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 . Q x . Q3o . x4q3o
3b x3d . o d . o3q
4 x3x4q . x3x . c b . o3o . u4o3q
5a x3u4o . d3x . Q x . Q3q . x4o3Q
5b u3d . o d . o3Q . d4o3o
6a u3x4o . u3x . c u . q3Q . x4o3Q
6b d3u . q . d4o3o
7a x3x4o .
opposite toe
b3u . o x . H3H . u4o3q
7b u3b . o e . o3o
8a   x3u . c b . o3Q . x4q3o
8b u3d . q
9a x3d . Q d . q3Q . u4o3o
9b d3u . o e . o3q
10 x3x . c u . H3H . x4o3o
opposite cube
11a x3u . Q d . Q3q  
11b d3x . o e . q3o
12 u3x . q b . Q3o
13a x3x . o
opposite {6}
x . H3H
13b e . o3o
14   u . Q3q
15a x . q3Q
15b d . Q3o
16 b . o3o
17a x . o3Q
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 . Q d . x4q . x3u4o
3b x3d . o x . d4o
4a x3x3d . x3x . c x . u4q . x3x4q
4b d3x3x . b . u4o
5a u3x3u . d3x . Q e . x4o . x3u4o
5b u3d . o d . d4o
5c x . x4Q
6a x3u3x . u3x . c e . x4o . u3x4o
6b d3u . q d . d4o
6c x . x4Q
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 . Q u . u4o
9b d3u . o
10 x3x . c x . x4o
opposite cube
11a x3u . Q  
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, Q=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     x4Q     d4o u4o
                           
x4q u4q x4Q     x4Q u4q x4q
                           
u4o d4o     x4Q     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   o3Q    o3Q   q3o      
   o3o                      o3o   
      Q3o   q3Q    q3Q   Q3o      
         Q3q          Q3q         
o3o         H3H    H3H         o3o
   Q3o                      Q3o   
q3o   Q3q                Q3q   q3o
         H3H          H3H         
o3q   q3Q                q3Q   o3q
   o3Q                      o3Q   
o3o         H3H    H3H         o3o
         q3Q          q3Q         
      o3Q   Q3q    Q3q   o3Q      
   o3o                      o3o   
      o3q   Q3o    Q3o   o3q      
         q3o          q3o         
            o3o    o3o            
Coordinates
  1. (3/sqrt(2), sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
  2. or wrt. dual positioning of underlying ico:
    • (5/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
      (inscribed o3o3q4x)
    • (3/2, 3/2, 3/2, 1/2)   & all permutations, all changes of sign
      (inscribed q3o3o4u)
    • (2, 1, 1, 1)               & all permutations, all changes of sign
      (inscribed Q3o3o4x)
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°
Face vector 192, 384, 240, 48
Confer
compounds:
tastic   tidox  
decompositions:
rico || tico  
diminishings:
oditico  
general polytopal classes:
Wythoffian polychora   lace simplices   partial Stott expansions  
External
links
hedrondude   wikipedia   polytopewiki   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, β3β4o3o

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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