Acronym rico
Name rectified icosatetrachoron,
cantellated hexadecachoron,
hexadecachoron-derived Gévay polychoron
 
©  
Cross sections
 ©
Circumradius sqrt(3) = 1.732051
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o4o3o o3o4o . o3o . o o . o3o . o4o3o
1o3x4o3o o3x4o .
co first
o3x . o
{3} first
o . o3o
vertex first
. x4o3o
cube first
2 x3x4o . x3x . q x . q3o
vertex figure
. o4q3o
3a x3o4q . x3o . Q u . o3q . x4o3q
3b u3x . o
4a x3x4o . x3u . q x . q3q . u4o3o
4b H . o3o
5a o3x4o .
opposite co
x3x . Q o . o3Q . x4o3q
5b H3o . o
5c o3H . o
6a   u3x . q x . Q3o . o4q3o
6b H . o3q
7a o3x . Q u . q3q . x4o3o
opposite cube
7b x3u . o
8a x3x . q x . o3Q  
8b H . q3o
9 x3o . o
opposite {3}
o . Q3o
10a   x . q3q
10b H . o3o
11 u . q3o
12 x . o3q
13 o . o3o
opposite vertex
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1x3o3x4o x3o3x .
co first
x3o . o
{3} first
x . x4o
cube first
. o3x4o
co first
2a x3x3x . x3x . q u . o4q . x3x4o
2b o . u4o
3a u3x3o . o3x . Q H . x4o . x3o4q
3b o3x3u . x3u . o x . x4q
4 x3x3x . u3x . q u . u4o . x3x4o
5a x3o3x .
opposite co
x3x . Q H . x4o . o3x4o
opposite co
5b H3o . o x . x4q
5c o3H . o
6a   x3u . q u . o4q  
6b o . u4o
7a x3o . Q x . x4o
opposite cube
7b u3x . o
8 x3x . q  
9 o3x . o
opposite {3}
 o3o3o *b3o o3o3o    . o3o . *b3o o . o    o . o3o *b3o
1x3o3x *b3x x3o3x    .
co first
x3o . *b3x
co first
x . x    x
cube first
. o3x *b3x
co first
2a x3x3x    . x3x . *b3x u . u    o . x3x *b3x
2b u . o    u
2c o . u    u
3a u3x3o    . u3x . *b3o x . x    H . x3u *b3o
3b o3x3u    . o3x . *b3u x . H    x . x3o *b3u
3c H . x    x
4 x3x3x    . x3x . *b3x u . u    u . x3x *b3x
5a x3o3x    .
opposite co
x3o . *b3x
opposite co
x . x    H . o3x *b3x
opposite co
5b x . H    x
5c H . x    x
6a     u . u    o  
6b u . o    u
6c o . u    u
7 x . x    x
opposite cube
(H=hh=3x, Q=2q)
Lace city
in approx. ASCII-art
 ©  
      o3x   x3x   x3o      
                           
                           
   x3x   u3x   x3u   x3x   
                           
                           
x3o   x3u  oH3Ho  u3x   o3x
                           
                           
   x3x   u3x   x3u   x3x   
                           
                           
      o3x   x3x   x3o      
 ©  
            o3o            
        o3q     o3q        
    q3o             q3o    
o3o     q3q     q3q     o3o
            Q3o            
q3o     o3Q     o3Q     q3o
    q3q             q3q    
o3q     Q3o     Q3o     o3q
            o3Q            
o3o     q3q     q3q     o3o
    o3q             o3q    
        q3o     q3o        
            o3o            
 ©  
    x4o o4q x4o    
                   
x4o u4o x4q u4o x4o
                   
o4q x4q     x4q o4q
                   
x4o u4o x4q u4o x4o
                   
    x4o o4q x4o    
Coordinates
  • (sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
  • or (3/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
    (wrt. dual positioning of underlying ico)
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: co cube oho toe
rico 242400
ini 240024
rawvhitto 80168
frico 024024
& others)
Dihedral angles
  • at {4} between co and cube:   135°
  • at {3} between co and co:   120°
Confer
Grünbaumian relatives:
2rico   2rico+64{6}+128{3}   2rico+64{6}+192{3}  
segmentochora:
coatoe  
related CRFs:
dirico   pabdirico   cytid rico   qo2ox3xx4oo&#zx  
decompositions:
ico || rico  
related Gévay polytopes:
oq3oo3qo3oc&#zx   oq3oo3qo5oc&#zx   oa3oo4bo3oc&#zx   oa4oo3bo3oc&#zx   oa5oo3bo3oc&#zx   xuo3uoo3oou3oux&#z(q,q,h)   aco3boo4oob3oca&#z(x,x,d)  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

Note that rico can be thought of as the external blend of 1 ico + 24 octacoes + 24 cubpies. This decomposition is described as the degenerate segmentoteron xo3ox4oo3oo&#x.


