Acronym prico
Name prismatorhombated icositetrachoron,
runcitruncated icositetrachoron
Circumradius sqrt[8+3 sqrt(2)] = 3.498949
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o4o3o o3o4o . o3o . o o . o3o . o4o3o
1x3x4o3x x3x4o .
toe first
x3x . x
hip first
x . o3x
trip first
. x4o3x
sirco first
2 x3x4x . w3x . o u . q3x . u4o3x
3a u3x4x . x3u . w x . Q3x . x4q3x
3b D . o3w
4 Q3x4o . w3u . q X . w3o . u4o3w
5a x3u4x . u3x . Y w . Y3o . x4w3o
5b Z . x3q
6a w3u4o . x3X . w x . Q3w . x4o3Y
6b D . o3Y
7a x3x4w . w3D . o U . x3o . u4x3q
7b X3x . Q
8a w3x4q . x3x . A u . q3Y . x4x3Q
8b . D4x3o
9a x3x4w . x3Z . x w . Y3q . x4x3Q
9b u3w . Y Z . x3q . D4x3o
10 w3u4o . x3w . A x . o3A . u4x3q
11a x3u4x . X3D . o X . w3Q . x4o3Y
11b Z3x . Q
12 Q3x4o . x3x . B x . Y3w . x4w3o
13a u3x4x . u3Z . x w . A3o . u4o3w
13b D3w . Y C . x3o
14 x3x4x . Z3u . q u . w3Y . x4q3x
15a x3x4o .
opposite toe
D3X . w U . x3Q . u4o3x
15b u3w . A
16a   x3U . o x . x3A . x4o3x
opposite sirco
16b Z3x . Y x . A3x
17a u3x . B Z . w3Q  
17b C . x3q
18 U3x . x X . A3o
19a Z3u . Y D . w3Y
19b X3x . A
20a u3Z . Y U . o3Y
20b x3X . A
21a x3U . x Z . Y3q
21b C . w3o
22a x3u . B x . x3A
22b x . A3x
23a U3x . o Z . q3Y
23b x3Z . Y C . o3w
24a X3D . w U . Y3o
24b w3u . A
25 u3Z . q D . Y3w
26a Z3u . x X . o3A
26b w3D . Y
27a x3x . B Z . Q3w
27b C . q3x
28a D3X . o x . x3A
28b x3Z . Q x . A3x
29 w3x . A U . Q3x
30a Z3x . x u . Y3w
30b w3u . Y
31a x3x . A w . o3A
31b C . o3x
32a D3w . o x . w3Y
32b x3X . Q
33 X3x . w X . Q3w
34 x3u . Y x . A3o
35a u3w . q w . q3Y
35b Z . q3x
36 u3x . w u . Y3q
37 x3w . o U . o3x
38a x3x . x
opposite hip
x . w3Q
38b D . Y3o
39a   w . o3Y
39b Z . q3x
40 X . o3w
41a x . x3Q
41b D . w3o
42 u . x3q
43 x . x3o
opposite trip
(D=3x, Q=2q, X=wq=x+w=2x+q, Y=x+2q=w+q, Z=3x+q=u+w, U=u+X=4x+q, A=Y+q=x+3q, B=A+x=2x+3q, C=5x+q)
Lace city
in approx. ASCII-art
 ©  
              o4x   o4u   q4x   o4u   o4x              
                                                       
          x4x   x4u   w4x     w4x   x4u   x4x          
                                                       
                                                       
    x4x         x4D   w4u     w4u   x4D         x4x    
                                                       
o4x                 o4Z   q4X   o4Z                 o4x
    x4u   x4D         Y4x     Y4x         x4D   x4u    
                                                       
o4u           o4Z         Q4w         o4Z           o4u
    w4x   w4u   Y4x                 Y4x   w4u   w4x    
                                                       
q4x           q4X   Q4w         Q4w   q4X           q4x
                                                       
    w4x   w4u   Y4x                 Y4x   w4u   w4x    
o4u           o4Z         Q4w         o4Z           o4u
                                                       
    x4u   x4D         Y4x     Y4x         x4D   x4u    
o4x                 o4Z   q4X   o4Z                 o4x
                                                       
