Acronym rahi
Name rectified hecatonicosachoron
 
Cross sections 
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Circumradius sqrt[(21+9 sqrt(5))/2] = 4.534568
Vertex figure 
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Vertex layers
LayerSymmetrySubsymmetries
 o3o3o5o o3o3o . o3o . o o . o5o . o3o5o
1o3o3x5o o3o3x .
tet first		 o3o . o
vertex first		 o . x5o
{5} first		 . o3x5o
id first
2 o3x3f . x3o . f
vertex figure		 x . o5f . o3o5f
3 o3F3o . F3o . x F . x5x . o3x5x
4 x3f3f . f3x . F f . o5F . x3f5o
5a F3o3F . V3x . o X . f5o . F3o5x
5b o3F . V
6a F3f3x . f3F . F o . o5V . f3f5o
6b V . F5o
6c Y . o5x
7a f3f3F . F3F . x f . x5F . o3F5o
7b X3x3o . f3f . X
8a o3F3V . x3X . f F . F5x . f3x5x
8b V3F3o . Z . f5o
9a f3x3X . Y3o . o x . F5f . x3o5F
9b Z3o3o . f3X . o X . V5o
9c F3o . Y
10a f3F3F . F3V . F o . X5o . F3o5f
10b x3f . Z
11a x3o3Z . Z3o . o F . f5F . V3x5o
11b F3V3x . F3f . Y Z . F5o . o3o5V
12a X3F3o . o3Z . f U . x5x . F3o5f
12b o3x . U
13a F3o3Y . Y3f . x o . V5f . x3o5F
13b x3X3f . V3F . X V . o5X
13c Z3x3o . Y . F5x
14a F3F3F . X3F . F X . f5F . f3x5x
14b o3Z3o .
15 o3o3U . o3F . U U . o5F . o3F5o
16a V3x3X . F3X . V F . f5V . f3f5o
16b Y3f3x . X3x . Y Z . x5F
16c T . o5f
17a X3f3F . Z3x . F x . F5F . F3o5x
17b o3Y3f . x3Z . F
17c F3F . Z
17d o3o . T
18a F3o3Z . o3U . x o . X5x . x3f5o
18b Z3o3F . Z3o . X Y . F5f
18c S . x5o
19a x3o3U . Y3F . f f . x5X . o3x5x
19b F3F3V . x3V . U U . o5V
20a x3X3F . f3Y . X F . F5F . o3o5f
20b Y3f3f .
21a f3x3Z . F3Y . F o . o5Y . o3x5o
opposite id
21b o3Z3x . f3X . Z Y . X5o
21c Y3o . Z S . o5f
21d o3F . T
22a f3F3X . Y3V . o x . Y5o  
22b x3U . o X . V5f
22c U3o . V
22d o3Z . Y
22e o3x . S
23a o3F3Y . X3X . f F . X5x
23b Y3F3o . F3f . U Z . F5f
23c F3V3F . T . o5F
24a X3F3f . F3Z . x f . o5Y
24b U . x5F
25a Z3x3f . Z3F . f V . F5F
25b x3Z3o . X3x . U S . x5x
26a F3X3x . f3Y . Y f . Y5o
26b f3f3Y . x3f . S U . F5x
27a U3o3x . V3Y . F F . x5X
27b V3F3F . U3x . F Z . f5F
27c Z3o . Z T . F5o
27d F3f . T
28a F3o3Z . U3o . X x . o5Y
28b Z3o3F . X . f5V
29a F3f3X . f3U . o o . Y5o
29b f3Y3o . F3o . S Y . o5X
29c S . f5o
30a X3x3V . V3F . U F . F5F
30b x3f3Y .
31a U3o3o . U3f . x f . X5x
31b F3Y . X U . V5o
32a F3F3F . Z3F . F o . x5X
32b o3Z3o . F3X . Z Y . f5F
32c S . o5x
33a Y3o3F . T3o . o x . F5F
33b f3X3x . o3T . o
33c o3x3Z . X3X . V
33d Z3x . Y
33e x3Z . Y
33f f3f . S
34a o3F3X . F3Z . F F . V5f
34b X3F . Z Z . F5x
34c T . f5o
35a Z3o3x . f3U . x U . F5o
35b x3V3F . Y3F . X
36 F3F3f . F3V . U X . F5f
37a X3x3f . U3f . o o . f5V
37b o3o3Z . o3F . S V . X5o
37c Y . x5F
38a o3F3V . o3U . X U . x5x
38b V3F3o .
39a F3f3f . Y3V . F F . F5f
39b o3x3X . x3U . F Z . o5F
39c o3Z . Z
39d f3F . T
40 x3f3F . Y3f . Y o . o5X
40b f3x . S
41a F3o3F . F3Z . f x . f5F
41b x3X . U X . o5V
42a f3f3x . Z3F . x F . x5F
42b Z . o5f
43 o3F3o . X3X . f f . F5x
43b f3F . U
44a o3x3f . V3Y . o o . V5o
44b U3x . o V . o5F
44c o3U . V Y . x5o
44d Z3o . Y
44e x3o . S
45a o3o3x .
opposite tet		 Y3F . F X . o5f
45b X3f . Z
45c o3Y . Z
45d F3o . T
46   Y3f . X f . F5o
47a F3Y . f F . x5x
47b V3x . U
48a U3o . x x . f5o
48b o3Z . X
49a x3Z . F o . o5x
opposite {5}
49b Z3x . F
49c F3F . Z
49d o3o . T
50a X3F . V  
50b x3X . Y
51 F3o . U
52 F3X . F
53a f3Y . x
53b F3V . X
54a Z3o . f
54b x3o . U
55a o3Z . o
55b f3F . Y
56a V3F . F
56b f3x . Z
57a o3Y . o
57b X3f . o
58 X3x . f
59a F3F . x
59b f3f . X
60 F3f . F
61a x3V . o
61b F3o . V
62 x3f . F
63 o3F . x
64 o3x . f
65 o3o . o
opposite vertex
(F=ff=x+f=2x+v, V=F+v=2f=2x+2v, X=fff=F+f=3x+2v, Y=X+x=2F=4x+2v, Z=Y+v=4x+3v, U=FF=5x+3v, T=3F=6x+3v, S=2X=6x+4v)
Lace city
in approx. ASCII-art 
 ©  

