Acronym tico
Name truncated icositetrachoron,
cantitruncated hexadecachoron
 
©  
Cross sections
 ©
Circumradius sqrt(7) = 2.645751
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o4o3o o3o4o . o3o . o o . o3o . o4o3o
1x3x4o3o x3x4o .
toe first
x3x . o
{6} first
x . o3o
edge first
. x4o3o
cube first
2 u3x4o . x3u . q u . q3o . u4o3o
3a x3u4o . u3x . a x . a3o . x4q3o
3b x3d . o d . o3q
4 x3x4q . x3x . c b . o3o . u4o3q
5a x3u4o . d3x . a x . a3q . x4o3a
5b u3d . o d . o3a . d4o3o
6a u3x4o . u3x . c u . q3a . x4o3a
6b d3u . q . d4o3o
7a x3x4o .
opposite toe
b3u . o x . H3H . u4o3q
7b u3b . o e . o3o
8a   x3u . c b . o3a . x4q3o
8b u3d . q
9a x3d . a d . q3a . u4o3o
9b d3u . o e . o3q
10 x3x . c u . H3H . x4o3o
opposite cube
11a x3u . a d . a3q  
11b d3x . o e . q3o
12 u3x . q b . a3o
13a x3x . o
opposite {6}
x . H3H
13b e . o3o
14   u . a3q
15a x . q3a
15b d . a3o
16 b . o3o
17a x . o3a
17b d . q3o
18 u . o3q
19 x . o3o
opposite edge
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1x3x3x4o x3x3x .
toe first
x3x . o
{6} first
x . x4o
cube first
. x3x4o
toe first
2 x3u3x . x3u . q u . u4o . u3x4o
3a u3x3u . u3x . a d . x4q . x3u4o
3b x3d . o x . d4o
4a x3x3d . x3x . c x . u4q . x3x4q
4b d3x3x . b . u4o
5a u3x3u . d3x . a e . x4o . x3u4o
5b u3d . o d . d4o
5c x . x4a
6a x3u3x . u3x . c e . x4o . u3x4o
6b d3u . q d . d4o
6c x . x4a
7a x3x3x .
opposite toe
b3u . o x . u4q . x3x4o
opposite toe
7b u3b . o b . u4o
8a   x3u . c d . x4q  
8b u3d . q x . d4o
9a x3d . a u . u4o
9b d3u . o
10 x3x . c x . x4o
opposite cube
11a x3u . a  
11b d3x . o
12 u3x . q
13 x3x . o
opposite {6}
 o3o3o *b3o o3o3o    . o3o . *b3o o . o    o . o3o *b3o
1x3x3x *b3x x3x3x    .
toe first
x3x . *b3x
toe first
x . x    x
cube first
. x3x *b3x
toe first
2 x3u3x    . x3u . *b3x u . u    u . u3x *b3x
3a u3x3u    . u3x . *b3u x . d    d . x3u *b3u
3b d . x    d
3c d . d    x
4a x3x3d    . x3x . *b3d b . u    u . x3x *b3d
4b d3x3x    . d3x . *b3x u . b    u . x3d *b3x
4c u . u    b
5a u3x3u    . u3x . *b3u d . d    d . x3u *b3u
5b e . x    x
5c x . e    x
5d x . x    e
6a x3u3x    . x3u . *b3x d . d    d . u3x *b3x
6b e . x    x
6c x . e    x
6d x . x    e
7a x3x3x    .
opposite toe
x3x . *b3x
opposite toe
b . u    u . x3x *b3x
opposite toe
7b u . b    u
7c u . u    b
8a     x . d    d  
8b d . x    d
8c d . d    x
9 u . u    u
10 x . x    x
opposite cube
(d=3x, a=2q, b=4x, c=3q, e=5x, H=hq)
Lace city
in approx. ASCII-art
 ©  
    x4o u4o x4q u4o x4o    
                           
x4o     d4o u4q d4o     x4o
                           
u4o d4o     x4a     d4o u4o
                           
x4q u4q x4a     x4a u4q x4q
                           
u4o d4o     x4a     d4o u4o
                           
x4o     d4o u4q d4o     x4o
                           
    x4o u4o x4q u4o x4o    
 ©  
            x3x            
        x3u     x3u        
    u3x     x3d     u3x    
x3x                     x3x
    d3x     u3d     d3x    
u3x     d3u     d3u     u3x
           bu3ub           
x3u     u3d     u3d     x3u
    x3d     d3u     x3d    
x3x                     x3x
    x3u     d3x     x3u    
        u3x     u3x        
            x3x            
 ©  
                o3o     o3o                
            o3q             o3q            
        q3o     o3a     o3a     q3o        
    o3o                             o3o    
        a3o     q3a     q3a     a3o        
            a3q             a3q            
o3o             H3H     H3H             o3o
    a3o                             a3o    
q3o     a3q                     a3q     q3o
            H3H             H3H            
o3q     q3a                     q3a     o3q
    o3a                             o3a    
o3o             H3H     H3H             o3o
            q3a             q3a            
        o3a     a3q     a3q     o3a        
    o3o                             o3o    
        o3q     a3o     a3o     o3q        
            q3o             q3o            
                o3o     o3o                
Coordinates (3/sqrt(2), sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: cube toe
tico 2424
)
Dihedral angles
  • at {4} between cube and toe:   135°
  • at {6} between toe and toe:   120°
Confer
compounds:
tidox  
decompositions:
rico || tico  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

