Acronym gippic
Name great prismatotetracontoctachoron,
omnitruncated icositetrachoron
Cross sections 
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Circumradius sqrt[14+9 sqrt(2)] = 5.169905
Vertex figure 
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Vertex layers
LayerSymmetrySubsymmetries
 o3o4o3o o3o4o . o3o . o o . o3o . o4o3o
1x3x4x3x x3x4x .
girco first		 x3x . x
hip first		 x . x3x
hip first		 . x4x3x
girco first
2 x3x4u . w3x . u u . x3w . u4x3x
3 x3w4x . Y3x . x x . x3Y . x4w3x
4 u3w4x . w3u . X X . u3w . x4w3u
5a X3x4u . Y3u . w w . u3Y . u4x3X
5b x3X . Z Z . X3x
6 x3X4x . X3x . W W . x3X . x4X3x
7a W3x4x . W3x . Y Y . x3W . x4x3W
7b u3w . V V . w3u
8a w3u4u . Y3X . w w . X3Y . u4u3w
8b x3W . Z Z . W3x
9 Y3u4x . x3w . S S . w3x . x4u3Y
10 w3x4X . w3W . X X . W3w . X4x3w
11a Y3x4w . Y3Z . x x . Z3Y . w4x3Y
11b x3x4Z . W3w . Y Y . w3W . Z4x3x
11c u3Y . V V . Y3u
12a Y3x4w . x3x . U U . x3x . w4x3Y
12b x3x4Z . . Z4x3x
13a w3x4X . w3V . u u . V3w . X4x3w
13b X3Y . W W . Y3X
14 Y3u4x . x3Y . S S . Y3x . x4u3Y
15 w3u4u . x3S . x x . S3x . u4u3w
16a W3x4x . W3Z . x x . Z3W . x4x3W
16b V3w . Y Y . w3V
17 x3X4x . x3x . T T . x3x . x4X3x
18a X3x4u . X3V . u u . V3X . u4x3X
18b Z3Y . W W . Y3Z
19 u3w4x . V3X . w w . X3V . x4w3u
20 x3w4x . x3Y . U U . Y3x . x4w3x
21a x3x4u . u3S . x x . S3u . u4x3x
21b S3x . Y Y . x3S
22 x3x4x .
opposite girco		 Z3W . X X . W3Z . x4x3x
opposite girco
23   x3w . T T . w3x  
24 S3u . w w . u3S
25 Z3Y . V V . Y3Z
26 u3Y . U U . Y3u
27a x3U . x x . U3x
27b U3x . x x . x3U
28 S3x . W W . x3S
29a Z3W . Z Z . W3Z
29b X3Y . S S . Y3X
29c u3w . T T . w3u
30 V3w . V V . w3V
31 S3u . X X . u3S
32 x3W . U U . W3x
33a V3X . Z Z . X3V
33b W3w . S S . w3W
33c X3x . T T . x3X
34a x3U . u u . U3x
34b U3x . u u . x3U
35a X3V . Z Z . V3X
35b w3W . S S . W3w
35c x3X . T T . X3x
36 W3x . U U . x3W
37 u3S . X X . S3u
38 w3V . V V . V3w
39a W3Z . Z Z . Z3W
39b Y3X . S S . X3Y
39c w3u . T T . u3w
40 x3S . W W . S3x
41a U3x . x x . x3U
41b x3U . x x . U3x
42 Y3u . U U . u3Y
43 Y3Z . V V . Z3Y
44 u3S . w w . S3u
45 w3x . T T . x3w
46 W3Z . X X . Z3W
47a S3u . x x . u3S
47b x3S . Y Y . S3x
48 Y3x . U U . x3Y
49 X3V . w w . V3X
50a V3X . u u . X3V
50b Y3Z . W W . Z3Y
51 x3x . T T . x3x
52a Z3W . x x . W3Z
52b w3V . Y Y . V3w
53 S3x . x x . x3S
54 Y3x . S S . x3Y
55a V3w . u u . w3V
55b Y3X . W W . X3Y
56 x3x . U U . x3x
57a Z3Y . x x . Y3Z
57b w3W . Y Y . W3w
57c Y3u . V V . u3Y
58 W3w . X X . w3W
59 w3x . S S . x3w
60a X3Y . w w . Y3X
60b W3x . Z Z . x3W
61a x3W . Y Y . W3x
61b w3u . V V . u3w
62 x3X . W W . X3x
63a u3Y . w w . Y3u
63b X3x . Z Z . x3X
64 u3w . X X . w3u
65 x3Y . x x . Y3x
66 x3w . u u . w3x
67 x3x . x
opposite hip		 x . x3x
opposite hip
(X=wq=x+w=2x+q, Y=x+2q=w+q, W=2w=2x+2q, Z=3x+q=u+w, V=3x+2q, S=3w=3x+3q, U=4x+3q, T=5x+3q)
Lace city
in approx. ASCII-art 
 ©  

