3o4o

.   . . . | 24   8 |  4  8 |  4 2
----------+----+----+-------+-----
.   x . . |  2 | 96 |  1  2 |  2 1
----------+----+----+-------+-----
o3/2x . . |  3 |  3 | 32  * |  2 0
.   x3o . |  3 |  3 |  * 64 |  1 1
----------+----+----+-------+-----
o3/2x3o .   6 | 12 |  4  4 | 16 *
.   x3o4o   6 | 12 |  0  8 |  * 8

o3/2x3o4/3o

.   . .   . | 24   8 |  4  8 |  4 2
------------+----+----+-------+-----
.   x .   . |  2 | 96 |  1  2 |  2 1
------------+----+----+-------+-----
o3/2x .   . |  3 |  3 | 32  * |  2 0
.   x3o   . |  3 |  3 |  * 64 |  1 1
------------+----+----+-------+-----
o3/2x3o   .   6 | 12 |  4  4 | 16 *
.   x3o4/3o   6 | 12 |  0  8 |  * 8

o3/2x3/2o4o

.   .   . . | 24   8 |  4  8 |  4 2
------------+----+----+-------+-----
.   x   . . |  2 | 96 |  1  2 |  2 1
------------+----+----+-------+-----
o3/2x   . . |  3 |  3 | 32  * |  2 0
.   x3/2o . |  3 |  3 |  * 64 |  1 1
------------+----+----+-------+-----
o3/2x3/2o .   6 | 12 |  4  4 | 16 *
.   x3/2o4o   6 | 12 |  0  8 |  * 8

o3/2x3/2o4/3o

.   .   .   . | 24   8 |  4  8 |  4 2
--------------+----+----+-------+-----
.   x   .   . |  2 | 96 |  1  2 |  2 1
--------------+----+----+-------+-----
o3/2x   .   . |  3 |  3 | 32  * |  2 0
.   x3/2o   . |  3 |  3 |  * 64 |  1 1
--------------+----+----+-------+-----
o3/2x3/2o   .   6 | 12 |  4  4 | 16 *
.   x3/2o4/3o   6 | 12 |  0  8 |  * 8

o3x3o *b3o

. . .    . | 24   8 |  4  4  4 | 2 2 2
-----------+----+----+----------+------
. x .    . |  2 | 96 |  1  1  1 | 1 1 1
-----------+----+----+----------+------
o3x .    . |  3 |  3 | 32  *  * | 1 1 0
. x3o    . |  3 |  3 |  * 32  * | 1 0 1
. x . *b3o |  3 |  3 |  *  * 32 | 0 1 1
-----------+----+----+----------+------
o3x3o    .   6 | 12 |  4  4  0 | 8 * *
o3x . *b3o   6 | 12 |  4  0  4 | * 8 *
. x3o *b3o   6 | 12 |  0  4  4 | * * 8

snubbed forms: o3β3o *b3o

o3x3o *b3/2o

. . .      . | 24   8 |  4  4  4 | 2 2 2
-------------+----+----+----------+------
. x .      . |  2 | 96 |  1  1  1 | 1 1 1
-------------+----+----+----------+------
o3x .      . |  3 |  3 | 32  *  * | 1 1 0
. x3o      . |  3 |  3 |  * 32  * | 1 0 1
. x . *b3/2o |  3 |  3 |  *  * 32 | 0 1 1
-------------+----+----+----------+------
o3x3o      .   6 | 12 |  4  4  0 | 8 * *
o3x . *b3/2o   6 | 12 |  4  0  4 | * 8 *
. x3o *b3/2o   6 | 12 |  0  4  4 | * * 8

o3x3/2o *b3/2o

. .   .      . | 24   8 |  4  4  4 | 2 2 2
---------------+----+----+----------+------
. x   .      . |  2 | 96 |  1  1  1 | 1 1 1
---------------+----+----+----------+------
o3x   .      . |  3 |  3 | 32  *  * | 1 1 0
. x3/2o      . |  3 |  3 |  * 32  * | 1 0 1
. x   . *b3/2o |  3 |  3 |  *  * 32 | 0 1 1
---------------+----+----+----------+------
o3x3/2o      .   6 | 12 |  4  4  0 | 8 * *
o3x   . *b3/2o   6 | 12 |  4  0  4 | * 8 *
. x3/2o *b3/2o   6 | 12 |  0  4  4 | * * 8

o3/2x3/2o *b3/2o

.   .   .      . | 24   8 |  4  4  4 | 2 2 2
-----------------+----+----+----------+------
.   x   .      . |  2 | 96 |  1  1  1 | 1 1 1
-----------------+----+----+----------+------
o3/2x   .      . |  3 |  3 | 32  *  * | 1 1 0
.   x3/2o      . |  3 |  3 |  * 32  * | 1 0 1
.   x   . *b3/2o |  3 |  3 |  *  * 32 | 0 1 1
-----------------+----+----+----------+------
o3/2x3/2o      .   6 | 12 |  4  4  0 | 8 * *
o3/2x   . *b3/2o   6 | 12 |  4  0  4 | * 8 *
.   x3/2o *b3/2o   6 | 12 |  0  4  4 | * * 8