    x4x         x4D   w4u     w4u   x4D         x4x    
                                                       
                                                       
          x4x   x4u   w4x     w4x   x4u   x4x          
                                                       
              o4x   o4u   q4x   o4u   o4x              
 ©  
               x3x   u3x   x3u   x3x               
                                                   
         x3x x3w   u3w # x3X w3u   w3x x3x         
                      (X3x)                        
                                                   
      u3x u3w   D3w Z3x     x3Z w3D   w3u x3u      
                                                   
        X3x   Z3x                 x3Z   x3X        
   x3u x3X         D3X # u3Z X3D         X3x u3x   
                      (Z3u)                        
     w3u         Z3u           u3Z         u3w     
x3x       x3Z   u3Z   U3x x3U   Z3u   Z3x       x3x
                                                   
  w3x   w3D   X3D   x3U     U3x   D3X   D3w   x3w  
                                                   
x3x       x3Z   u3Z   U3x x3U   Z3u   Z3x       x3x
     w3u         Z3u           u3Z         u3w     
                      (Z3u)                        
   x3u x3X         D3X # u3Z X3D         X3x u3x   
        X3x   Z3x                 x3Z   x3X        
                                                   
      u3x u3w   D3w Z3x     x3Z w3D   w3u x3u      
                                                   
                      (X3x)                        
         x3x x3w   u3w # x3X w3u   w3x x3x         
                                                   
               x3x   u3x   x3u   x3x               
 ©  
                      x3o   x3q   # o3w   q3x   o3x                      
                                 (w3o)                                   
                                                                         
             x3o         x3Q     o3Y Y3o     Q3x         o3x             
                                                                         
                                 (Y3q)                                   
          x3q   x3Q         w3Q   # q3Y   Q3w         Q3x   q3x          
                                                                         
                                                                         
       w3o         w3Q         A3o     o3A         Q3w         o3w       
      o3w   o3Y                 w3Y   Y3w                 Y3o   w3o      
                                                                         
          Y3o   Y3q   A3o                       o3A   q3Y   o3Y          
   q3x         q3Y     w3Y        xA3Ax        Y3w     Y3q         x3q   
                                                                         
                                                                         
o3x   Q3x   Q3w   # Y3w  xA3Ax             xA3Ax  # A3o   w3Q   x3Q   x3o
                 (o3A)                           (w3Y)                   
                                                                         
                                                                         
                                                                         
                 (o3A)                           (w3Y)                   
o3x   Q3x   Q3w   # Y3w  xA3Ax             xA3Ax  # A3o   w3Q   x3Q   x3o
                                                                         
                                                                         
   q3x         q3Y     w3Y        xA3Ax        Y3w     Y3q         x3q   
          Y3o   Y3q   A3o                       o3A   q3Y   o3Y          
                                                                         
      o3w   o3Y                 w3Y   Y3w                 Y3o   w3o      
       w3o         w3Q         A3o     o3A         Q3w         o3w       
                                                                         
                                                                         
          x3q   x3Q         w3Q   # q3Y   Q3w         Q3x   q3x          
                                 (Y3q)                                   
                                                                         
             x3o         x3Q     o3Y Y3o     Q3x         o3x             
                                                                         
                                 (w3o)                                   
                      x3o   x3q   # o3w   q3x   o3x                      
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: girco hip sirco socco toe trip
sipti 244848242496
prico 0962402496
& others)
Dihedral angles
  • at {4} between hip and trip:   arccos(-sqrt[8/9]) = 160.528779°
  • at {6} between hip and toe:   150°
  • at {3} between sirco and trip:   150°
  • at {4} between hip and sirco:   arccos(-sqrt[2/3]) = 144.735610°
  • at {4} between sirco and toe:   135°
Confer
Grünbaumian relatives:
2prico  
uniform relative:
gidpith  
segmentochora:
toe || girco  
decompositions:
tico || gyro prico   srico || prico  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope prico is isomorphic to paqri, thereby replacing sirco by querco.

Diminishing the prico by toagircoes at hexadecachoral positions results in the gidpith.