                      x4x   u4x   x4w     x4w   u4x   x4x                      
                                                                               
                  x4u   u4u   x4X             x4X   u4u   x4u                  
                                                                               
              w4x   X4x           x4Z     x4Z           X4x   w4x              
                                                                               
                                                                               
        w4x         Z4x           u4Z     u4Z           Z4x         w4x        
                                                                               
    x4u                 Z4u   X4X             X4X   Z4u                 x4u    
        X4x   Z4x                 x4V     x4V                 Z4x   X4x        
x4x                         V4x   W4w     W4w   V4x                         x4x
    u4u           Z4u         w4W             w4W         Z4u           u4u    
                                                                               
u4x                   V4x         Y4Y     Y4Y         V4x                   u4x
    x4X           X4X   w4W                         w4W   X4X           x4X    
                                                                               
x4w     x4Z   u4Z   # W4w   Y4Y                 Y4Y   # x4V   u4Z   x4Z     x4w
                   (x4V)                             (W4w)                     
                                                                               
                   (x4V)                             (W4w)                     
x4w     x4Z   u4Z   # W4w   Y4Y                 Y4Y   # x4V   u4Z   x4Z     x4w
                                                                               
    x4X           X4X   w4W                         w4W   X4X           x4X    
u4x                   V4x         Y4Y     Y4Y         V4x                   u4x
                                                                               
    u4u           Z4u         w4W             w4W         Z4u           u4u    
x4x                         V4x   W4w     W4w   V4x                         x4x
        X4x   Z4x                 x4V     x4V                 Z4x   X4x        
    x4u                 Z4u   X4X             X4X   Z4u                 x4u    
                                                                               
        w4x         Z4x           u4Z     u4Z           Z4x         w4x        
                                                                               
                                                                               
              w4x   X4x           x4Z     x4Z           X4x   w4x              
                                                                               
                  x4u   u4u   x4X             x4X   u4u   x4u                  
                                                                               
                      x4x   u4x   x4w     x4w   u4x   x4x                      

 ©  

                              x3x   x3w     u3w   # x3X   w3u     w3x   x3x                              
                                                 (X3x)                                                   
                                                                                                         
                     x3x         x3Y     u3Y     x3W W3x     Y3u     Y3x         x3x                     
                                                                                                         
                                                                                                         
                  x3w   x3Y                 X3Y   # w3W   Y3X                 Y3x   w3x                  
                                                 (W3w)                                                   
                                                                                                         
                                                                                                         
              u3w   u3Y                 Z3Y   V3w       w3V   Y3Z                 Y3u   w3u              
                                                                                                         
                                                                                                         
           X3x         X3Y     Z3Y         S3x             x3S         Y3Z     Y3X         x3X           
          x3X   x3W                         Z3W   # X3V   W3Z                         W3x   X3x          
                                                 (V3X)                                                   
              W3x   W3w     V3w   S3x                               x3S   w3V     w3W   x3W              
       w3u         w3W             Z3W         S3u     u3S         W3Z             W3w         u3w       
                                                                                                         
                                                                                                         
          Y3u   Y3X             V3X   S3u                       u3S   X3V             X3Y   u3Y          
   w3x                 w3V     X3V                xU3Ux                V3X     V3w                 x3w   
                                                                                                         