xox3oxo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(oct || pseudo co || oct)

o..3o..4o..     | 6  * *   4  4  0  0  0 | 4  4  4 0  0  0 0 | 1 4 1 0 0
.o.3.o.4.o.     | * 12 *   0  2  4  2  0 | 0  1  4 2  4  1 0 | 0 2 2 2 0
..o3..o4..o     | *  * 6   0  0  0  4  4 | 0  0  0 0  4  4 4 | 0 0 1 4 1
----------------+--------+----------------+-------------------+----------
x.. ... ...     | 2  0 0 | 12  *  *  *  * | 2  1  0 0  0  0 0 | 1 2 0 0 0
oo.3oo.4oo.&#x  | 1  1 0 |  * 24  *  *  * | 0  1  2 0  0  0 0 | 0 2 1 0 0
... .x. ...     | 0  2 0 |  *  * 24  *  * | 0  0  1 1  1  0 0 | 0 1 1 1 0
.oo3.oo4.oo&#x  | 0  1 1 |  *  *  * 24  * | 0  0  0 0  2  1 0 | 0 0 1 2 0
..x ... ...     | 0  0 2 |  *  *  *  * 12 | 0  0  0 0  0  1 2 | 0 0 0 2 1
----------------+--------+----------------+-------------------+----------
x..3o.. ...     | 3  0 0 |  3  0  0  0  0 | 8  *  * *  *  * * | 1 1 0 0 0
xo. ... ...&#x  | 2  1 0 |  1  2  0  0  0 | * 12  * *  *  * * | 0 2 0 0 0
... ox. ...&#x  | 1  2 0 |  0  2  1  0  0 | *  * 24 *  *  * * | 0 1 1 0 0
.o.3.x. ...     | 0  3 0 |  0  0  3  0  0 | *  *  * 8  *  * * | 0 1 0 1 0
... .xo ...&#x  | 0  2 1 |  0  0  1  2  0 | *  *  * * 24  * * | 0 0 1 1 0
.ox ... ...&#x  | 0  1 2 |  0  0  0  2  1 | *  *  * *  * 12 * | 0 0 0 2 0
..x3..o ...     | 0  0 3 |  0  0  0  0  3 | *  *  * *  *  * 8 | 0 0 0 1 1
----------------+--------+----------------+-------------------+----------
x..3o..4o..      6  0 0 | 12  0  0  0  0 | 8  0  0 0  0  0 0 | 1 * * * *
xo.3ox. ...&#x   3  3 0 |  3  6  3  0  0 | 1  3  3 1  0  0 0 | * 8 * * *
... oxo4ooo&#xt  1  4 1 |  0  4  4  4  0 | 0  0  4 0  4  0 0 | * * 6 * *
.ox3.xo ...&#x   0  3 3 |  0  0  3  6  3 | 0  0  0 1  3  3 1 | * * * 8 *
..x3..o4..o      0  0 6 |  0  0  0  0 12 | 0  0  0 0  0  0 8 | * * * * 1
or
o..3o..4o..     & | 12  *   4  4  0 |  4  4  4 0 | 1  4 1
.o.3.o.4.o.       |  * 12   0  4  4 |  0  2  8 2 | 0  4 2
------------------+-------+----------+------------+-------
x.. ... ...     & |  2  0 | 24  *  * |  2  1  0 0 | 1  2 0
oo.3oo.4oo.&#x  & |  1  1 |  * 48  * |  0  1  2 0 | 0  2 1
... .x. ...       |  0  2 |  *  * 24 |  0  0  2 1 | 0  2 1
------------------+-------+----------+------------+-------
x..3o.. ...     & |  3  0 |  3  0  0 | 16  *  * * | 1  1 0
xo. ... ...&#x  & |  2  1 |  1  2  0 |  * 24  * * | 0  2 0
... ox. ...&#x  & |  1  2 |  0  2  1 |  *  * 48 * | 0  1 1
.o.3.x. ...       |  0  3 |  0  0  3 |  *  *  * 8 | 0  2 0
------------------+-------+----------+------------+-------
x..3o..4o..     &   6  0 | 12  0  0 |  8  0  0 0 | 2  * *
xo.3ox. ...&#x  &   3  3 |  3  6  3 |  1  3  3 1 | * 16 *
... oxo4ooo&#xt     2  4 |  0  8  4 |  0  0  8 0 | *  * 6

oxo3xox3oxo&#xt   → both heights = 1/sqrt(2) = 0.707107
(oct || pseudo co || oct)