Note that prico can be thought of as the external blend of 1 tico + 24 cubasircoes + 96 tepes + 96 thiddips + 24 topes. This decomposition is described as the degenerate segmentoteron ox3oo4xx3xx&#x. – Alternatively it can be decomposed into 1 srico + 24 coatoes + 96 tricupes + 96 triddips + 24 sircopes according to ox3xx4oo3xx&#x.


Incidence matrix according to Dynkin symbol

x3x4o3x

. . . . | 576 |   1   2   2 |   2   2   1   2   1 |  1  2  1  1
--------+-----+-------------+---------------------+------------
x . . . |   2 | 288   *   * |   2   2   0   0   0 |  1  2  1  0
. x . . |   2 |   * 576   * |   1   0   1   1   0 |  1  1  0  1
. . . x |   2 |   *   * 576 |   0   1   0   1   1 |  0  1  1  1
--------+-----+-------------+---------------------+------------
x3x . . |   6 |   3   3   0 | 192   *   *   *   * |  1  1  0  0
x . . x |   4 |   2   0   2 |   * 288   *   *   * |  0  1  1  0
. x4o . |   4 |   0   4   0 |   *   * 144   *   * |  1  0  0  1
. x . x |   4 |   0   2   2 |   *   *   * 288   * |  0  1  0  1
. . o3x |   3 |   0   0   3 |   *   *   *   * 192 |  0  0  1  1
--------+-----+-------------+---------------------+------------
x3x4o .   24 |  12  24   0 |   8   0   6   0   0 | 24  *  *  *
x3x . x   12 |   6   6   6 |   2   3   0   3   0 |  * 96  *  *
x . o3x    6 |   3   0   6 |   0   3   0   0   2 |  *  * 96  *
. x4o3x   24 |   0  24  24 |   0   0   6  12   8 |  *  *  * 24

snubbed forms: β3x4o3x, x3β4o3x, x3x4o3β, s3s4o3x, β3x4o3β, x3β4o3β, β3β4o3β

x3x4/3o3/2x

. .   .   . | 576 |   1   2   2 |   2   2   1   2   1 |  1  2  1  1
------------+-----+-------------+---------------------+------------
x .   .   . |   2 | 288   *   * |   2   2   0   0   0 |  1  2  1  0
. x   .   . |   2 |   * 576   * |   1   0   1   1   0 |  1  1  0  1
. .   .   x |   2 |   *   * 576 |   0   1   0   1   1 |  0  1  1  1
------------+-----+-------------+---------------------+------------
x3x   .   . |   6 |   3   3   0 | 192   *   *   *   * |  1  1  0  0
x .   .   x |   4 |   2   0   2 |   * 288   *   *   * |  0  1  1  0
. x4/3o   . |   4 |   0   4   0 |   *   * 144   *   * |  1  0  0  1
. x   .   x |   4 |   0   2   2 |   *   *   * 288   * |  0  1  0  1
. .   o3/2x |   3 |   0   0   3 |   *   *   *   * 192 |  0  0  1  1
------------+-----+-------------+---------------------+------------
x3x4/3o   .   24 |  12  24   0 |   8   0   6   0   0 | 24  *  *  *
x3x   .   x   12 |   6   6   6 |   2   3   0   3   0 |  * 96  *  *
x .   o3/2x    6 |   3   0   6 |   0   3   0   0   2 |  *  * 96  *
. x4/3o3/2x   24 |   0  24  24 |   0   0   6  12   8 |  *  *  * 24

