Acronym grico
Name great rhombated icositetrachoron,
cantitruncated icositetrachoron
 
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Cross sections
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Circumradius sqrt[10+6 sqrt(2)] = 4.299451
Vertex figure
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Vertex layers
LayerSymmetrySubsymmetries
 o3o4o3o o3o4o . o3o . o o . o3o . o4o3o
1x3x4x3o x3x4x .
girco first
x3x . o
{6} first
x . x3o
trip first
. x4x3o
tic first
2 x3w4o . w3x . x u . w3o . u4x3o
3a u3w4o . w3u . w x . Y3o . x4w3o
3b X . w3x
4a X3x4x . x3X . X w . Y3x . x4w3x
4b Z . x3w
5 x3X4o . X3x . Y V . o3w . u4x3w
6a w3u4x . w3X . w w . Y3w . x4x3Y
6b Z . x3Y
7 w3x4w . u3w . W U . o3x . X4o3w
8a x3x4X . w3Z . x X . w3Y . Z4o3x
8b X3w . Y . w4o3Y
9a w3x4w . x3w . T x . Y3X . Z4o3x
9b V . o3Y . w4o3Y
10 w3u4x . x3V . o u . w3W . X4o3w
11 x3X4o . x3x . S w . W3w . x4x3Y
12a X3x4x . X3Z . x x . x3T . u4x3w
12b Z3w . Y Q . o3x
13 u3w4o . x3w . S X . X3Y . x4w3x
14 x3w4o . u3V . o U . o3Y . x4w3o
15 x3x4x .
opposite girco
Z3X . w w . T3x . u4x3o
16   V3x . Y Q . o3w . x4x3o
opposite tic
17 Z3w . W x . R3R  
18a V3u . w Z . X3Y
18b u3w . S
19 x3U . o U . x3Y
20a Z3X . X X . T3x
20b X3w . T
21a U3x . x V . w3Y
21b Q . x3w
22 X3x . S Z . W3w
23 x3X . S u . R3R
24 x3U . x Z . w3W
25a X3Z . X V . Y3w
25b w3X . T Q . w3x
26 U3x . o X . x3T
27a u3V . w U . Y3x
27b w3u . S
28 w3Z . W Z . Y3X
29 x3V . Y x . R3R
30 X3Z . w Q . w3o
31 V3u . o w . x3T
32 w3x . S U . Y3o
33a Z3X . x X . Y3X
33b w3Z . Y
34a x3x . S x . T3x
34b Q . x3o
35 V3x . o w . w3W
36 w3x . T u . W3w
37a Z3w . x x . X3Y
37b w3X . Y V . Y3o
38 w3u . W X . Y3w
39 X3w . w U . x3o
40a x3X . Y w . w3Y
40b Z . Y3x
41 X3x . X V . w3o
42a u3w . w w . x3Y
42b Z . w3x
43a x3w . x x . o3Y
43b X . x3w
44 x3x . o
opposite {6}
u . o3w
45   x . o3x
opposite trip
(X=wq=x+w=2x+q, W=2w=2x+2q, Y=x+2q=w+q, Z=3x+q=u+w, V=3x+2q, U=2X=4x+2q, T=2x+3q, S=3w=3x+3q, R=wh, Q=5x+2q)
Lace city
in approx. ASCII-art
 ©  
              x4x   x4u   w4x     w4x   x4u   x4x              
                                                               
          o4w   o4X           X4x           o4X   o4w          
                                                               
                                                               
    o4w         o4Z           X4u           o4Z         o4w    
                                                               
x4x                 x4Z   w4X     w4X   x4Z                 x4x
    o4X   o4Z                 W4x                 o4Z   o4X    
                                                               
x4u           x4Z         Y4w     Y4w         x4Z           x4u
                                                               
                                                               
w4x           w4X   Y4w                 Y4w   w4X           w4x
                                                               
    X4x   X4u   W4x                         W4x   X4u   X4x    
                                                               
w4x           w4X   Y4w                 Y4w   w4X           w4x
                                                               
                                                               
x4u           x4Z         Y4w     Y4w         x4Z           x4u
                                                               
    o4X   o4Z                 W4x                 o4Z   o4X    
x4x                 x4Z   w4X     w4X   x4Z                 x4x
                                                               
    o4w         o4Z           X4u           o4Z         o4w    
                                                               
                                                               
          o4w   o4X           X4x           o4X   o4w          
                                                               
              x4x   x4u   w4x     w4x   x4u   x4x              
                                        (X3x)                                          
                     x3x   x3w     u3w   # x3X   w3u     w3x   x3x                     
                                                                                       