Note that tico can be thought of as the external blend of 1 rico + 24 coatoes + 24 teses. This decomposition is described as the degenerate segmentoteron ox3xx4oo3oo&#x.


Incidence matrix according to Dynkin symbol

x3x4o3o

. . . . | 192 |  1   3 |  3   3 |  3  1
--------+-----+--------+--------+------
x . . . |   2 | 96   * |  3   0 |  3  0
. x . . |   2 |  * 288 |  1   2 |  2  1
--------+-----+--------+--------+------
x3x . . |   6 |  3   3 | 96   * |  2  0
. x4o . |   4 |  0   4 |  * 144 |  1  1
--------+-----+--------+--------+------
x3x4o .   24 | 12  24 |  8   6 | 24  *
. x4o3o    8 |  0  12 |  0   6 |  * 24

snubbed forms: β3x4o3o, x3β4o3o, s3s4o3o

x3x4o3/2o

. . .   . | 192 |  1   3 |  3   3 |  3  1
----------+-----+--------+--------+------
x . .   . |   2 | 96   * |  3   0 |  3  0
. x .   . |   2 |  * 288 |  1   2 |  2  1
----------+-----+--------+--------+------
x3x .   . |   6 |  3   3 | 96   * |  2  0
. x4o   . |   4 |  0   4 |  * 144 |  1  1
----------+-----+--------+--------+------
x3x4o   .   24 | 12  24 |  8   6 | 24  *
. x4o3/2o    8 |  0  12 |  0   6 |  * 24

x3x4/3o3o

. .   . . | 192 |  1   3 |  3   3 |  3  1
----------+-----+--------+--------+------
x .   . . |   2 | 96   * |  3   0 |  3  0
. x   . . |   2 |  * 288 |  1   2 |  2  1
----------+-----+--------+--------+------
x3x   . . |   6 |  3   3 | 96   * |  2  0
. x4/3o . |   4 |  0   4 |  * 144 |  1  1
----------+-----+--------+--------+------
x3x4/3o .   24 | 12  24 |  8   6 | 24  *
. x4/3o3o    8 |  0  12 |  0   6 |  * 24

x3x4/3o3/2o

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

x3x3x4o

. . . . | 192 |  1  1   2 |  1  2  2  1 |  2  1 1
--------+-----+-----------+-------------+--------
x . . . |   2 | 96  *   * |  1  2  0  0 |  2  1 0
. x . . |   2 |  * 96   * |  1  0  2  0 |  2  0 1
. . x . |   2 |  *  * 192 |  0  1  1  1 |  1  1 1
--------+-----+-----------+-------------+--------
x3x . . |   6 |  3  3   0 | 32  *  *  * |  2  0 0
x . x . |   4 |  2  0   2 |  * 96  *  * |  1  1 0
. x3x . |   6 |  0  3   3 |  *  * 64  * |  1  0 1
. . x4o |   4 |  0  0   4 |  *  *  * 48 |  0  1 1
--------+-----+-----------+-------------+--------
x3x3x .   24 | 12 12  12 |  4  6  4  0 | 16  * *
x . x4o    8 |  4  0   8 |  0  4  0  2 |  * 24 *
. x3x4o   24 |  0 12  24 |  0  0  8  6 |  *  * 8

snubbed forms: β3x3x4o, x3β3x4o, x3x3β4o, β3β3x4o, β3x3β4o, x3β3β4o, s3s3s4o

x3x3x4/3o

. . .   . | 192 |  1  1   2 |  1  2  2  1 |  2  1 1
----------+-----+-----------+-------------+--------
x . .   . |   2 | 96  *   * |  1  2  0  0 |  2  1 0
. x .   . |   2 |  * 96   * |  1  0  2  0 |  2  0 1
. . x   . |   2 |  *  * 192 |  0  1  1  1 |  1  1 1
----------+-----+-----------+-------------+--------
x3x .   . |   6 |  3  3   0 | 32  *  *  * |  2  0 0
x . x   . |   4 |  2  0   2 |  * 96  *  * |  1  1 0
. x3x   . |   6 |  0  3   3 |  *  * 64  * |  1  0 1
. . x4/3o |   4 |  0  0   4 |  *  *  * 48 |  0  1 1
----------+-----+-----------+-------------+--------
x3x3x   .   24 | 12 12  12 |  4  6  4  0 | 16  * *
x . x4/3o    8 |  4  0   8 |  0  4  0  2 |  * 24 *
. x3x4/3o   24 |  0 12  24 |  0  0  8  6 |  *  * 8