s3s4x3x

demi( . . . . ) | 576 |   1   1   2   1 |  1   1   1   2   2  1 |  1  1  1  2
----------------+-----+-----------------+-----------------------+------------
demi( . . x . ) |   2 | 288   *   *   * |  1   0   1   1   0  0 |  1  0  1  1
demi( . . . x ) |   2 |   * 288   *   * |  1   0   0   0   2  1 |  0  1  1  2
sefa( s3s . . ) |   2 |   *   * 576   * |  0   1   0   1   1  0 |  1  1  0  1
sefa( . s4x . ) |   2 |   *   *   * 288 |  0   0   1   1   0  1 |  1  0  1  1
----------------+-----+-----------------+-----------------------+------------
demi( . . x3x ) |   6 |   3   3   0   0 | 96   *   *   *   *  * |  0  0  1  1
      s3s . .      3 |   0   0   3   0 |  * 192   *   *   *  * |  1  1  0  0
      . s4x .      4 |   2   0   0   2 |  *   * 144   *   *  * |  1  0  1  0
sefa( s3s4x . ) |   4 |   1   0   2   1 |  *   *   * 288   *  * |  1  0  0  1
sefa( s3s 2 x ) |   4 |   0   2   2   0 |  *   *   *   * 288  * |  0  1  0  1
sefa( . s4x3x ) |   6 |   0   3   0   3 |  *   *   *   *   * 96 |  0  0  1  1
----------------+-----+-----------------+-----------------------+------------
      s3s4x .     24 |  12   0  24  12 |  0   8   6  12   0  0 | 24  *  *  *
      s3s 2 x      6 |   0   3   6   0 |  0   2   0   0   3  0 |  * 96  *  *
      . s4x3x     24 |  12  12   0  12 |  4   0   6   0   0  4 |  *  * 24  *
sefa( s3s4x3x )   12 |   3   6   6   3 |  1   0   0   3   3  1 |  *  *  * 96

starting figure: x3x4x3x

wx3xx3xx4ox&#zx   → height = 0
(tegum sum of (w,x,x,x)-tico and gidpith)

o.3o.3o.4o.     | 192   * |  1   2   2   0   0   0   0 |  2  1   2   2   1  0  0  0  0  0 | 1  1  2  1  0  0
.o3.o3.o4.o     |   * 384 |  0   0   1   1   1   1   1 |  0  0   1   1   1  1  1  1  1  1 | 0  1  1  1  1  1
----------------+---------+----------------------------+----------------------------------+-----------------
.. x. .. ..     |   2   0 | 96   *   *   *   *   *   * |  2  0   2   0   0  0  0  0  0  0 | 1  0  2  1  0  0
.. .. x. ..     |   2   0 |  * 192   *   *   *   *   * |  1  1   0   1   0  0  0  0  0  0 | 1  1  1  0  0  0
oo3oo3oo4oo&#x  |   1   1 |  *   * 384   *   *   *   * |  0  0   1   1   1  0  0  0  0  0 | 0  1  1  1  0  0
.x .. .. ..     |   0   2 |  *   *   * 192   *   *   * |  0  0   0   0   0  1  1  1  0  0 | 0  1  0  0  1  1