o..3o..3o..     | 6  * *   4  4  0  0  0  0 | 2 2  2  4  2 0 0  0  0  0 0 0 | 1 2 2 1 0 0 0
.o.3.o.3.o.     | * 12 *   0  2  2  2  2  0 | 0 0  2  1  2 1 1  2  1  2 0 0 | 0 1 1 2 1 1 0
..o3..o3..o     | *  * 6   0  0  0  0  4  4 | 0 0  0  0  0 0 0  2  4  2 2 2 | 0 0 0 1 2 2 1
----------------+--------+-------------------+-------------------------------+--------------
... x.. ...     | 2  0 0 | 12  *  *  *  *  * | 1 1  0  1  0 0 0  0  0  0 0 0 | 1 1 1 0 0 0 0
oo. oo. oo.&#x  | 1  1 0 |  * 24  *  *  *  * | 0 0  1  1  1 0 0  0  0  0 0 0 | 0 1 1 1 0 0 0
.x. ... ...     | 0  2 0 |  *  * 12  *  *  * | 0 0  1  0  0 1 0  1  0  0 0 0 | 0 1 0 1 1 0 0
... ... .x.     | 0  2 0 |  *  *  * 12  *  * | 0 0  0  0  1 0 1  1  0  0 0 0 | 0 0 1 1 0 1 0
.oo .oo .oo&#x  | 0  1 1 |  *  *  *  * 24  * | 0 0  0  0  0 0 0  1  1  1 0 0 | 0 0 0 1 1 1 0
... ..x ...     | 0  0 2 |  *  *  *  *  * 12 | 0 0  0  0  0 0 0  0  1  0 1 1 | 0 0 0 0 1 1 1
----------------+--------+-------------------+-------------------------------+--------------
o..3x.. ...     | 3  0 0 |  3  0  0  0  0  0 | 4 *  *  *  * * *  *  *  * * * | 1 1 0 0 0 0 0
... x..3o..     | 3  0 0 |  3  0  0  0  0  0 | * 4  *  *  * * *  *  *  * * * | 1 0 1 0 0 0 0
ox. ... ...&#x  | 1  2 0 |  0  2  1  0  0  0 | * * 12  *  * * *  *  *  * * * | 0 1 0 1 0 0 0
... xo. ...&#x  | 2  1 0 |  1  2  0  0  0  0 | * *  * 12  * * *  *  *  * * * | 0 1 1 0 0 0 0
... ... ox.&#x  | 1  2 0 |  0  2  0  1  0  0 | * *  *  * 12 * *  *  *  * * * | 0 0 1 1 0 0 0
.x.3.o. ...     | 0  3 0 |  0  0  3  0  0  0 | * *  *  *  * 4 *  *  *  * * * | 0 1 0 0 1 0 0
... .o.3.x.     | 0  3 0 |  0  0  0  3  0  0 | * *  *  *  * * 4  *  *  * * * | 0 0 1 0 0 1 0
.xo ... ...&#x  | 0  2 1 |  0  0  1  0  2  0 | * *  *  *  * * * 12  *  * * * | 0 0 0 1 1 0 0
... .ox ...&#x  | 0  1 2 |  0  0  0  0  2  1 | * *  *  *  * * *  * 12  * * * | 0 0 0 0 1 1 0
... ... .xo&#x  | 0  2 1 |  0  0  0  1  2  0 | * *  *  *  * * *  *  * 12 * * | 0 0 0 1 0 1 0
..o3..x ...     | 0  0 3 |  0  0  0  0  0  3 | * *  *  *  * * *  *  *  * 4 * | 0 0 0 0 1 0 1
... ..x3..o     | 0  0 3 |  0  0  0  0  0  3 | * *  *  *  * * *  *  *  * * 4 | 0 0 0 0 0 1 1
----------------+--------+-------------------+-------------------------------+--------------
o..3x..3o..      6  0 0 | 12  0  0  0  0  0 | 4 4  0  0  0 0 0  0  0  0 0 0 | 1 * * * * * *
ox.3xo. ...&#x   3  3 0 |  3  6  3  0  0  0 | 1 0  3  3  0 1 0  0  0  0 0 0 | * 4 * * * * *
... xo.3ox.&#x   3  3 0 |  3  6  0  3  0  0 | 0 1  0  3  3 0 1  0  0  0 0 0 | * * 4 * * * *
oxo ... oxo&#xt  1  4 1 |  0  4  2  2  4  0 | 0 0  2  0  2 0 0  2  0  2 0 0 | * * * 6 * * *
.xo3.ox ...&#x   0  3 3 |  0  0  3  0  6  3 | 0 0  0  0  0 1 0  3  3  0 1 0 | * * * * 4 * *
... .ox3.xo&#x   0  3 3 |  0  0  0  3  6  3 | 0 0  0  0  0 0 1  0  3  3 0 1 | * * * * * 4 *
..o3..x3..o      0  0 6 |  0  0  0  0  0 12 | 0 0  0  0  0 0 0  0  0  0 4 4 | * * * * * * 1
or
o..3o..3o..     & | 12  *   4  4  0  0 | 2 2  2  4  2 0 0 | 1 2 2 1
.o.3.o.3.o.       |  * 12   0  4  2  2 | 0 0  4  2  4 1 1 | 0 2 2 2
------------------+-------+-------------+------------------+--------
... x.. ...     & |  2  0 | 24  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
oo. oo. oo.&#x  & |  1  1 |  * 48  *  * | 0 0  1  1  1 0 0 | 0 1 1 1
.x. ... ...       |  0  2 |  *  * 12  * | 0 0  2  0  0 1 0 | 0 2 0 1
... ... .x.       |  0  2 |  *  *  * 12 | 0 0  0  0  2 0 1 | 0 0 2 1
------------------+-------+-------------+------------------+--------
o..3x.. ...     & |  3  0 |  3  0  0  0 | 8 *  *  *  * * * | 1 1 0 0
... x..3o..     & |  3  0 |  3  0  0  0 | * 8  *  *  * * * | 1 0 1 0
ox. ... ...&#x  & |  1  2 |  0  2  1  0 | * * 24  *  * * * | 0 1 0 1
... xo. ...&#x  & |  2  1 |  1  2  0  0 | * *  * 24  * * * | 0 1 1 0
... ... ox.&#x  & |  1  2 |  0  2  0  1 | * *  *  * 24 * * | 0 0 1 1
.x.3.o. ...       |  0  3 |  0  0  3  0 | * *  *  *  * 4 * | 0 2 0 0
... .o.3.x.       |  0  3 |  0  0  0  3 | * *  *  *  * * 4 | 0 0 2 0
------------------+-------+-------------+------------------+--------
o..3x..3o..     &   6  0 | 12  0  0  0 | 4 4  0  0  0 0 0 | 2 * * *
ox.3xo. ...&#x  &   3  3 |  3  6  3  0 | 1 0  3  3  0 1 0 | * 8 * *
... xo.3ox.&#x  &   3  3 |  3  6  0  3 | 0 1  0  3  3 0 1 | * * 8 *
oxo ... oxo&#xt     2  4 |  0  8  2  2 | 0 0  4  0  4 0 0 | * * * 6