Incidence matrix according to Dynkin symbol

o3x4o3o

. . . . | 96    6 |  3   6 |  3  2
--------+----+-----+--------+------
. x . . |  2 | 288 |  1   2 |  2  1
--------+----+-----+--------+------
o3x . . |  3 |   3 | 96   * |  2  0
. x4o . |  4 |   4 |  * 144 |  1  1
--------+----+-----+--------+------
o3x4o .  12 |  24 |  8   6 | 24  *
. x4o3o   8 |  12 |  0   6 |  * 24

snubbed forms: o3β4o3o

o3x4o3/2o

. . .   . | 96    6 |  3   6 |  3  2
----------+----+-----+--------+------
. x .   . |  2 | 288 |  1   2 |  2  1
----------+----+-----+--------+------
o3x .   . |  3 |   3 | 96   * |  2  0
. x4o   . |  4 |   4 |  * 144 |  1  1
----------+----+-----+--------+------
o3x4o   .  12 |  24 |  8   6 | 24  *
. x4o3/2o   8 |  12 |  0   6 |  * 24

o3x4/3o3o

. .   . . | 96    6 |  3   6 |  3  2
----------+----+-----+--------+------
. x   . . |  2 | 288 |  1   2 |  2  1
----------+----+-----+--------+------
o3x   . . |  3 |   3 | 96   * |  2  0
. x4/3o . |  4 |   4 |  * 144 |  1  1
----------+----+-----+--------+------
o3x4/3o .  12 |  24 |  8   6 | 24  *
. x4/3o3o   8 |  12 |  0   6 |  * 24

o3x4/3o3/2o

. .   .   . | 96    6 |  3   6 |  3  2
------------+----+-----+--------+------
. x   .   . |  2 | 288 |  1   2 |  2  1
------------+----+-----+--------+------
o3x   .   . |  3 |   3 | 96   * |  2  0
. x4/3o   . |  4 |   4 |  * 144 |  1  1
------------+----+-----+--------+------
o3x4/3o   .  12 |  24 |  8   6 | 24  *
. x4/3o3/2o   8 |  12 |  0   6 |  * 24

o3/2x4o3o

.   . . . | 96    6 |  3   6 |  3  2
----------+----+-----+--------+------
.   x . . |  2 | 288 |  1   2 |  2  1
----------+----+-----+--------+------
o3/2x . . |  3 |   3 | 96   * |  2  0
.   x4o . |  4 |   4 |  * 144 |  1  1
----------+----+-----+--------+------
o3/2x4o .  12 |  24 |  8   6 | 24  *
.   x4o3o   8 |  12 |  0   6 |  * 24

o3/2x4o3/2o

.   . .   . | 96    6 |  3   6 |  3  2
------------+----+-----+--------+------
.   x .   . |  2 | 288 |  1   2 |  2  1
------------+----+-----+--------+------
o3/2x .   . |  3 |   3 | 96   * |  2  0
.   x4o   . |  4 |   4 |  * 144 |  1  1
------------+----+-----+--------+------
o3/2x4o   .  12 |  24 |  8   6 | 24  *
.   x4o3/2o   8 |  12 |  0   6 |  * 24

o3/2x4/3o3o

.   .   . . | 96    6 |  3   6 |  3  2
------------+----+-----+--------+------
.   x   . . |  2 | 288 |  1   2 |  2  1
------------+----+-----+--------+------
o3/2x   . . |  3 |   3 | 96   * |  2  0
.   x4/3o . |  4 |   4 |  * 144 |  1  1
------------+----+-----+--------+------
o3/2x4/3o .  12 |  24 |  8   6 | 24  *
.   x4/3o3o   8 |  12 |  0   6 |  * 24

o3/2x4/3o3/2o

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

x3o3x4o

. . . . | 96   2   4 |  1  4  2  2 |  2  2 1
--------+----+--------+-------------+--------
x . . . |  2 | 96   * |  1  2  0  0 |  2  1 0
. . x . |  2 |  * 192 |  0  1  1  1 |  1  1 1
--------+----+--------+-------------+--------
x3o . . |  3 |  3   0 | 32  *  *  * |  2  0 0
x . x . |  4 |  2   2 |  * 96  *  * |  1  1 0
. o3x . |  3 |  0   3 |  *  * 64  * |  1  0 1
. . x4o |  4 |  0   4 |  *  *  * 48 |  0  1 1
--------+----+--------+-------------+--------
x3o3x .  12 | 12  12 |  4  6  4  0 | 16  * *
x . x4o   8 |  4   8 |  0  4  0  2 |  * 24 *
. o3x4o  12 |  0  24 |  0  0  8  6 |  *  * 8