.. .x .. ..     |   0   2 |  *   *   *   * 192   *   * |  0  0   1   0   0  1  0  0  1  1 | 0  0  1  1  1  1
.. .. .x ..     |   0   2 |  *   *   *   *   * 192   * |  0  0   0   1   0  0  1  0  1  0 | 0  1  1  0  1  0
.. .. .. .x     |   0   2 |  *   *   *   *   *   * 192 |  0  0   0   0   1  0  0  1  0  1 | 0  1  0  1  0  1
----------------+---------+----------------------------+----------------------------------+-----------------
.. x.3x. ..     |   6   0 |  3   3   0   0   0   0   0 | 64  *   *   *   *  *  *  *  *  * | 1  0  1  0  0  0
.. .. x.4o.     |   4   0 |  0   4   0   0   0   0   0 |  * 48   *   *   *  *  *  *  *  * | 1  1  0  0  0  0
.. xx .. ..&#x  |   2   2 |  1   0   2   0   1   0   0 |  *  * 192   *   *  *  *  *  *  * | 0  0  1  1  0  0
.. .. xx ..&#x  |   2   2 |  0   1   2   0   0   1   0 |  *  *   * 192   *  *  *  *  *  * | 0  1  1  0  0  0
.. .. .. ox&#x  |   1   2 |  0   0   2   0   0   0   1 |  *  *   *   * 192  *  *  *  *  * | 0  1  0  1  0  0
.x3.x .. ..     |   0   6 |  0   0   0   3   3   0   0 |  *  *   *   *   * 64  *  *  *  * | 0  0  0  0  1  1
.x .. .x ..     |   0   4 |  0   0   0   2   0   2   0 |  *  *   *   *   *  * 96  *  *  * | 0  1  0  0  1  0
.x .. .. .x     |   0   4 |  0   0   0   2   0   0   2 |  *  *   *   *   *  *  * 96  *  * | 0  1  0  0  0  1
.. .x3.x ..     |   0   6 |  0   0   0   0   3   3   0 |  *  *   *   *   *  *  *  * 64  * | 0  0  1  0  1  0
.. .x .. .x     |   0   4 |  0   0   0   0   2   0   2 |  *  *   *   *   *  *  *  *  * 96 | 0  0  0  1  0  1
----------------+---------+----------------------------+----------------------------------+-----------------
.. x.3x.4o.       24   0 | 12  24   0   0   0   0   0 |  8  6   0   0   0  0  0  0  0  0 | 8  *  *  *  *  *
wx .. xx4ox&#zx    8  16 |  0   8  16   8   0   8   8 |  0  2   0   8   8  0  4  4  0  0 | * 24  *  *  *  *
.. xx3xx ..&#x     6   6 |  3   3   6   0   3   3   0 |  1  0   3   3   0  0  0  0  1  0 | *  * 64  *  *  *
.. xx .. ox&#x     2   4 |  1   0   4   0   2   0   2 |  0  0   2   0   2  0  0  0  0  1 | *  *  * 96  *  *
.x3.x3.x ..        0  24 |  0   0   0  12  12  12   0 |  0  0   0   0   0  4  6  0  4  0 | *  *  *  * 16  *
.x3.x .. .x        0  12 |  0   0   0   6   6   0   6 |  0  0   0   0   0  2  0  3  0  3 | *  *  *  *  * 32