ooqoo3ooooo4oxoxo&#xt   → all heights = 1/2
(pt  || pseudo cube || pseudo q-oct || pseudo cube || pt)

o....3o....4o....     | 1 * * * *  8  0  0 0  0  0 0 | 12  0  0  0  0 | 6  0 0
.o...3.o...4.o...     | * 8 * * *  1  3  3 1  0  0 0 |  3  6  3  0  0 | 3  3 0
..o..3..o..4..o..     | * * 6 * *  0  0  4 0  4  0 0 |  0  4  4  4  0 | 1  4 1
...o.3...o.4...o.     | * * * 8 *  0  0  0 1  3  3 1 |  0  0  3  6  3 | 0  3 3
....o3....o4....o     | * * * * 1  0  0  0 0  0  0 8 |  0  0  0  0 12 | 0  0 6
----------------------+-----------+-------------------+----------------+-------
oo...3oo...4oo...&#x  | 1 1 0 0 0 | 8  *  * *  *  * * |  3  0  0  0  0 | 3  0 0
..... ..... .x...     | 0 2 0 0 0 | * 12  * *  *  * * |  1  2  0  0  0 | 2  1 0
.oo..3.oo..4.oo..&#x  | 0 1 1 0 0 | *  * 24 *  *  * * |  0  2  1  0  0 | 1  2 0
.o.o.3.o.o.4.o.o.&#x  | 0 1 0 1 0 | *  *  * 8  *  * * |  0  0  3  0  0 | 0  3 0
..oo.3..oo.4..oo.&#x  | 0 0 1 1 0 | *  *  * * 24  * * |  0  0  1  2  0 | 0  2 1
..... ..... ...x.     | 0 0 0 2 0 | *  *  * *  * 12 * |  0  0  0  2  1 | 0  1 2
...oo3...oo4...oo&#x  | 0 0 0 1 1 | *  *  * *  *  * 8 |  0  0  0  0  3 | 0  0 3
----------------------+-----------+-------------------+----------------+-------
..... ..... ox...&#x  | 1 2 0 0 0 | 2  1  0 0  0  0 0 | 12  *  *  *  * | 2  0 0
..... ..... .xo..&#x  | 0 2 1 0 0 | 0  1  2 0  0  0 0 |  * 24  *  *  * | 1  1 0
.ooo.3.ooo.4.ooo.&#xt | 0 1 1 1 0 | 0  0  1 1  1  0 0 |  *  * 24  *  * | 0  2 0
..... ..... ..ox.&#x  | 0 0 1 2 0 | 0  0  0 0  2  1 0 |  *  *  * 24  * | 0  1 1
..... ..... ...xo&#x  | 0 0 0 2 1 | 0  0  0 0  0  1 2 |  *  *  *  * 12 | 0  0 2
----------------------+-----------+-------------------+----------------+-------
..... ooo..4oxo..&#xt  1 4 1 0 0 | 4  4  4 0  0  0 0 |  4  4  0  0  0 | 6  * *
.oqo. ..... .xox.&#xt  0 2 2 2 0 | 0  1  4 2  4  1 0 |  0  2  4  2  0 | * 12 *
..... ..ooo4..oxo&#xt  0 0 1 4 1 | 0  0  0 0  4  4 4 |  0  0  0  4  4 | *  * 6
or
o....3o....4o....      & | 2  * *   8  0  0 0 | 12  0  0 |  6  0
.o...3.o...4.o...      & | * 16 *   1  3  3 1 |  3  6  3 |  3  3
..o..3..o..4..o..        | *  * 6   0  0  8 0 |  0  8  4 |  2  4
-------------------------+--------+------------+----------+------
oo...3oo...4oo...&#x   & | 1  1 0 | 16  *  * * |  3  0  0 |  3  0
..... ..... .x...      & | 0  2 0 |  * 24  * * |  1  2  0 |  2  1
.oo..3.oo..4.oo..&#x   & | 0  1 1 |  *  * 48 * |  0  2  1 |  1  2
.o.o.3.o.o.4.o.o.&#x     | 0  2 0 |  *  *  * 8 |  0  0  3 |  0  3
-------------------------+--------+------------+----------+------
..... ..... ox...&#x   & | 1  2 0 |  2  1  0 0 | 24  *  * |  2  0
..... ..... .xo..&#x   & | 0  2 1 |  0  1  2 0 |  * 48  * |  1  1
.ooo.3.ooo.4.ooo.&#xt    | 0  2 1 |  0  0  2 1 |  *  * 24 |  0  2
-------------------------+--------+------------+----------+------
..... ooo..4oxo..&#xt  &  1  4 1 |  4  4  4 0 |  4  4  0 | 12  *
.oqo. ..... .xox.&#xt     0  4 2 |  0  2  8 2 |  0  4  4 |  * 12