snubbed forms: β3o3x4o, x3o3β4o, β3o3β4o

x3o3x4/3o

. . .   . | 96   2   4 |  1  4  2  2 |  2  2 1
----------+----+--------+-------------+--------
x . .   . |  2 | 96   * |  1  2  0  0 |  2  1 0
. . x   . |  2 |  * 192 |  0  1  1  1 |  1  1 1
----------+----+--------+-------------+--------
x3o .   . |  3 |  3   0 | 32  *  *  * |  2  0 0
x . x   . |  4 |  2   2 |  * 96  *  * |  1  1 0
. o3x   . |  3 |  0   3 |  *  * 64  * |  1  0 1
. . x4/3o |  4 |  0   4 |  *  *  * 48 |  0  1 1
----------+----+--------+-------------+--------
x3o3x   .  12 | 12  12 |  4  6  4  0 | 16  * *
x . x4/3o   8 |  4   8 |  0  4  0  2 |  * 24 *
. o3x4/3o  12 |  0  24 |  0  0  8  6 |  *  * 8

x3/2o3/2x4o

.   .   . . | 96   2   4 |  1  4  2  2 |  2  2 1
------------+----+--------+-------------+--------
x   .   . . |  2 | 96   * |  1  2  0  0 |  2  1 0
.   .   x . |  2 |  * 192 |  0  1  1  1 |  1  1 1
------------+----+--------+-------------+--------
x3/2o   . . |  3 |  3   0 | 32  *  *  * |  2  0 0
x   .   x . |  4 |  2   2 |  * 96  *  * |  1  1 0
.   o3/2x . |  3 |  0   3 |  *  * 64  * |  1  0 1
.   .   x4o |  4 |  0   4 |  *  *  * 48 |  0  1 1
------------+----+--------+-------------+--------
x3/2o3/2x .  12 | 12  12 |  4  6  4  0 | 16  * *
x   .   x4o   8 |  4   8 |  0  4  0  2 |  * 24 *
.   o3/2x4o  12 |  0  24 |  0  0  8  6 |  *  * 8

x3/2o3/2x4/3o

.   .   .   . | 96   2   4 |  1  4  2  2 |  2  2 1
--------------+----+--------+-------------+--------
x   .   .   . |  2 | 96   * |  1  2  0  0 |  2  1 0
.   .   x   . |  2 |  * 192 |  0  1  1  1 |  1  1 1
--------------+----+--------+-------------+--------
x3/2o   .   . |  3 |  3   0 | 32  *  *  * |  2  0 0
x   .   x   . |  4 |  2   2 |  * 96  *  * |  1  1 0
.   o3/2x   . |  3 |  0   3 |  *  * 64  * |  1  0 1
.   .   x4/3o |  4 |  0   4 |  *  *  * 48 |  0  1 1
--------------+----+--------+-------------+--------
x3/2o3/2x   .  12 | 12  12 |  4  6  4  0 | 16  * *
x   .   x4/3o   8 |  4   8 |  0  4  0  2 |  * 24 *
.   o3/2x4/3o  12 |  0  24 |  0  0  8  6 |  *  * 8

x3o3x *b3x

. . .    . | 96   2  2  2 |  1  2  2  1  2  1 | 1 1  2 1
-----------+----+----------+-------------------+---------
x . .    . |  2 | 96  *  * |  1  1  1  0  0  0 | 1 1  1 0
. . x    . |  2 |  * 96  * |  0  1  0  1  1  0 | 1 0  1 1
. . .    x |  2 |  *  * 96 |  0  0  1  0  1  1 | 0 1  1 1
-----------+----+----------+-------------------+---------
x3o .    . |  3 |  3  0  0 | 32  *  *  *  *  * | 1 1  0 0
x . x    . |  4 |  2  2  0 |  * 48  *  *  *  * | 1 0  1 0
x . .    x |  4 |  2  0  2 |  *  * 48  *  *  * | 0 1  1 0
. o3x    . |  3 |  0  3  0 |  *  *  * 32  *  * | 1 0  0 1
. . x    x |  4 |  0  2  2 |  *  *  *  * 48  * | 0 0  1 1
  o . *b3x |  3 |  0  0  3 |  *  *  *  *  * 32 | 0 1  0 1
-----------+----+----------+-------------------+---------
x3o3x    .  12 | 12 12  0 |  4  6  0  4  0  0 | 8 *  * *
x3o . *b3x  12 | 12  0 12 |  4  0  6  0  0  4 | * 8  * *
x . x    x   8 |  4  4  4 |  0  2  2  0  2  0 | * * 24 *
. o3x *b3x  12 |  0 12 12 |  0  0  0  4  6  4 | * *  * 8