                                                                                       
                  x3w                 X3w     w3X                 w3x                  
                                                                                       
                                                                                       
                                                                                       
              u3w                 Z3w             w3Z                 w3u              
                                                                                       
                                                                                       
           X3x   X3w     Z3w   V3x                   x3V   w3Z     w3X   x3X           
          x3X                         Z3X     X3Z                         X3x          
                                                                                       
                                                                                       
       w3u   w3X             Z3X   V3u           u3V   X3Z             X3w   u3w       
                                                                                       
                                                                                       
                                                                                       
   w3x           w3Z     X3Z           U3x   x3U           Z3X     Z3w           x3w   
                                                                                       
                                                                                       
x3x                 x3V     u3V     x3U         U3x     V3u     V3x                 x3x
                                                                                       
                                                                                       
   w3x           w3Z     X3Z           U3x   x3U           Z3X     Z3w           x3w   
                                                                                       
                                                                                       
                                                                                       
       w3u   w3X             Z3X   V3u           u3V   X3Z             X3w   u3w       
                                                                                       
                                                                                       
          x3X                         Z3X     X3Z                         X3x          
           X3x   X3w     Z3w   V3x                   x3V   w3Z     w3X   x3X           
                                                                                       
                                                                                       
              u3w                 Z3w             w3Z                 w3u              
                                                                                       
                                                                                       
                                                                                       
                  x3w                 X3w     w3X                 w3x                  
                                                                                       
                                                                                       
                     x3x   x3w     u3w   # x3X   w3u     w3x   x3x                     
                                        (X3x)                                          
 ©  
                 o3x o3w   x3w w3x   w3o x3o                 
                                                             
           o3x     o3Y   x3Y     Y3x   Y3o     x3o           
                                                             
         o3w o3Y           w3Y Y3w           Y3o w3o         
                                                             
                           (W3w)                             
      x3w x3Y           X3Y # w3W Y3X           Y3x w3x      
                                                             
    w3x     w3Y   X3Y     T3x   x3T     Y3X   Y3w     x3w    
                                                             
      Y3x Y3w   W3w T3x               x3T w3W   w3Y x3Y      
  w3o          w3W           R3R           W3w          o3w  
                                                             
x3o Y3o      Y3X x3T   R3R         R3R   T3x X3Y      o3Y o3x
                                                             
                                                             
                                                             
x3o Y3o      Y3X x3T   R3R         R3R   T3x X3Y      o3Y o3x
                                                             
  w3o          w3W           R3R           W3w          o3w  
      Y3x Y3w   W3w T3x               x3T w3W   w3Y x3Y      
                                                             
    w3x     w3Y   X3Y     T3x   x3T     Y3X   Y3w     x3w    
                                                             
      x3w x3Y           X3Y # w3W Y3X           Y3x w3x      
                           (W3w)                             
                                                             
         o3w o3Y           w3Y Y3w           Y3o w3o         
                                                             
           o3x     o3Y   x3Y     Y3x   Y3o     x3o           
                                                             
                 o3x o3w   x3w w3x   w3o x3o                 
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: girco tic trip
grico 242496
)
Dihedral angles
  • at {3} between tic and trip:   150°
  • at {4} between girco and trip:   arccos(-sqrt[2/3]) = 144.735610°
  • at {8} between girco and tic:   135°
  • at {6} between girco and girco:   120°
Confer
Grünbaumian relatives:
2grico  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope grico is isomorphic to gaqri, thereby replacing the octagons by octagrams, resp. replacing girco by quitco and tic by quith.

Note that grico can be thought of as the external blend of 1 prico + 24 sircoatics + 96 opes + 96 thiddips + 24 toagircoes. This decomposition is described as the degenerate segmentoteron xo3ox4xx3xx&#x.