o3m3o4o =
qo3oo3oo4ox&#zx   → height = 0
(tegum sum of q-hex and tes)

o.3o.3o.4o.     | 8  *   8  0 | 12 |  6
.o3.o3.o4.o     | * 16   4  4 | 12 |  6
----------------+------+-------+----+---
oo3oo3oo4oo&#x  | 1  1 | 64  * |  3 |  3
.. .. .. .x     | 0  2 |  * 32 |  3 |  3
----------------+------+-------+----+---
.. .. .. ox&#x  | 1  2 |  2  1 | 96 |  2
----------------+------+-------+----+---
qo .. oo4ox&#zx  2  4 |  8  4 |  8 | 24

qoo3ooo3oqo *b3ooq&#zx   → height = 0
(tegum sum of 3 mutually gyrated q-hexs)

o..3o..3o.. *b3o..     | 8 * *   4  4  0 | 12 |  6
.o.3.o.3.o. *b3.o.     | * 8 *   4  0  4 | 12 |  6
..o3..o3..o *b3..o     | * * 8   0  4  4 | 12 |  6
-----------------------+-------+----------+----+---
oo.3oo.3oo. *b3oo.&#x  | 1 1 0 | 32  *  * |  3 |  3
o.o3o.o3o.o *b3o.o&#x  | 1 0 1 |  * 32  * |  3 |  3
.oo3.oo3.oo *b3.oo&#x  | 0 1 1 |  *  * 32 |  3 |  3
-----------------------+-------+----------+----+---
ooo3ooo3ooo *b3ooo&#x  | 1 1 1 |  1  1  1 | 96 |  2
-----------------------+-------+----------+----+---
qoo ... oqo    ooq&#zx  2 2 2 |  4  4  4 |  8 | 24

qo xo3ox4oo&#zx   → height = 0
(tegum sum of (q,x)-ope and para co)

o. o.3o.4o.     & | 12  *   4  4  0 |  4  4  4 0 | 1 1  4
.o .o3.o4.o       |  * 12   0  4  4 |  0  2  8 2 | 2 0  4
------------------+-------+----------+------------+-------
.. x. .. ..     & |  2  0 | 24  *  * |  2  1  0 0 | 0 1  2
oo oo3oo4oo&#x  & |  1  1 |  * 48  * |  0  1  2 0 | 1 0  2
.. .. .x ..       |  0  2 |  *  * 24 |  0  0  2 1 | 1 0  2
------------------+-------+----------+------------+-------
.. x.3o. ..     & |  3  0 |  3  0  0 | 16  *  * * | 0 1  1
.. xo .. ..&#x  & |  2  1 |  1  2  0 |  * 24  * * | 0 0  2
.. .. ox ..&#x  & |  1  2 |  0  2  1 |  *  * 48 * | 1 0  1
.. .o3.x ..       |  0  3 |  0  0  3 |  *  *  * 8 | 0 0  2
------------------+-------+----------+------------+-------
qo .. ox4oo&#zx     2  4 |  0  8  4 |  0  0  8 0 | 6 *  *
.. x.3o.4o.     &   6  0 | 12  0  0 |  8  0  0 0 | * 2  *
.. xo3ox ..&#x  &   3  3 |  3  6  3 |  1  3  3 1 | * * 16

oxo4ooq oxo4qoo&#zx   → all heights = 0 - except not existing lacing(1,3)
(tegum sum of 2 perpendicular q-{4}'s and a tes)

o..4o.. o..4o..     & | 8  *   8  0 |  8  4 |  4 2
.o.4.o. .o.4.o.       | * 16   4  4 |  8  4 |  4 2
----------------------+------+-------+-------+-----
oo.4oo. oo.4oo.&#x  & | 1  1 | 64  * |  2  1 |  2 1
.x. ... ... ...     & | 0  2 |  * 32 |  2  1 |  2 1
----------------------+------+-------+-------+-----
ox. ... ... ...&#x  & | 1  2 |  2  1 | 64  * |  1 1
.xo ... ... ...&#x  & | 1  2 |  2  1 |  * 32 |  2 0
----------------------+------+-------+-------+-----
oxo ... oxo ...&#xt    2  4 |  8  4 |  4  4 | 16 *
ox.4oo. ... qo.&#zx &  2  4 |  8  4 |  8  0 |  * 8