snubbed forms: β3o3x *b3x, β3o3β *b3x, β3o3β *b3β

x3/2o3/2x *b3/2x

.   .   .      . | 96   2  2  2 |  1  2  2  1  2  1 | 1 1  2 1
-----------------+----+----------+-------------------+---------
x   .   .      . |  2 | 96  *  * |  1  1  1  0  0  0 | 1 1  1 0
.   .   x      . |  2 |  * 96  * |  0  1  0  1  1  0 | 1 0  1 1
.   .   .      x |  2 |  *  * 96 |  0  0  1  0  1  1 | 0 1  1 1
-----------------+----+----------+-------------------+---------
x3/2o   .      . |  3 |  3  0  0 | 32  *  *  *  *  * | 1 1  0 0
x   .   x      . |  4 |  2  2  0 |  * 48  *  *  *  * | 1 0  1 0
x   .   .      x |  4 |  2  0  2 |  *  * 48  *  *  * | 0 1  1 0
.   o3/2x      . |  3 |  0  3  0 |  *  *  * 32  *  * | 1 0  0 1
.   .   x      x |  4 |  0  2  2 |  *  *  *  * 48  * | 0 0  1 1
.   o   . *b3/2x |  3 |  0  0  3 |  *  *  *  *  * 32 | 0 1  0 1
-----------------+----+----------+-------------------+---------
x3/2o3/2x      .  12 | 12 12  0 |  4  6  0  4  0  0 | 8 *  * *
x3/2o   . *b3/2x  12 | 12  0 12 |  4  0  6  0  0  4 | * 8  * *
x   .   x      x   8 |  4  4  4 |  0  2  2  0  2  0 | * * 24 *
.   o3/2x *b3/2x  12 |  0 12 12 |  0  0  0  4  6  4 | * *  * 8

s4x3o3x

demi( . . . . ) | 96   2  2  2 |  2  1  2  1  1  2 | 1  2 1 1
----------------+----+----------+-------------------+---------
demi( . x . . ) |  2 | 96  *  * |  1  1  1  0  0  0 | 1  1 1 0
demi( . . . x ) |  2 |  * 96  * |  0  0  1  1  0  1 | 0  1 1 1
sefa( s4x . . ) |  2 |  *  * 96 |  1  0  0  0  1  1 | 1  1 0 1
----------------+----+----------+-------------------+---------
      s4x . .     4 |  2  0  2 | 48  *  *  *  *  * | 1  1 0 0
demi( . x3o . ) |  3 |  3  0  0 |  * 32  *  *  *  * | 1  0 1 0
demi( . x . x ) |  4 |  2  2  0 |  *  * 48  *  *  * | 0  1 1 0
demi( . . o3x ) |  3 |  0  3  0 |  *  *  * 32  *  * | 0  0 1 1
sefa( s4x3o . ) |  3 |  0  0  3 |  *  *  *  * 32  * | 1  0 0 1
sefa( s4x 2 x ) |  4 |  0  2  2 |  *  *  *  *  * 48 | 0  1 0 1
----------------+----+----------+-------------------+---------
      s4x3o .    12 | 12  0 12 |  6  4  0  0  4  0 | 8  * * *
      s4x 2 x     8 |  4  4  4 |  2  0  2  0  0  2 | * 24 * *
demi( . x3o3x )  12 | 12 12  0 |  0  4  6  4  0  0 | *  * 8 *
sefa( s4x3o3x )  12 |  0 12 12 |  0  0  0  4  4  6 | *  * * 8

starting figure: x4x3o3x

oxxxo3xxoxx4ooqoo&#xt   → all heights = 1/sqrt(2) = 0.707107
(co || pseudo toe || pseudo (x,q)-sirco || pseudo toe || co)