wxx3xxx3xwx *b3xxw&#zx   → all heights = 0
(tegum sum of 3 mutually gyrated (w,x,x)-ticoes)

o..3o..3o.. *b3o..     | 192   *   * |  1  1  1   1   1  0  0  0   0  0  0  0 |  1  1  1  1  1  1  1   1  0  0  0  0  0  0  0  0 | 1  1  1  1  1 0  0 0
.o.3.o.3.o. *b3.o.     |   * 192   * |  0  0  0   1   0  1  1  1   1  0  0  0 |  0  0  0  1  1  0  0   1  1  1  1  1  1  0  0  0 | 0  1  0  1  1 1  1 0
..o3..o3..o *b3..o     |   *   * 192 |  0  0  0   0   1  0  0  0   1  1  1  1 |  0  0  0  0  0  1  1   1  0  0  0  1  1  1  1  1 | 0  0  1  1  1 0  1 1
-----------------------+-------------+----------------------------------------+--------------------------------------------------+---------------------
... x.. ...    ...     |   2   0   0 | 96  *  *   *   *  *  *  *   *  *  *  * |  1  1  0  1  0  1  0   0  0  0  0  0  0  0  0  0 | 1  1  1  0  1 0  0 0
... ... x..    ...     |   2   0   0 |  * 96  *   *   *  *  *  *   *  *  *  * |  1  0  1  0  0  0  1   0  0  0  0  0  0  0  0  0 | 1  0  1  1  0 0  0 0
... ... ...    x..     |   2   0   0 |  *  * 96   *   *  *  *  *   *  *  *  * |  0  1  1  0  1  0  0   0  0  0  0  0  0  0  0  0 | 1  1  0  1  0 0  0 0
oo.3oo.3oo. *b3oo.&#x  |   1   1   0 |  *  *  * 192   *  *  *  *   *  *  *  * |  0  0  0  1  1  0  0   1  0  0  0  0  0  0  0  0 | 0  1  0  1  1 0  0 0
o.o3o.o3o.o3*b3o.o&#x  |   1   0   1 |  *  *  *   * 192  *  *  *   *  *  *  * |  0  0  0  0  0  1  1   1  0  0  0  0  0  0  0  0 | 0  0  1  1  1 0  0 0
.x. ... ...    ...     |   0   2   0 |  *  *  *   *   * 96  *  *   *  *  *  * |  0  0  0  0  0  0  0   0  1  1  0  1  0  0  0  0 | 0  0  0  1  0 1  1 0
... .x. ...    ...     |   0   2   0 |  *  *  *   *   *  * 96  *   *  *  *  * |  0  0  0  1  0  0  0   0  1  0  1  0  1  0  0  0 | 0  1  0  0  1 1  1 0
... ... ...    .x.     |   0   2   0 |  *  *  *   *   *  *  * 96   *  *  *  * |  0  0  0  0  1  0  0   0  0  1  1  0  0  0  0  0 | 0  1  0  1  0 1  0 0
.oo3.oo3.oo *b3.oo&#x  |   0   1   1 |  *  *  *   *   *  *  *  * 192  *  *  * |  0  0  0  0  0  0  0   1  0  0  0  1  1  0  0  0 | 0  0  0  1  1 0  1 0
..x ... ...    ...     |   0   0   2 |  *  *  *   *   *  *  *  *   * 96  *  * |  0  0  0  0  0  0  0   0  0  0  0  1  0  1  1  0 | 0  0  0  1  0 0  1 1
... ..x ...    ...     |   0   0   2 |  *  *  *   *   *  *  *  *   *  * 96  * |  0  0  0  0  0  1  0   0  0  0  0  0  1  1  0  1 | 0  0  1  0  1 0  1 1
... ... ..x    ...     |   0   0   2 |  *  *  *   *   *  *  *  *   *  *  * 96 |  0  0  0  0  0  0  1   0  0  0  0  0  0  0  1  1 | 0  0  1  1  0 0  0 1
-----------------------+-------------+----------------------------------------+--------------------------------------------------+---------------------
... x..3x..    ...     |   6   0   0 |  3  3  0   0   0  0  0  0   0  0  0  0 | 32  *  *  *  *  *  *   *  *  *  *  *  *  *  *  * | 1  0  1  0  0 0  0 0
... x.. ... *b3x..     |   6   0   0 |  3  0  3   0   0  0  0  0   0  0  0  0 |  * 32  *  *  *  *  *   *  *  *  *  *  *  *  *  * | 1  1  0  0  0 0  0 0
... ... x..    x..     |   4   0   0 |  0  2  2   0   0  0  0  0   0  0  0  0 |  *  * 48  *  *  *  *   *  *  *  *  *  *  *  *  * | 1  0  0  1  0 0  0 0
... xx. ...    ...&#x  |   2   2   0 |  1  0  0   2   0  0  1  0   0  0  0  0 |  *  *  * 96  *  *  *   *  *  *  *  *  *  *  *  * | 0  1  0  0  1 0  0 0