xxo3xox oqo3ooq&#zx   → existing heights = 0
(tegum sum of unit-{6} and 2 bidual (x,q)-triddips)

o..3o.. o..3o..     | 6 * *  1 1  3  3 0  0 0 | 3 3  6 0  0  0 0 | 3 3 0
.o.3.o. .o.3.o.     | * 9 *  0 0  2  0 2  4 0 | 1 0  4 1  4  2 0 | 2 2 2
..o3..o ..o3..o     | * * 9  0 0  0  2 0  4 2 | 0 1  4 0  2  4 1 | 2 2 2
--------------------+-------+------------------+------------------+------
x.. ... ... ...     | 2 0 0 | 3 *  *  * *  * * | 0 3  0 0  0  0 0 | 3 0 0
... x.. ... ...     | 2 0 0 | * 3  *  * *  * * | 3 0  0 0  0  0 0 | 0 3 0
oo.3oo. oo.3oo.&#x  | 1 1 0 | * * 18  * *  * * | 1 0  2 0  0  0 0 | 1 2 0
o.o3o.o o.o3o.o&#x  | 1 0 1 | * *  * 18 *  * * | 0 1  2 0  0  0 0 | 2 1 0
.x. ... ... ...     | 0 2 0 | * *  *  * 9  * * | 0 0  0 1  2  0 0 | 1 0 2
.oo3.oo .oo3.oo&#x  | 0 1 1 | * *  *  * * 36 * | 0 0  1 0  1  1 0 | 1 1 1
... ..x ... ...     | 0 0 2 | * *  *  * *  * 9 | 0 0  0 0  0  2 1 | 0 1 2
--------------------+-------+------------------+------------------+------
... xo. ... ...&#x  | 2 1 0 | 0 1  2  0 0  0 0 | 9 *  * *  *  * * | 0 2 0
x.o ... ... ...&#x  | 2 0 1 | 1 0  0  2 0  0 0 | * 9  * *  *  * * | 2 0 0
ooo3ooo ooo3ooo&#x  | 1 1 1 | 0 0  1  1 0  1 0 | * * 36 *  *  * * | 1 1 0
.x.3.o. ... ...     | 0 3 0 | 0 0  0  0 3  0 0 | * *  * 3  *  * * | 0 0 2
.xo ... ... ...&#x  | 0 2 1 | 0 0  0  0 1  2 0 | * *  * * 18  * * | 1 0 1
... .ox ... ...&#x  | 0 1 2 | 0 0  0  0 0  2 1 | * *  * *  * 18 * | 0 1 1
..o3..x ... ...     | 0 0 3 | 0 0  0  0 0  0 3 | * *  * *  *  * 3 | 0 0 2
--------------------+-------+------------------+------------------+------
xxo ... ... ooq&#xt  2 2 2 | 1 0  2  4 1  4 0 | 0 2  4 0  2  0 0 | 9 * *
... xox oqo ...&#xt  2 2 2 | 0 1  4  2 0  4 1 | 2 0  4 0  0  2 0 | * 9 *
.xo3.ox ... ...&#x   0 3 3 | 0 0  0  0 3  6 3 | 0 0  0 1  3  3 1 | * * 6
or
o..3o.. o..3o..       | 6  *  2  6  0  0 |  6  6 0  0 |  6 0
.o.3.o. .o.3.o.     & | * 18  0  2  2  4 |  1  4 1  6 |  4 2
----------------------+------+------------+------------+-----
x.. ... ... ...     & | 2  0 | 6  *  *  * |  3  0 0  0 |  3 0
oo.3oo. oo.3oo.&#x  & | 1  1 | * 36  *  * |  1  2 0  0 |  3 0
.x. ... ... ...     & | 0  2 | *  * 18  * |  0  0 1  2 |  1 2
.oo3.oo .oo3.oo&#x    | 0  2 | *  *  * 36 |  0  1 0  2 |  2 1
----------------------+------+------------+------------+-----
... xo. ... ...&#x  & | 2  1 | 1  2  0  0 | 18  * *  * |  2 0
ooo3ooo ooo3ooo&#x    | 1  2 | 0  2  0  1 |  * 36 *  * |  2 0
.x.3.o. ... ...     & | 0  3 | 0  0  3  0 |  *  * 6  * |  0 2
.xo ... ... ...&#x  & | 0  3 | 0  0  1  2 |  *  * * 36 |  1 1
----------------------+------+------------+------------+-----
xxo ... ... ooq&#xt &  2  4 | 1  6  1  4 |  2  4 0  2 | 18 *
.xo3.ox ... ...&#x     0  6 | 0  0  6  6 |  0  0 2  6 |  * 6

uooox ouoox oouox oooux&#zx   → all existing heights = 0
(tegum sum of 4 pairwise perpendicular u-lines and a tes)