o....3o....4o....     | 12  *  *  *  *   4  2  0  0  0  0  0  0  0  0  0 | 2 2  1  4 0  0  0  0 0  0  0 0  0  0 0 0 | 1 2 2  0 0 0 0 0
.o...3.o...4.o...     |  * 24  *  *  *   0  1  1  2  2  0  0  0  0  0  0 | 0 0  1  2 1  2  2  1 0  0  0 0  0  0 0 0 | 0 2 1  1 1 0 0 0
..o..3..o..4..o..     |  *  * 24  *  *   0  0  0  0  2  2  2  0  0  0  0 | 0 0  0  0 0  2  1  2 1  2  1 0  0  0 0 0 | 0 1 0  2 1 1 0 0
...o.3...o.4...o.     |  *  *  * 24  *   0  0  0  0  0  0  2  1  2  1  0 | 0 0  0  0 0  0  0  1 0  2  2 1  1  2 0 0 | 0 0 0  1 1 2 1 0
....o3....o4....o     |  *  *  *  * 12   0  0  0  0  0  0  0  0  0  2  4 | 0 0  0  0 0  0  0  0 0  0  0 0  1  4 2 2 | 0 0 0  0 0 2 2 1
----------------------+----------------+----------------------------------+------------------------------------------+-----------------
..... x.... .....     |  2  0  0  0  0 | 24  *  *  *  *  *  *  *  *  *  * | 1 1  0  1 0  0  0  0 0  0  0 0  0  0 0 0 | 1 1 1  0 0 0 0 0
oo...3oo...4oo...&#x  |  1  1  0  0  0 |  * 24  *  *  *  *  *  *  *  *  * | 0 0  1  2 0  0  0  0 0  0  0 0  0  0 0 0 | 0 2 1  0 0 0 0 0
.x... ..... .....     |  0  2  0  0  0 |  *  * 12  *  *  *  *  *  *  *  * | 0 0  1  0 0  2  0  0 0  0  0 0  0  0 0 0 | 0 2 0  1 0 0 0 0
..... .x... .....     |  0  2  0  0  0 |  *  *  * 24  *  *  *  *  *  *  * | 0 0  0  1 1  0  1  0 0  0  0 0  0  0 0 0 | 0 1 1  0 1 0 0 0
.oo..3.oo..4.oo..&#x  |  0  1  1  0  0 |  *  *  *  * 48  *  *  *  *  *  * | 0 0  0  0 0  1  1  1 0  0  0 0  0  0 0 0 | 0 1 0  1 1 0 0 0
..x.. ..... .....     |  0  0  2  0  0 |  *  *  *  *  * 24  *  *  *  *  * | 0 0  0  0 0  1  0  0 1  1  0 0  0  0 0 0 | 0 1 0  1 0 1 0 0
..oo.3..oo.4..oo.&#x  |  0  0  1  1  0 |  *  *  *  *  *  * 48  *  *  *  * | 0 0  0  0 0  0  0  1 0  1  1 0  0  0 0 0 | 0 0 0  1 1 1 0 0
...x. ..... .....     |  0  0  0  2  0 |  *  *  *  *  *  *  * 12  *  *  * | 0 0  0  0 0  0  0  0 0  2  0 0  1  0 0 0 | 0 0 0  1 0 2 0 0
..... ...x. .....     |  0  0  0  2  0 |  *  *  *  *  *  *  *  * 24  *  * | 0 0  0  0 0  0  0  0 0  0  1 1  0  1 0 0 | 0 0 0  0 1 1 1 0
...oo3...oo4...oo&#x  |  0  0  0  1  1 |  *  *  *  *  *  *  *  *  * 24  * | 0 0  0  0 0  0  0  0 0  0  0 0  1  2 0 0 | 0 0 0  0 0 2 1 0
..... ....x .....     |  0  0  0  0  2 |  *  *  *  *  *  *  *  *  *  * 24 | 0 0  0  0 0  0  0  0 0  0  0 0  0  1 1 1 | 0 0 0  0 0 1 1 1
----------------------+----------------+----------------------------------+------------------------------------------+-----------------
o....3x.... .....     |  3  0  0  0  0 |  3  0  0  0  0  0  0  0  0  0  0 | 8 *  *  * *  *  *  * *  *  * *  *  * * * | 1 1 0  0 0 0 0 0
..... x....4o....     |  4  0  0  0  0 |  4  0  0  0  0  0  0  0  0  0  0 | * 6  *  * *  *  *  * *  *  * *  *  * * * | 1 0 1  0 0 0 0 0
ox... ..... .....&#x  |  1  2  0  0  0 |  0  2  1  0  0  0  0  0  0  0  0 | * * 12  * *  *  *  * *  *  * *  *  * * * | 0 2 0  0 0 0 0 0