x3x3x *b3x

. . .    . | 192 |  1  1  1  1 |  1  1  1  1  1  1 | 1 1  1 1
-----------+-----+-------------+-------------------+---------
x . .    . |   2 | 96  *  *  * |  1  1  1  0  0  0 | 1 1  1 0
. x .    . |   2 |  * 96  *  * |  1  0  0  1  1  0 | 1 1  0 1
. . x    . |   2 |  *  * 96  * |  0  1  0  1  0  1 | 1 0  1 1
. . .    x |   2 |  *  *  * 96 |  0  0  1  0  1  1 | 0 1  1 1
-----------+-----+-------------+-------------------+---------
x3x .    . |   6 |  3  3  0  0 | 32  *  *  *  *  * | 1 1  0 0
x . x    . |   4 |  2  0  2  0 |  * 48  *  *  *  * | 1 0  1 0
x . .    x |   4 |  2  0  0  2 |  *  * 48  *  *  * | 0 1  1 0
. x3x    . |   6 |  0  3  3  0 |  *  *  * 32  *  * | 1 0  0 1
. x . *b3x |   6 |  0  3  0  3 |  *  *  *  * 32  * | 0 1  0 1
. . x    x |   4 |  0  0  2  2 |  *  *  *  *  * 48 | 0 0  1 1
-----------+-----+-------------+-------------------+---------
x3x3x    .   24 | 12 12 12  0 |  4  6  0  4  0  0 | 8 *  * *
x3x . *b3x   24 | 12 12  0 12 |  4  0  6  0  4  0 | * 8  * *
x . x    x    8 |  4  0  4  4 |  0  2  2  0  0  2 | * * 24 *
. x3x *b3x   24 |  0 12 12 12 |  0  0  0  4  4  6 | * *  * 8

snubbed forms: β3x3x *b3x, x3β3x *b3x, β3β3x *b3x, β3x3β *b3x, β3β3β *b3x, β3x3β *b3β, s3s3s *b3s

s4x3x3x

demi( . . . . ) | 192 |  1  1  1  1 |  1  1  1  1  1  1 | 1  1 1 1
----------------+-----+-------------+-------------------+---------
demi( . x . . ) |   2 | 96  *  *  * |  1  1  1  0  0  0 | 1  1 1 0
demi( . . x . ) |   2 |  * 96  *  * |  0  1  0  1  1  0 | 1  0 1 1
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  0  2 | 48  *  *  *  *  * | 1  1 0 0
demi( . x3x . ) |   6 |  3  3  0  0 |  * 32  *  *  *  * | 1  0 1 0
demi( . x . x ) |   4 |  2  0  2  0 |  *  * 48  *  *  * | 0  1 1 0
demi( . . x3x ) |   6 |  0  3  3  0 |  *  *  * 32  *  * | 0  0 1 1
sefa( s4x3x . ) |   6 |  0  3  0  3 |  *  *  *  * 32  * | 1  0 0 1
sefa( s4x . x ) |   4 |  0  0  2  2 |  *  *  *  *  * 48 | 0  1 0 1
----------------+-----+-------------+-------------------+---------
      s4x3x .     24 | 12 12  0 12 |  6  4  0  0  4  0 | 8  * * *
      s4x . x      8 |  4  0  4  4 |  2  0  2  0  0  2 | * 24 * *
demi( . x3x3x )   24 | 12 12 12  0 |  0  4  6  4  0  0 | *  * 8 *
sefa( s4x3x3x )   24 |  0 12 12 12 |  0  0  0  4  4  6 | *  * * 8

starting figure: x4x3x3x

xuxxxux3xxuxuxx4oooqooo&#xt   → all heights = 1/sqrt(2) = 0.707107
(toe || pseudo (u,x)-toe || pseudo (x,u)-toe || pseudo (x,x,q)-girco || pseudo (x,u)-toe || pseudo (u,x)-toe || toe)