Incidence matrix according to Dynkin symbol

x3x4x3o

. . . . | 576 |   1   1   2 |  1   2   2   1 |  2  1  1
--------+-----+-------------+----------------+---------
x . . . |   2 | 288   *   * |  1   2   0   0 |  2  1  0
. x . . |   2 |   * 288   * |  1   0   2   0 |  2  0  1
. . x . |   2 |   *   * 576 |  0   1   1   1 |  1  1  1
--------+-----+-------------+----------------+---------
x3x . . |   6 |   3   3   0 | 96   *   *   * |  2  0  0
x . x . |   4 |   2   0   2 |  * 288   *   * |  1  1  0
. x4x . |   8 |   0   4   4 |  *   * 144   * |  1  0  1
. . x3o |   3 |   0   0   3 |  *   *   * 192 |  0  1  1
--------+-----+-------------+----------------+---------
x3x4x .   48 |  24  24  24 |  8  12   6   0 | 24  *  *
x . x3o    6 |   3   0   6 |  0   3   0   2 |  * 96  *
. x4x3o   24 |   0  12  24 |  0   0   6   8 |  *  * 24

snubbed forms: β3x4x3o, x3β4x3o, x3x4β3o, s3s4x3o, β3x4β3o, x3β4β3o, β3β4β3o

x3x4x3/2o

. . .   . | 576 |   1   1   2 |  1   2   2   1 |  2  1  1
----------+-----+-------------+----------------+---------
x . .   . |   2 | 288   *   * |  1   2   0   0 |  2  1  0
. x .   . |   2 |   * 288   * |  1   0   2   0 |  2  0  1
. . x   . |   2 |   *   * 576 |  0   1   1   1 |  1  1  1
----------+-----+-------------+----------------+---------
x3x .   . |   6 |   3   3   0 | 96   *   *   * |  2  0  0
x . x   . |   4 |   2   0   2 |  * 288   *   * |  1  1  0
. x4x   . |   8 |   0   4   4 |  *   * 144   * |  1  0  1
. . x3/2o |   3 |   0   0   3 |  *   *   * 192 |  0  1  1
----------+-----+-------------+----------------+---------
x3x4x   .   48 |  24  24  24 |  8  12   6   0 | 24  *  *
x . x3/2o    6 |   3   0   6 |  0   3   0   2 |  * 96  *
. x4x3/2o   24 |   0  12  24 |  0   0   6   8 |  *  * 24

wx3xx3xw4xo&#zx   → height = 0
(tegum sum of (w,x,x,x)-gidpith and (x,x,w)-tico)

o.3o.3o.4o.     | 384   * |   1   1   1   1  0  0 |  1  1  1  1   1   1  0 | 1  1  1  1
.o3.o3.o4.o     |   * 192 |   0   0   0   2  1  1 |  0  0  0  2   2   1  1 | 0  2  1  1
----------------+---------+-----------------------+------------------------+-----------
.. x. .. ..     |   2   0 | 192   *   *   *  *  * |  1  1  0  0   1   0  0 | 1  1  0  1
.. .. x. ..     |   2   0 |   * 192   *   *  *  * |  1  0  1  1   0   0  0 | 1  1  1  0
.. .. .. x.     |   2   0 |   *   * 192   *  *  * |  0  1  1  0   0   1  0 | 1  0  1  1
oo3oo3oo4oo&#x  |   1   1 |   *   *   * 384  *  * |  0  0  0  1   1   1  0 | 0  1  1  1
.x .. .. ..     |   0   2 |   *   *   *   * 96  * |  0  0  0  2   0   0  1 | 0  2  1  0
.. .x .. ..     |   0   2 |   *   *   *   *  * 96 |  0  0  0  0   2   0  1 | 0  2  0  1
----------------+---------+-----------------------+------------------------+-----------
.. x.3x. ..     |   6   0 |   3   3   0   0  0  0 | 64  *  *  *   *   *  * | 1  1  0  0
.. x. .. x.     |   4   0 |   2   0   2   0  0  0 |  * 96  *  *   *   *  * | 1  0  0  1
.. .. x.4x.     |   8   0 |   0   4   4   0  0  0 |  *  * 48  *   *   *  * | 1  0  1  0
wx .. xw ..&#zx |   4   4 |   0   2   0   4  2  0 |  *  *  * 96   *   *  * | 0  1  1  0
.. xx .. ..&#x  |   2   2 |   1   0   0   2  0  1 |  *  *  *  * 192   *  * | 0  1  0  1
.. .. .. xo&#x  |   2   1 |   0   0   1   2  0  0 |  *  *  *  *   * 192  * | 0  0  1  1
.x3.x .. ..     |   0   6 |   0   0   0   0  3  3 |  *  *  *  *   *   * 32 | 0  2  0  0
----------------+---------+-----------------------+------------------------+-----------
.. x.3x.4x.       48   0 |  24  24  24   0  0  0 |  8 12  6  0   0   0  0 | 8  *  *  *
wx3xx3xw ..&#zx   24  24 |  12  12   0  24 12 12 |  4  0  0  6  12   0  4 | * 16  *  *
wx .. xw4xo&#zx   16   8 |   0   8   8  16  4  0 |  0  0  2  4   0   8  0 | *  * 24  *
.. xx .. xo&#x     4   2 |   2   0   2   4  0  1 |  0  1  0  0   2   2  0 | *  *  * 96