..... xx... .....&#x  |  2  2  0  0  0 |  1  2  0  1  0  0  0  0  0  0  0 | * *  * 24 *  *  *  * *  *  * *  *  * * * | 0 1 1  0 0 0 0 0
..... .x...4.o...     |  0  4  0  0  0 |  0  0  0  4  0  0  0  0  0  0  0 | * *  *  * 6  *  *  * *  *  * *  *  * * * | 0 0 1  0 1 0 0 0
.xx.. ..... .....&#x  |  0  2  2  0  0 |  0  0  1  0  2  1  0  0  0  0  0 | * *  *  * * 24  *  * *  *  * *  *  * * * | 0 1 0  1 0 0 0 0
..... .xo.. .....&#x  |  0  2  1  0  0 |  0  0  0  1  2  0  0  0  0  0  0 | * *  *  * *  * 24  * *  *  * *  *  * * * | 0 1 0  0 1 0 0 0
..... ..... .oqo.&#xt |  0  1  2  1  0 |  0  0  0  0  2  0  2  0  0  0  0 | * *  *  * *  *  * 24 *  *  * *  *  * * * | 0 0 0  1 1 0 0 0
..x..3..o.. .....     |  0  0  3  0  0 |  0  0  0  0  0  3  0  0  0  0  0 | * *  *  * *  *  *  * 8  *  * *  *  * * * | 0 1 0  0 0 1 0 0
..xx. ..... .....&#x  |  0  0  2  2  0 |  0  0  0  0  0  1  2  1  0  0  0 | * *  *  * *  *  *  * * 24  * *  *  * * * | 0 0 0  1 0 1 0 0
..... ..ox. .....&#x  |  0  0  1  2  0 |  0  0  0  0  0  0  2  0  1  0  0 | * *  *  * *  *  *  * *  * 24 *  *  * * * | 0 0 0  0 1 1 0 0
..... ...x.4...o.     |  0  0  0  4  0 |  0  0  0  0  0  0  0  0  4  0  0 | * *  *  * *  *  *  * *  *  * 6  *  * * * | 0 0 0  0 1 0 1 0
...xo ..... .....&#x  |  0  0  0  2  1 |  0  0  0  0  0  0  0  1  0  2  0 | * *  *  * *  *  *  * *  *  * * 12  * * * | 0 0 0  0 0 2 0 0
..... ...xx .....&#x  |  0  0  0  2  2 |  0  0  0  0  0  0  0  0  1  2  1 | * *  *  * *  *  *  * *  *  * *  * 24 * * | 0 0 0  0 0 1 1 0
....o3....x .....     |  0  0  0  0  3 |  0  0  0  0  0  0  0  0  0  0  3 | * *  *  * *  *  *  * *  *  * *  *  * 8 * | 0 0 0  0 0 1 0 1
..... ....x4....o     |  0  0  0  0  4 |  0  0  0  0  0  0  0  0  0  0  4 | * *  *  * *  *  *  * *  *  * *  *  * * 6 | 0 0 0  0 0 0 1 1
----------------------+----------------+----------------------------------+------------------------------------------+-----------------
o....3x....4o....      12  0  0  0  0 | 24  0  0  0  0  0  0  0  0  0  0 | 8 6  0  0 0  0  0  0 0  0  0 0  0  0 0 0 | 1 * *  * * * * *
oxx..3xxo.. .....&#xt   3  6  3  0  0 |  3  6  3  3  6  3  0  0  0  0  0 | 1 0  3  3 0  3  3  0 1  0  0 0  0  0 0 0 | * 8 *  * * * * *
..... xx...4oo...&#x    4  4  0  0  0 |  4  4  0  4  0  0  0  0  0  0  0 | 0 1  0  4 1  0  0  0 0  0  0 0  0  0 0 0 | * * 6  * * * * *
.xxx. ..... .oqo.&#xt   0  2  4  2  0 |  0  0  1  0  4  2  4  1  0  0  0 | 0 0  0  0 0  2  0  2 0  2  0 0  0  0 0 0 | * * * 12 * * * *
..... .xox.4.oqo.&#xt   0  4  4  4  0 |  0  0  0  4  8  0  8  0  4  0  0 | 0 0  0  0 1  0  4  4 0  0  4 1  0  0 0 0 | * * *  * 6 * * *
..xxo3..oxx .....&#xt   0  0  3  6  3 |  0  0  0  0  0  3  6  3  3  6  3 | 0 0  0  0 0  0  0  0 1  3  3 0  3  3 1 0 | * * *  * * 8 * *