o.... o.... o.... o....     | 2 * * *  *   8  0  0  0 0 0 0 0 | 4 4 4 0 0 0 0 0 0 0 0 0 | 2 2 2 0 0 0
.o... .o... .o... .o...     | * 2 * *  *   0  8  0  0 0 0 0 0 | 0 0 0 4 4 4 0 0 0 0 0 0 | 2 0 0 2 2 0
..o.. ..o.. ..o.. ..o..     | * * 2 *  *   0  0  8  0 0 0 0 0 | 0 0 0 0 0 0 4 4 4 0 0 0 | 0 2 0 2 0 2
...o. ...o. ...o. ...o.     | * * * 2  *   0  0  0  8 0 0 0 0 | 0 0 0 0 0 0 0 0 0 4 4 4 | 0 0 2 0 2 2
....o ....o ....o ....o     | * * * * 16   1  1  1  1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1
----------------------------+------------+---------------------+-------------------------+------------
o...o o...o o...o o...o&#x  | 1 0 0 0  1 | 16  *  *  * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
.o..o .o..o .o..o .o..o&#x  | 0 1 0 0  1 |  * 16  *  * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 | 1 0 0 1 1 0
..o.o ..o.o ..o.o ..o.o&#x  | 0 0 1 0  1 |  *  * 16  * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 | 0 1 0 1 0 1
...oo ...oo ...oo ...oo&#x  | 0 0 0 1  1 |  *  *  * 16 * * * * | 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 1 0 1 1
....x ..... ..... .....     | 0 0 0 0  2 |  *  *  *  * 8 * * * | 0 0 0 1 0 0 1 0 0 1 0 0 | 0 0 0 1 1 1
..... ....x ..... .....     | 0 0 0 0  2 |  *  *  *  * * 8 * * | 1 0 0 0 0 0 0 1 0 0 1 0 | 0 1 1 0 0 1
..... ..... ....x .....     | 0 0 0 0  2 |  *  *  *  * * * 8 * | 0 1 0 0 1 0 0 0 0 0 0 1 | 1 0 1 0 1 0
..... ..... ..... ....x     | 0 0 0 0  2 |  *  *  *  * * * * 8 | 0 0 1 0 0 1 0 0 1 0 0 0 | 1 1 0 1 0 0
----------------------------+------------+---------------------+-------------------------+------------
..... o...x ..... .....&#x  | 1 0 0 0  2 |  2  0  0  0 0 1 0 0 | 8 * * * * * * * * * * * | 0 1 1 0 0 0
..... ..... o...x .....&#x  | 1 0 0 0  2 |  2  0  0  0 0 0 1 0 | * 8 * * * * * * * * * * | 1 0 1 0 0 0
..... ..... ..... o...x&#x  | 1 0 0 0  2 |  2  0  0  0 0 0 0 1 | * * 8 * * * * * * * * * | 1 1 0 0 0 0
.o..x ..... ..... .....&#x  | 0 1 0 0  2 |  0  2  0  0 1 0 0 0 | * * * 8 * * * * * * * * | 0 0 0 1 1 0
..... ..... .o..x .....&#x  | 0 1 0 0  2 |  0  2  0  0 0 0 1 0 | * * * * 8 * * * * * * * | 1 0 0 0 1 0
..... ..... ..... .o..x&#x  | 0 1 0 0  2 |  0  2  0  0 0 0 0 1 | * * * * * 8 * * * * * * | 1 0 0 1 0 0
..o.x ..... ..... .....&#x  | 0 0 1 0  2 |  0  0  2  0 1 0 0 0 | * * * * * * 8 * * * * * | 0 0 0 1 0 1
..... ..o.x ..... .....&#x  | 0 0 1 0  2 |  0  0  2  0 0 1 0 0 | * * * * * * * 8 * * * * | 0 1 0 0 0 1
..... ..... ..... ..o.x&#x  | 0 0 1 0  2 |  0  0  2  0 0 0 0 1 | * * * * * * * * 8 * * * | 0 1 0 1 0 0
...ox ..... ..... .....&#x  | 0 0 0 1  2 |  0  0  0  2 1 0 0 0 | * * * * * * * * * 8 * * | 0 0 0 0 1 1
..... ...ox ..... .....&#x  | 0 0 0 1  2 |  0  0  0  2 0 1 0 0 | * * * * * * * * * * 8 * | 0 0 1 0 0 1
..... ..... ...ox .....&#x  | 0 0 0 1  2 |  0  0  0  2 0 0 1 0 | * * * * * * * * * * * 8 | 0 0 1 0 1 0
----------------------------+------------+---------------------+-------------------------+------------
..... ..... oo..x oo..x&#xt  1 1 0 0  4 |  4  4  0  0 0 0 2 2 | 0 2 2 0 2 2 0 0 0 0 0 0 | 4 * * * * * (tower: a-e-b)
..... o.o.x ..... o.o.x&#xt  1 0 1 0  4 |  4  0  4  0 0 2 0 2 | 2 0 2 0 0 0 0 2 2 0 0 0 | * 4 * * * * (tower: a-e-c)
..... o..ox o..ox .....&#xt  1 0 0 1  4 |  4  0  0  4 0 2 2 0 | 2 2 0 0 0 0 0 0 0 0 2 2 | * * 4 * * * (tower: a-e-d)
.oo.x ..... ..... .oo.x&#xt  0 1 1 0  4 |  0  4  4  0 2 0 0 2 | 0 0 0 2 0 2 2 0 2 0 0 0 | * * * 4 * * (tower: b-e-c)
.o.ox ..... .o.ox .....&#xt  0 1 0 1  4 |  0  4  0  4 2 0 2 0 | 0 0 0 2 2 0 0 0 0 2 0 2 | * * * * 4 * (tower: b-e-d)
..oox ..oox ..... .....&#xt  0 0 1 1  4 |  0  0  4  4 2 2 0 0 | 0 0 0 0 0 0 2 2 0 2 2 0 | * * * * * 4 (tower: c-e-d)