                                                                                                         
x3x   Y3x           Y3Z   # W3Z   u3S    xU3Ux             xU3Ux    S3u   # S3x   Z3Y           x3Y   x3x
                         (x3S)                                           (Z3W)                           
                                                                                                         
                                                                                                         
                                                                                                         
                         (x3S)                                           (Z3W)                           
x3x   Y3x           Y3Z   # W3Z   u3S    xU3Ux             xU3Ux    S3u   # S3x   Z3Y           x3Y   x3x
                                                                                                         
                                                                                                         
   w3x                 w3V     X3V                xU3Ux                V3X     V3w                 x3w   
          Y3u   Y3X             V3X   S3u                       u3S   X3V             X3Y   u3Y          
                                                                                                         
                                                                                                         
       w3u         w3W             Z3W         S3u     u3S         W3Z             W3w         u3w       
              W3x   W3w     V3w   S3x                               x3S   w3V     w3W   x3W              
                                                 (V3X)                                                   
          x3X   x3W                         Z3W   # X3V   W3Z                         W3x   X3x          
           X3x         X3Y     Z3Y         S3x             x3S         Y3Z     Y3X         x3X           
                                                                                                         
                                                                                                         
              u3w   u3Y                 Z3Y   V3w       w3V   Y3Z                 Y3u   w3u              
                                                                                                         
                                                                                                         
                                                 (W3w)                                                   
                  x3w   x3Y                 X3Y   # w3W   Y3X                 Y3x   w3x                  
                                                                                                         
                                                                                                         
                     x3x         x3Y     u3Y     x3W W3x     Y3u     Y3x         x3x                     
                                                                                                         
                                                 (X3x)                                                   
                              x3x   x3w     u3w   # x3X   w3u     w3x   x3x
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: girco hip
gippic 48192
)
Dihedral angles
  • at {4} between hip and hip:   arccos[-sqrt(8)/3] = 160.528779°
  • at {6} between girco and hip:   150°
  • at {4} between girco and hip:   arccos[-sqrt(2/3)] = 144.735610°
  • at {8} between girco and girco:   135°
Face vector 1152, 2304, 1392, 240
Confer
decompositions:
grico || gippic  
general polytopal classes:
Wythoffian polychora  
External
links 		hedrondude   wikipedia   polytopewiki   WikiChoron   quickfur

As abstract polytope gippic is isomorphic to gaquapac, thereby replacing the octagons by octagrams, resp. replacing the girco by quitco.

Note that gippic can be thought of as the external blend of 1 grico + 24 ticagircoes + 96 tricupes + 96 thiddips + 24 gircopes. This decomposition is described as the degenerate segmentoteron ox3xx4xx3xx&#x.


Incidence matrix according to Dynkin symbol

x3x4x3x

. . . . | 1152 |   1   1   1   1 |   1   1   1   1   1   1 |  1  1  1  1
--------+------+-----------------+-------------------------+------------
x . . . |    2 | 576   *   *   * |   1   1   1   0   0   0 |  1  1  1  0
. x . . |    2 |   * 576   *   * |   1   0   0   1   1   0 |  1  1  0  1
. . x . |    2 |   *   * 576   * |   0   1   0   1   0   1 |  1  0  1  1
. . . x |    2 |   *   *   * 576 |   0   0   1   0   1   1 |  0  1  1  1
--------+------+-----------------+-------------------------+------------
x3x . . |    6 |   3   3   0   0 | 192   *   *   *   *   * |  1  1  0  0
x . x . |    4 |   2   0   2   0 |   * 288   *   *   *   * |  1  0  1  0
x . . x |    4 |   2   0   0   2 |   *   * 288   *   *   * |  0  1  1  0
. x4x . |    8 |   0   4   4   0 |   *   *   * 144   *   * |  1  0  0  1
. x . x |    4 |   0   2   0   2 |   *   *   *   * 288   * |  0  1  0  1
. . x3x |    6 |   0   0   3   3 |   *   *   *   *   * 192 |  0  0  1  1
--------+------+-----------------+-------------------------+------------
x3x4x . ♦   48 |  24  24  24   0 |   8  12   0   6   0   0 | 24  *  *  *
x3x . x ♦   12 |   6   6   0   6 |   2   0   3   0   3   0 |  * 96  *  *
x . x3x ♦   12 |   6   0   6   6 |   0   3   3   0   0   2 |  *  * 96  *
. x4x3x ♦   48 |   0  24  24  24 |   0   0   0   6  12   8 |  *  *  * 24