o......3o......4o......      & | 48  *  *  * |  1  2  1  0  0  0  0  0  0 |  2  1  1  2  0  0  0  0 0 | 1  2  1 0  0
.o.....3.o.....4.o.....      & |  * 48  *  * |  0  0  1  2  1  0  0  0  0 |  0  0  1  2  1  2  0  0 0 | 0  2  1 1  0
..o....3..o....4..o....      & |  *  * 48  * |  0  0  0  0  1  1  2  0  0 |  0  0  1  0  0  2  2  1 0 | 0  2  0 1  1
...o...3...o...4...o...        |  *  *  * 48 |  0  0  0  0  0  0  2  1  1 |  0  0  0  0  0  2  2  1 1 | 0  2  0 1  1
-------------------------------+-------------+----------------------------+---------------------------+-------------
x...... ....... .......      & |  2  0  0  0 | 24  *  *  *  *  *  *  *  * |  2  0  1  0  0  0  0  0 0 | 1  2  0 0  0
....... x...... .......      & |  2  0  0  0 |  * 48  *  *  *  *  *  *  * |  1  1  0  1  0  0  0  0 0 | 1  1  1 0  0
oo.....3oo.....4oo.....&#x   & |  1  1  0  0 |  *  * 48  *  *  *  *  *  * |  0  0  1  2  0  0  0  0 0 | 0  2  1 0  0
....... .x..... .......      & |  0  2  0  0 |  *  *  * 48  *  *  *  *  * |  0  0  0  1  1  1  0  0 0 | 0  1  1 1  0
.oo....3.oo....4.oo....&#x   & |  0  1  1  0 |  *  *  *  * 48  *  *  *  * |  0  0  1  0  0  2  0  0 0 | 0  2  0 1  0
..x.... ....... .......      & |  0  0  2  0 |  *  *  *  *  * 24  *  *  * |  0  0  1  0  0  0  2  0 0 | 0  2  0 0  1
..oo...3..oo...4..oo...&#x   & |  0  0  1  1 |  *  *  *  *  *  * 96  *  * |  0  0  0  0  0  1  1  1 0 | 0  1  0 1  1
...x... ....... .......        |  0  0  0  2 |  *  *  *  *  *  *  * 24  * |  0  0  0  0  0  0  2  0 1 | 0  2  0 0  1
....... ...x... .......        |  0  0  0  2 |  *  *  *  *  *  *  *  * 24 |  0  0  0  0  0  2  0  0 1 | 0  2  0 1  0
-------------------------------+-------------+----------------------------+---------------------------+-------------
x......3x...... .......      & |  6  0  0  0 |  3  3  0  0  0  0  0  0  0 | 16  *  *  *  *  *  *  * * | 1  1  0 0  0
....... x......4o......      & |  4  0  0  0 |  0  4  0  0  0  0  0  0  0 |  * 12  *  *  *  *  *  * * | 1  0  1 0  0
xux.... ....... .......&#xt  & |  2  2  2  0 |  1  0  2  0  2  1  0  0  0 |  *  * 24  *  *  *  *  * * | 0  2  0 0  0
....... xx..... .......&#x   & |  2  2  0  0 |  0  1  2  1  0  0  0  0  0 |  *  *  * 48  *  *  *  * * | 0  1  1 0  0
....... .x.....4.o.....      & |  0  4  0  0 |  0  0  0  4  0  0  0  0  0 |  *  *  *  * 12  *  *  * * | 0  0  1 1  0
....... .xux... .......&#xt  & |  0  2  2  2 |  0  0  0  1  2  0  2  0  1 |  *  *  *  *  * 48  *  * * | 0  1  0 1  0
..xx... ....... .......&#x   & |  0  0  2  2 |  0  0  0  0  0  1  2  1  0 |  *  *  *  *  *  * 48  * * | 0  1  0 0  1
....... ....... ..oqo..&#xt    |  0  0  2  2 |  0  0  0  0  0  0  4  0  0 |  *  *  *  *  *  *  * 24 * | 0  0  0 1  1
...x...3...x... .......        |  0  0  0  6 |  0  0  0  0  0  0  0  3  3 |  *  *  *  *  *  *  *  * 8 | 0  2  0 0  0
-------------------------------+-------------+----------------------------+---------------------------+-------------
x......3x......4o......      &  24  0  0  0 | 12 24  0  0  0  0  0  0  0 |  8  6  0  0  0  0  0  0 0 | 2  *  * *  *
xuxx...3xxux... .......&#xt  &   6  6  6  6 |  3  3  6  3  6  3  6  3  3 |  1  0  3  3  0  3  3  0 1 | * 16  * *  *
....... xx.....4oo.....&#x   &   4  4  0  0 |  0  4  4  4  0  0  0  0  0 |  0  1  0  4  1  0  0  0 0 | *  * 12 *  *
....... .xuxux.4.ooqoo.&#xt      0  8  8  8 |  0  0  0  8  8  0 16  0  4 |  0  0  0  0  2  8  0  4 0 | *  *  * 6  *
..xxx.. ....... ..oqo..&#xt      0  0  4  4 |  0  0  0  0  0  2  8  2  0 |  0  0  0  0  0  0  4  2 0 | *  *  * * 12

oqQ3ooo3qoo4xux&#zxt   → all existing heights = 0, Q = 2q = 2.828427

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

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