(qo)(qo)(qo) (ox)(xo)(ox)4(oo)(oq)(oo)&#xt   → both heights = 1/sqrt(2) = 0.707107
(oct || pseudo co || oct)

(o.)(..)(..) (o.)(..)(..)4(o.)(..)(..)     & | 4 * * *   4  4 0  0  0 0  0 |  4  4  4 0  0 0 | 1 1  4 0
(.o)(..)(..) (.o)(..)(..)4(.o)(..)(..)     & | * 8 * *   2  0 2  2  2 0  0 |  4  0  2 2  4 0 | 1 0  4 1
(..)(o.)(..) (..)(o.)(..)4(..)(o.)(..)       | * * 8 *   0  2 0  2  0 2  2 |  0  4  2 0  4 2 | 0 1  4 1
(..)(.o)(..) (..)(.o)(..)4(..)(.o)(..)       | * * * 4   0  0 0  0  4 0  4 |  0  0  0 2  8 2 | 0 0  4 2
---------------------------------------------+---------+--------------------+-----------------+---------
(oo)(..)(..) (oo)(..)(..)4(oo)(..)(..)&#x  & | 1 1 0 0 | 16  * *  *  * *  * |  2  0  1 0  0 0 | 1 0  2 0
(o.)(o.)(..) (o.)(o.)(..)4(o.)(o.)(..)&#x  & | 1 0 1 0 |  * 16 *  *  * *  * |  0  2  1 0  0 0 | 0 1  2 0
(..)(..)(..) (.x)(..)(..) (..)(..)(..)       | 0 2 0 0 |  *  * 8  *  * *  * |  2  0  0 1  0 0 | 1 0  2 0
(.o)(o.)(..) (.o)(o.)(..)4(.o)(o.)(..)&#x  & | 0 1 1 0 |  *  * * 16  * *  * |  0  0  1 0  2 0 | 0 0  2 1
(.o)(.o)(..) (.o)(.o)(..)4(.o)(.o)(..)&#x  & | 0 1 0 1 |  *  * *  * 16 *  * |  0  0  0 1  2 0 | 0 0  2 1
(..)(..)(..) (..)(x.)(..) (..)(..)(..)       | 0 0 2 0 |  *  * *  *  * 8  * |  0  2  0 0  0 1 | 0 1  2 0
(..)(oo)(..) (..)(oo)(..)4(..)(oo)(..)&#x    | 0 0 1 1 |  *  * *  *  * * 16 |  0  0  0 0  2 1 | 0 0  2 1
---------------------------------------------+---------+--------------------+-----------------+---------
(..)(..)(..) (ox)(..)(..) (..)(..)(..)&#x  & | 1 2 0 0 |  2  0 1  0  0 0  0 | 16  *  * *  * * | 1 0  1 0
(..)(..)(..) (o.)(x.)(..) (..)(..)(..)&#x  & | 1 0 2 0 |  0  2 0  0  0 1  0 |  * 16  * *  * * | 0 1  1 0
(oo)(o.)(..) (oo)(o.)(..)4(oo)(o.)(..)&#x  & | 1 1 1 0 |  1  1 0  1  0 0  0 |  *  * 16 *  * * | 0 0  2 0
(..)(..)(..) (.x)(.o)(..) (..)(..)(..)&#x  & | 0 2 0 1 |  0  0 1  0  2 0  0 |  *  *  * 8  * * | 0 0  2 0
(.o)(oo)(..) (.o)(oo)(..)4(.o)(oo)(..)&#x  & | 0 1 1 1 |  0  0 0  1  1 0  1 |  *  *  * * 32 * | 0 0  1 1
(..)(..)(..) (..)(xo)(..) (..)(..)(..)&#x    | 0 0 2 1 |  0  0 0  0  0 1  2 |  *  *  * *  * 8 | 0 0  2 0
---------------------------------------------+---------+--------------------+-----------------+---------
(qo)(..)(..) (ox)(..)(..) (..)(..)(..)&#zx &  2 4 0 0 |  8  0 4  0  0 0  0 |  8  0  0 0  0 0 | 2 *  * *
(..)(..)(..) (o.)(x.)(o.)4(o.)(o.)(o.)&#xt    2 0 4 0 |  0  8 0  0  0 4  0 |  0  8  0 0  0 0 | * 2  * *
(..)(..)(..) (ox)(xo)(..) (..)(..)(..)&#xr &  1 2 2 1 |  2  2 1  2  2 1  2 |  1  1  2 1  2 1 | * * 16 *
(.o)(qo)(.o) (..)(..)(..) (.o)(oq)(.o)&#zx    0 2 2 2 |  0  0 0  4  4 0  4 |  0  0  0 0  8 0 | * *  * 4

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