... ... ...    xx.&#x  |   2   2   0 |  0  0  1   2   0  0  0  1   0  0  0  0 |  *  *  *  * 96  *  *   *  *  *  *  *  *  *  *  * | 0  1  0  1  0 0  0 0
... x.x ...    ...&#x  |   2   0   2 |  1  0  0   0   2  0  0  0   0  0  1  0 |  *  *  *  *  * 96  *   *  *  *  *  *  *  *  *  * | 0  0  1  0  1 0  0 0
... ... x.x    ...&#x  |   2   0   2 |  0  1  0   0   2  0  0  0   0  0  0  1 |  *  *  *  *  *  * 96   *  *  *  *  *  *  *  *  * | 0  0  1  1  0 0  0 0
ooo3ooo3ooo *b3ooo&#x  |   1   1   1 |  0  0  0   1   1  0  0  0   1  0  0  0 |  *  *  *  *  *  *  * 192  *  *  *  *  *  *  *  * | 0  0  0  1  1 0  0 0
.x.3.x. ...    ...     |   0   6   0 |  0  0  0   0   0  3  3  0   0  0  0  0 |  *  *  *  *  *  *  *   * 32  *  *  *  *  *  *  * | 0  0  0  0  0 1  1 0
.x. ... ...    .x.     |   0   4   0 |  0  0  0   0   0  2  0  2   0  0  0  0 |  *  *  *  *  *  *  *   *  * 48  *  *  *  *  *  * | 0  0  0  1  0 1  0 0
... .x. ... *b3.x.     |   0   6   0 |  0  0  0   0   0  0  3  3   0  0  0  0 |  *  *  *  *  *  *  *   *  *  * 32  *  *  *  *  * | 0  1  0  0  0 1  0 0
.xx ... ...    ...&#x  |   0   2   2 |  0  0  0   0   0  1  0  0   2  1  0  0 |  *  *  *  *  *  *  *   *  *  *  * 96  *  *  *  * | 0  0  0  1  0 0  1 0
... .xx ...    ...&#x  |   0   2   2 |  0  0  0   0   0  0  1  0   2  0  1  0 |  *  *  *  *  *  *  *   *  *  *  *  * 96  *  *  * | 0  0  0  0  1 0  1 0
..x3..x ...    ...     |   0   0   6 |  0  0  0   0   0  0  0  0   0  3  3  0 |  *  *  *  *  *  *  *   *  *  *  *  *  * 32  *  * | 0  0  0  0  0 0  1 1
..x ... ..x    ...     |   0   0   4 |  0  0  0   0   0  0  0  0   0  2  0  2 |  *  *  *  *  *  *  *   *  *  *  *  *  *  * 48  * | 0  0  0  1  0 0  0 1
... ..x3..x    ...     |   0   0   6 |  0  0  0   0   0  0  0  0   0  0  3  3 |  *  *  *  *  *  *  *   *  *  *  *  *  *  *  * 32 | 0  0  1  0  0 0  0 1
-----------------------+-------------+----------------------------------------+--------------------------------------------------+---------------------
... x..3x.. *b3x..       24   0   0 | 12 12 12   0   0  0  0  0   0  0  0  0 |  4  4  6  0  0  0  0   0  0  0  0  0  0  0  0  0 | 8  *  *  *  * *  * *
... xx. ... *b3xx.&#x     6   6   0 |  3  0  3   6   0  0  3  3   0  0  0  0 |  0  1  0  3  3  0  0   0  0  0  1  0  0  0  0  0 | * 32  *  *  * *  * *
... x.x3x.x    ...&#x     6   0   6 |  3  3  0   0   6  0  0  0   0  0  3  3 |  1  0  0  0  0  3  3   0  0  0  0  0  0  0  0  1 | *  * 32  *  * *  * *
wxx ... xwx    xxw&#zx    8   8   8 |  0  4  4   8   8  4  0  4   8  4  0  4 |  0  0  2  0  4  0  4   8  0  2  0  4  0  0  2  0 | *  *  * 24  * *  * *
... xxx ...    ...&#x     2   2   2 |  1  0  0   2   2  0  1  0   2  0  1  0 |  0  0  0  1  0  1  0   2  0  0  0  0  1  0  0  0 | *  *  *  * 96 *  * *
.x.3.x. ... *b3.x.        0  24   0 |  0  0  0   0   0 12 12 12   0  0  0  0 |  0  0  0  0  0  0  0   0  4  6  4  0  0  0  0  0 | *  *  *  *  * 8  * *
.xx3.xx ...    ...&#x     0   6   6 |  0  0  0   0   0  3  3  0   6  3  3  0 |  0  0  0  0  0  0  0   0  1  0  0  3  3  1  0  0 | *  *  *  *  * * 32 *
..x3..x3..x    ...        0   0  24 |  0  0  0   0   0  0  0  0   0 12 12 12 |  0  0  0  0  0  0  0   0  0  0  0  0  0  4  6  4 | *  *  *  *  * *  * 8