..... ...xx4...oo&#x    0  0  0  4  4 |  0  0  0  0  0  0  0  0  4  4  4 | 0 0  0  0 0  0  0  0 0  0  0 1  0  4 0 1 | * * *  * * * 6 *
....o3....x4....o       0  0  0  0 12 |  0  0  0  0  0  0  0  0  0  0 24 | 0 0  0  0 0  0  0  0 0  0  0 0  0  0 8 6 | * * *  * * * * 1
or
o....3o....4o....      & | 24  *  *   4  2  0  0  0  0 |  2  2  1  4  0  0  0  0 0 | 1  2  2  0 0
.o...3.o...4.o...      & |  * 48  *   0  1  1  2  2  0 |  0  0  1  2  1  2  2  1 0 | 0  2  1  1 1
..o..3..o..4..o..        |  *  * 24   0  0  0  0  4  2 |  0  0  0  0  0  4  2  2 1 | 0  2  0  2 1
-------------------------+----------+-------------------+---------------------------+-------------
..... x.... .....      & |  2  0  0 | 48  *  *  *  *  * |  1  1  0  1  0  0  0  0 0 | 1  1  1  0 0
oo...3oo...4oo...&#x   & |  1  1  0 |  * 48  *  *  *  * |  0  0  1  2  0  0  0  0 0 | 0  2  1  0 0
.x... ..... .....      & |  0  2  0 |  *  * 24  *  *  * |  0  0  1  0  0  2  0  0 0 | 0  2  0  1 0
..... .x... .....      & |  0  2  0 |  *  *  * 48  *  * |  0  0  0  1  1  0  1  0 0 | 0  1  1  0 1
.oo..3.oo..4.oo..&#x   & |  0  1  1 |  *  *  *  * 96  * |  0  0  0  0  0  1  1  1 0 | 0  1  0  1 1
..x.. ..... .....        |  0  0  2 |  *  *  *  *  * 24 |  0  0  0  0  0  2  0  0 1 | 0  2  0  1 0
-------------------------+----------+-------------------+---------------------------+-------------
o....3x.... .....      & |  3  0  0 |  3  0  0  0  0  0 | 16  *  *  *  *  *  *  * * | 1  1  0  0 0
..... x....4o....      & |  4  0  0 |  4  0  0  0  0  0 |  * 12  *  *  *  *  *  * * | 1  0  1  0 0
ox... ..... .....&#x   & |  1  2  0 |  0  2  1  0  0  0 |  *  * 24  *  *  *  *  * * | 0  2  0  0 0
..... xx... .....&#x   & |  2  2  0 |  1  2  0  1  0  0 |  *  *  * 48  *  *  *  * * | 0  1  1  0 0
..... .x...4.o...      & |  0  4  0 |  0  0  0  4  0  0 |  *  *  *  * 12  *  *  * * | 0  0  1  0 1
.xx.. ..... .....&#x   & |  0  2  2 |  0  0  1  0  2  1 |  *  *  *  *  * 48  *  * * | 0  1  0  1 0
..... .xo.. .....&#x   & |  0  2  1 |  0  0  0  1  2  0 |  *  *  *  *  *  * 48  * * | 0  1  0  0 1
..... ..... .oqo.&#xt    |  0  2  2 |  0  0  0  0  4  0 |  *  *  *  *  *  *  * 24 * | 0  0  0  1 1
..x..3..o.. .....        |  0  0  3 |  0  0  0  0  0  3 |  *  *  *  *  *  *  *  * 8 | 0  2  0  0 0
-------------------------+----------+-------------------+---------------------------+-------------
o....3x....4o....      &  12  0  0 | 24  0  0  0  0  0 |  8  6  0  0  0  0  0  0 0 | 2  *  *  * *
oxx..3xxo.. .....&#xt  &   3  6  3 |  3  6  3  3  6  3 |  1  0  3  3  0  3  3  0 1 | * 16  *  * *
..... xx...4oo...&#x   &   4  4  0 |  4  4  0  4  0  0 |  0  1  0  4  1  0  0  0 0 | *  * 12  * *
.xxx. ..... .oqo.&#xt      0  4  4 |  0  0  2  0  8  2 |  0  0  0  0  0  4  0  2 0 | *  *  * 12 *
..... .xox.4.oqo.&#xt      0  8  4 |  0  0  0  8 16  0 |  0  0  0  0  2  0  8  4 0 | *  *  *  * 6