xwX3ooo3wxx4xux&#zxt   → height = 0, X=Q+x=w+q = 3.828427

o..3o..3o..4o..      | 192   *   * |   2  1   1   0   0   0  0 |  1  2  2  1  0   0  0  0 |  1  1  2  0 0
.o.3.o.3.o.4.o.      |   * 192   * |   0  0   1   2   1   0  0 |  0  0  2  1  1   2  0  0 |  0  1  2  1 0
..o3..o3..o4..o      |   *   * 192 |   0  0   0   0   1   2  1 |  0  0  0  1  0   2  1  2 |  0  0  2  1 1
---------------------+-------------+---------------------------+--------------------------+--------------
x.. ... ... ...      |   2   0   0 | 192  *   *   *   *   *  * |  1  1  1  0  0   0  0  0 |  1  1  1  0 0
... ... ... x..      |   2   0   0 |   * 96   *   *   *   *  * |  0  2  0  1  0   0  0  0 |  1  0  2  0 0
oo.3oo.3oo.4oo.&#x   |   1   1   0 |   *  * 192   *   *   *  * |  0  0  2  1  0   0  0  0 |  0  1  2  0 0
... ... .x. ...      |   0   2   0 |   *  *   * 192   *   *  * |  0  0  1  0  1   1  0  0 |  0  1  1  1 0
.oo3.oo3.oo4.oo&#x   |   0   1   1 |   *  *   *   * 192   *  * |  0  0  0  1  0   2  0  0 |  0  0  2  1 0
... ... ..x ...      |   0   0   2 |   *  *   *   *   * 192  * |  0  0  0  0  0   1  1  1 |  0  0  1  1 1
... ... ... ..x      |   0   0   2 |   *  *   *   *   *   * 96 |  0  0  0  1  0   0  0  2 |  0  0  2  0 1
---------------------+-------------+---------------------------+--------------------------+--------------
x..3o.. ... ...      |   3   0   0 |   3  0   0   0   0   0  0 | 64  *  *  *  *   *  *  * |  1  1  0  0 0
x.. ... ... x..      |   4   0   0 |   2  2   0   0   0   0  0 |  * 96  *  *  *   *  *  * |  1  0  1  0 0
xw. ... wx. ...&#zx  |   4   4   0 |   2  0   4   2   0   0  0 |  *  * 96  *  *   *  *  * |  0  1  1  0 0
... ... ... xux&#xt  |   2   2   2 |   0  1   2   0   2   0  1 |  *  *  * 96  *   *  *  * |  0  0  2  0 0
... .o.3.x. ...      |   0   3   0 |   0  0   0   3   0   0  0 |  *  *  *  * 64   *  *  * |  0  1  0  1 0
... ... .xx ...&#x   |   0   2   2 |   0  0   0   1   2   1  0 |  *  *  *  *  * 192  *  * |  0  0  1  1 0
... ..o3..x ...      |   0   0   3 |   0  0   0   0   0   3  0 |  *  *  *  *  *   * 64  * |  0  0  0  1 1
... ... ..x4..x      |   0   0   8 |   0  0   0   0   0   4  4 |  *  *  *  *  *   *  * 48 |  0  0  1  0 1
---------------------+-------------+---------------------------+--------------------------+--------------
x..3o.. ... x..         6   0   0 |   6  3   0   0   0   0  0 |  2  3  0  0  0   0  0  0 | 32  *  *  * *
xw.3oo.3wx. ...&#zx    12  12   0 |  12  0  12  12   0   0  0 |  4  0  6  0  4   0  0  0 |  * 16  *  * *
xwX ... wxx4xux&#zxt   16  16  16 |   8  8  16   8  16   8  8 |  0  4  4  8  0   8  0  2 |  *  * 24  * *
... .oo3.xx ...&#x      0   3   3 |   0  0   0   3   3   3  0 |  0  0  0  0  1   3  1  0 |  *  *  * 64 *
... ..o3..x4..x         0   0  24 |   0  0   0   0   0  24 12 |  0  0  0  0  0   0  8  6 |  *  *  *  * 8

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