or
. . . .    | 1152 |    2    2 |   2   2   1   1 |  2   2
-----------+------+-----------+-----------------+-------
x . . .  & |    2 | 1152    * |   1   1   1   0 |  1   2
. x . .  & |    2 |    * 1152 |   1   1   0   1 |  2   1
-----------+------+-----------+-----------------+-------
x3x . .  & |    6 |    3    3 | 384   *   *   * |  1   1
x . x .  & |    4 |    2    2 |   * 576   *   * |  1   1
x . . x    |    4 |    4    0 |   *   * 288   * |  0   2
. x4x .    |    8 |    0    8 |   *   *   * 144 |  2   0
-----------+------+-----------+-----------------+-------
x3x4x .  & ♦   48 |   24   48 |   8  12   0   6 | 48   *
x3x . x  & ♦   12 |   12    6 |   2   3   3   0 |  * 192

snubbed forms: β3x4x3x, x3β4x3x, s3s4x3x, β3x4β3x, β3x4x3β, x3β4β3x, β3β4β3x, β3β4x3β, s3s4s3s, s'3s'4s3s


xwX3xxx3wxx4xux&#zxt   → heights = 0, X=Q+x=w+q = 3.828427
(tegum sum of (x,x,w,x)-gidpith, (w,x,x,u)-gidpith, and (X,x,x,x)-gidpith)