oqQ3xxx3qoo4xux&#zxt   → heights = 0, Q=2q = 2.828427
(tegum sum of (x,q,x)-grit, (q,x,u)-prit, and (Q,x,x)-prit)

o..3o..3o..4o..      | 192   *   * |   2  1   2   0   0   0   0 |  1  2  1   2   2  0   0  0  0  0 |  1  1  1  2  0 0
.o.3.o.3.o.4.o.      |   * 192   * |   0  0   2   2   1   0   0 |  0  0  1   2   2  1   2  0  0  0 |  0  1  1  2  1 0
..o3..o3..o4..o      |   *   * 192 |   0  0   0   0   1   2   2 |  0  0  0   0   2  0   2  1  2  1 |  0  0  1  2  1 1
---------------------+-------------+----------------------------+----------------------------------+-----------------
... x.. ... ...      |   2   0   0 | 192  *   *   *   *   *   * |  1  1  0   1   0  0   0  0  0  0 |  1  1  0  1  0 0
... ... ... x..      |   2   0   0 |   * 96   *   *   *   *   * |  0  2  0   0   2  0   0  0  0  0 |  1  0  1  2  0 0
oo.3oo.3oo.4oo.&#x   |   1   1   0 |   *  * 384   *   *   *   * |  0  0  1   1   1  0   0  0  0  0 |  0  1  1  1  0 0
... .x. ... ...      |   0   2   0 |   *  *   * 192   *   *   * |  0  0  0   1   0  1   1  0  0  0 |  0  1  0  1  1 0
.oo3.oo3.oo4.oo&#x   |   0   1   1 |   *  *   *   * 192   *   * |  0  0  0   0   2  0   2  0  0  0 |  0  0  1  2  1 0
... ..x ... ...      |   0   0   2 |   *  *   *   *   * 192   * |  0  0  0   0   0  0   1  1  1  0 |  0  0  0  1  1 1
... ... ... ..x      |   0   0   2 |   *  *   *   *   *   * 192 |  0  0  0   0   1  0   0  0  1  1 |  0  0  1  1  0 1
---------------------+-------------+----------------------------+----------------------------------+-----------------
o..3x.. ... ...      |   3   0   0 |   3  0   0   0   0   0   0 | 64  *  *   *   *  *   *  *  *  * |  1  1  0  0  0 0
... x.. ... x..      |   4   0   0 |   2  2   0   0   0   0   0 |  * 96  *   *   *  *   *  *  *  * |  1  0  0  1  0 0
oq. ... qo. ...&#zx  |   2   2   0 |   0  0   4   0   0   0   0 |  *  * 96   *   *  *   *  *  *  * |  0  1  1  0  0 0
... xx. ... ...&#x   |   2   2   0 |   1  0   2   1   0   0   0 |  *  *  * 192   *  *   *  *  *  * |  0  1  0  1  0 0
... ... ... xux&#xt  |   2   2   2 |   0  1   2   0   2   0   1 |  *  *  *   * 192  *   *  *  *  * |  0  0  1  1  0 0
... .x.3.o. ...      |   0   3   0 |   0  0   0   3   0   0   0 |  *  *  *   *   * 64   *  *  *  * |  0  1  0  0  1 0
... .xx ... ...&#x   |   0   2   2 |   0  0   0   1   2   1   0 |  *  *  *   *   *  * 192  *  *  * |  0  0  0  1  1 0
... ..x3..o ...      |   0   0   3 |   0  0   0   0   0   3   0 |  *  *  *   *   *  *   * 64  *  * |  0  0  0  0  1 1
... ..x ... ..x      |   0   0   4 |   0  0   0   0   0   2   2 |  *  *  *   *   *  *   *  * 96  * |  0  0  0  1  0 1
... ... ..o4..x      |   0   0   4 |   0  0   0   0   0   0   4 |  *  *  *   *   *  *   *  *  * 48 |  0  0  1  0  0 1
---------------------+-------------+----------------------------+----------------------------------+-----------------
o..3x.. ... x..         6   0   0 |   6  3   0   0   0   0   0 |  2  3  0   0   0  0   0  0  0  0 | 32  *  *  *  * *
oq.3xx.3qo. ...&#zx    12  12   0 |  12  0  24  12   0   0   0 |  4  0  6  12   0  4   0  0  0  0 |  * 16  *  *  * *
oqQ ... qoo4xux&#zxt    8   8   8 |   0  4  16   0   8   0   8 |  0  0  4   0   8  0   0  0  0  2 |  *  * 24  *  * *
... xxx ... xux&#xt     4   4   4 |   2  2   4   2   4   2   2 |  0  1  0   2   2  0   2  0  1  0 |  *  *  * 96  * *
... .xx3.oo ...&#x      0   3   3 |   0  0   0   3   3   3   0 |  0  0  0   0   0  1   3  1  0  0 |  *  *  *  * 64 *
... ..x3..o4..x         0   0  24 |   0  0   0   0   0  24  24 |  0  0  0   0   0  0   0  8 12  6 |  *  *  *  *  * 8

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