ooqoqoo3oqoooqo4xoxuxox&#xt   → all heights = 1/2
(cube || pseudo q-co || pseudo (x,q)-sirco || pseudo u-cube || pseudo (x,q)-sirco || pseudo q-co || cube)

o......3o......4o......      & | 16  *  * *   3  3  0  0  0  0 |  3  3  3  0  0  0  0  0 | 1  3  1  0 0
.o.....3.o.....4.o.....      & |  * 24  * *   0  2  4  0  0  0 |  0  1  4  2  2  0  0  0 | 0  2  2  1 0
..o....3..o....4..o....      & |  *  * 48 *   0  0  2  2  1  1 |  0  0  1  2  2  1  2  1 | 0  1  1  2 1
...o...3...o...4...o...        |  *  *  * 8   0  0  0  0  6  0 |  0  0  0  0  6  0  0  3 | 0  0  2  3 0
-------------------------------+------------+-------------------+-------------------------+-------------
....... ....... x......      & |  2  0  0 0 | 24  *  *  *  *  * |  2  1  0  0  0  0  0  0 | 1  2  0  0 0
oo.....3oo.....4oo.....&#x   & |  1  1  0 0 |  * 48  *  *  *  * |  0  1  2  0  0  0  0  0 | 0  2  1  0 0
.oo....3.oo....4.oo....&#x   & |  0  1  1 0 |  *  * 96  *  *  * |  0  0  1  1  1  0  0  0 | 0  1  1  1 0
....... ....... ..x....      & |  0  0  2 0 |  *  *  * 48  *  * |  0  0  0  1  0  1  1  0 | 0  1  0  1 1
..oo...3..oo...4..oo...&#x   & |  0  0  1 1 |  *  *  *  * 48  * |  0  0  0  0  2  0  0  1 | 0  0  1  2 0
..o.o..3..o.o..4..o.o..&#x     |  0  0  2 0 |  *  *  *  *  * 24 |  0  0  0  0  0  0  2  1 | 0  0  0  2 1
-------------------------------+------------+-------------------+-------------------------+-------------
....... o......4x......      & |  4  0  0 0 |  4  0  0  0  0  0 | 12  *  *  *  *  *  *  * | 1  1  0  0 0
....... ....... xo.....&#x   & |  2  1  0 0 |  1  2  0  0  0  0 |  * 24  *  *  *  *  *  * | 0  2  0  0 0
....... oqo.... .......&#xt  & |  1  2  1 0 |  0  2  2  0  0  0 |  *  * 48  *  *  *  *  * | 0  1  1  0 0
....... ....... .ox....&#x   & |  0  1  2 0 |  0  0  2  1  0  0 |  *  *  * 48  *  *  *  * | 0  1  0  1 0
.oqo... ....... .......&#xt  & |  0  1  2 1 |  0  0  2  0  2  0 |  *  *  *  * 48  *  *  * | 0  0  1  1 0
....... ..o....4..x....      & |  0  0  4 0 |  0  0  0  4  0  0 |  *  *  *  *  * 12  *  * | 0  1  0  0 1
....... ....... ..x.x..&#x     |  0  0  4 0 |  0  0  0  2  0  2 |  *  *  *  *  *  * 24  * | 0  0  0  1 1
..ooo..3..ooo..4..ooo..&#xt    |  0  0  2 1 |  0  0  0  0  2  1 |  *  *  *  *  *  *  * 24 | 0  0  0  2 0
-------------------------------+------------+-------------------+-------------------------+-------------
o......3o......4x......      &   8  0  0 0 | 12  0  0  0  0  0 |  6  0  0  0  0  0  0  0 | 2  *  *  * *
....... oqo....4xox....&#xt  &   4  4  4 0 |  4  8  8  4  0  0 |  1  4  4  4  0  1  0  0 | * 12  *  * *
ooqo...3oqoo... .......&#xt  &   1  3  3 1 |  0  3  6  0  3  0 |  0  0  3  0  3  0  0  0 | *  * 16  * *
.oqoqo. ....... .oxuxo.&#xt      0  2  8 2 |  0  0  8  4  8  4 |  0  0  0  4  4  0  2  4 | *  *  * 12 *
....... ..o.o..4..x.x..&#x       0  0  8 0 |  0  0  0  8  0  4 |  0  0  0  0  0  2  4  0 | *  *  *  * 6

qo3oo3oq4xo&#zx   → height = 0
(tegum sum of (q,x)-sidpith and q-rit)

o.3o.3o.4o.     | 64  *   3   3 |  3  3  3 | 1  1  3
.o3.o3.o4.o     |  * 32   0   6 |  0  6  3 | 0  2  3
----------------+-------+--------+----------+--------
.. .. .. x.     |  2  0 | 96   * |  2  0  1 | 1  0  2
oo3oo3oo4oo&#x  |  1  1 |  * 192 |  0  2  1 | 0  1  2
----------------+-------+--------+----------+--------
.. .. o.4x.     |  4  0 |  4   0 | 48  *  * | 1  0  1
qo .. oq ..&#zx |  2  2 |  0   4 |  * 96  * | 0  1  1
.. .. .. xo&#x  |  2  1 |  1   2 |  *  * 96 | 0  0  2
----------------+-------+--------+----------+--------
.. o.3o.4x.       8  0 | 12   0 |  6  0  0 | 8  *  *
qo3oo3oq ..&#zx   4  4 |  0  12 |  0  6  0 | * 16  *
qo .. oq4xo&#zx   8  4 |  8  16 |  2  4  8 | *  * 24

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