o..3o..3o..4o..      | 384   *   * |   1   1   1   1   0   0   0   0   0   0 |  1  1  1  1   1   1  0   0   0  0  0  0 |  1  1  1  1  0 0
.o.3.o.3.o.4.o.      |   * 384   * |   0   0   0   1   1   1   1   0   0   0 |  0  0  0  1   1   1  1   1   1  0  0  0 |  0  1  1  1  1 0
..o3..o3..o4..o      |   *   * 384 |   0   0   0   0   0   0   1   1   1   1 |  0  0  0  0   0   1  0   1   1  1  1  1 |  0  0  1  1  1 1
---------------------+-------------+-----------------------------------------+-----------------------------------------+-----------------
x.. ... ... ...      |   2   0   0 | 192   *   *   *   *   *   *   *   *   * |  1  1  0  1   0   0  0   0   0  0  0  0 |  1  1  1  0  0 0
... x.. ... ...      |   2   0   0 |   * 192   *   *   *   *   *   *   *   * |  1  0  1  0   1   0  0   0   0  0  0  0 |  1  1  0  1  0 0
... ... ... x..      |   2   0   0 |   *   * 192   *   *   *   *   *   *   * |  0  1  1  0   0   1  0   0   0  0  0  0 |  1  0  1  1  0 0
oo.3oo.3oo.4oo.&#x   |   1   1   0 |   *   *   * 384   *   *   *   *   *   * |  0  0  0  1   1   1  0   0   0  0  0  0 |  0  1  1  1  0 0
... .x. ... ...      |   0   2   0 |   *   *   *   * 192   *   *   *   *   * |  0  0  0  0   1   0  1   1   0  0  0  0 |  0  1  0  1  1 0
... ... .x. ...      |   0   2   0 |   *   *   *   *   * 192   *   *   *   * |  0  0  0  1   0   0  1   0   1  0  0  0 |  0  1  1  0  1 0
.oo3.oo3.oo4.oo&#x   |   0   1   1 |   *   *   *   *   *   * 384   *   *   * |  0  0  0  0   0   1  0   1   1  0  0  0 |  0  0  1  1  1 0
... ..x ... ...      |   0   0   2 |   *   *   *   *   *   *   * 192   *   * |  0  0  0  0   0   0  0   1   0  1  1  0 |  0  0  0  1  1 1
... ... ..x ...      |   0   0   2 |   *   *   *   *   *   *   *   * 192   * |  0  0  0  0   0   0  0   0   1  1  0  1 |  0  0  1  0  1 1
... ... ... ..x      |   0   0   2 |   *   *   *   *   *   *   *   *   * 192 |  0  0  0  0   0   1  0   0   0  0  1  1 |  0  0  1  1  0 1
---------------------+-------------+-----------------------------------------+-----------------------------------------+-----------------
x..3x.. ... ...      |   6   0   0 |   3   3   0   0   0   0   0   0   0   0 | 64  *  *  *   *   *  *   *   *  *  *  * |  1  1  0  0  0 0
x.. ... ... x..      |   4   0   0 |   2   0   2   0   0   0   0   0   0   0 |  * 96  *  *   *   *  *   *   *  *  *  * |  1  0  1  0  0 0
... x.. ... x..      |   4   0   0 |   0   2   2   0   0   0   0   0   0   0 |  *  * 96  *   *   *  *   *   *  *  *  * |  1  0  0  1  0 0
xw. ... wx. ...&#zx  |   4   4   0 |   2   0   0   4   0   2   0   0   0   0 |  *  *  * 96   *   *  *   *   *  *  *  * |  0  1  1  0  0 0
... xx. ... ...&#x   |   2   2   0 |   0   1   0   2   1   0   0   0   0   0 |  *  *  *  * 192   *  *   *   *  *  *  * |  0  1  0  1  0 0
... ... ... xux&#xt  |   2   2   2 |   0   0   1   2   0   0   2   0   0   1 |  *  *  *  *   * 192  *   *   *  *  *  * |  0  0  1  1  0 0
... .x.3.x. ...      |   0   6   0 |   0   0   0   0   3   3   0   0   0   0 |  *  *  *  *   *   * 64   *   *  *  *  * |  0  1  0  0  1 0
... .xx ... ...&#x   |   0   2   2 |   0   0   0   0   1   0   2   1   0   0 |  *  *  *  *   *   *  * 192   *  *  *  * |  0  0  0  1  1 0
... ... .xx ...&#x   |   0   2   2 |   0   0   0   0   0   1   2   0   1   0 |  *  *  *  *   *   *  *   * 192  *  *  * |  0  0  1  0  1 0
... ..x3..x ...      |   0   0   6 |   0   0   0   0   0   0   0   3   3   0 |  *  *  *  *   *   *  *   *   * 64  *  * |  0  0  0  0  1 1
... ..x ... ..x      |   0   0   4 |   0   0   0   0   0   0   0   2   0   2 |  *  *  *  *   *   *  *   *   *  * 96  * |  0  0  0  1  0 1
... ... ..x4..x      |   0   0   8 |   0   0   0   0   0   0   0   0   4   4 |  *  *  *  *   *   *  *   *   *  *  * 48 |  0  0  1  0  0 1
---------------------+-------------+-----------------------------------------+-----------------------------------------+-----------------
x..3x.. ... x..      ♦  12   0   0 |   6   6   6   0   0   0   0   0   0   0 |  2  3  3  0   0   0  0   0   0  0  0  0 | 32  *  *  *  * *
xw.3xx.3wx. ...&#zx  ♦  24  24   0 |  12  12   0  24  12  12   0   0   0   0 |  4  0  0  6  12   0  4   0   0  0  0  0 |  * 16  *  *  * *
xwX ... wxx4xux&#zxt ♦  16  16  16 |   8   0   8  16   0   8  16   0   8   8 |  0  4  0  4   0   8  0   0   8  0  0  2 |  *  * 24  *  * *
... xxx ... xux&#xt  ♦   4   4   4 |   0   2   2   4   2   0   4   2   0   2 |  0  0  1  0   2   2  0   2   0  0  1  0 |  *  *  * 96  * *
... .xx3.xx ...&#x   ♦   0   6   6 |   0   0   0   0   3   3   6   3   3   0 |  0  0  0  0   0   0  1   3   3  1  0  0 |  *  *  *  * 64 *
... ..x3..x4..x      ♦   0   0  48 |   0   0   0   0   0   0   0  24  24  24 |  0  0  0  0   0   0  0   0   0  8 12  6 |  *  *  *  *  * 8

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