                                                                x5o                                                                
                                                        o5f             o5f                                                        
                                                                                                                                   
                                            x5x                                     x5x                                            
                                                    o5F                     o5F                                                    
                                f5o                                                             f5o                                
                        o5x             F5o                     o5V                     F5o             o5x                        
                                                                                                                                   
                                                    x5F                     x5F                                                    
                    f5o                     F5x                                     F5x                     f5o                    
                                                                                                                                   
                                V5o                     F5f             F5f                     V5o                                
                                                                X5o                                                                
                    F5o                     f5F                                     f5F                     F5o                    
            x5x                                                                                                     x5x            
                                                                                                                                   
                        F5x             o5X                     V5f                     o5X             F5x                        
                                f5F                                                             f5F                                
            o5F                                                                                                     o5F            
    o5f             x5F                     f5V                                     f5V                     x5F             o5f    
                                                                                                                                   
                                                        F5F             F5F                                                        
x5o                     F5f                                     X5x                                     F5f                     x5o
                                                                                                                                   
            o5V                                     x5X                      x5X                                    o5V            
                                            F5F                                     F5F                                            
o5f                     X5o                                     o5Y                                     X5o                     o5f
                                V5f                     Y5o             Y5o                     V5f                                
                                                                                                                                   
    o5F             F5f                     X5x                                     X5x                     F5f             o5F    
            x5F                                     o5Y                     o5Y                                     x5F            
                                                                                                                                   
x5x                                     F5F                                             F5F                                     x5x
                                                                                                                                   
            F5x                                     Y5o                     Y5o                                     F5x            
    F5o             f5F                     x5X                                     x5X                     f5F             F5o    
                                                                                                                                   
                                f5V                     o5Y             o5Y                     f5V                                
f5o                     o5X                                     Y5o                                     o5X                     f5o
                                            F5F                                     F5F                                            
            V5o                                     X5x                      X5x                                    V5o            
                                                                                                                                   
o5x                     f5F                                     x5X                                     f5F                     o5x
                                                        F5F             F5F                                                        
                                                                                                                                   
    f5o             F5x                     V5f                                     V5f                     F5x             f5o    
            F5o                                                                                                     F5o            
                                F5f                                                             F5f                                
                        x5F             X5o                     f5V                     X5o             x5F                        
                                                                                                                                   
            x5x                                                                                                     x5x            
                    o5F                     F5f                                     F5f                     o5F                    
                                                                o5X                                                                
                                o5V                     f5F             f5F                     o5V                                
                                                                                                                                   
                    o5f                     x5F                                     x5F                     o5f                    
                                                    F5x                     F5x                                                    
                                                                                                                                   
                        x5o             o5F                     V5o                     o5F             x5o                        
                                o5f                                                             o5f                                
                                                    F5o                     F5o                                                    
                                            x5x                                     x5x                                            
                                                                                                                                   
                                                        f5o             f5o                                                        
                                                                o5x                                                                

 ©  

                                o3x   x3f F3o   f3f   o3F f3x   x3o                                
                                                                                                   
                        o3o   o3F       F3f             f3F       F3o   o3o                        
                                                                                                   
                                                                                                   
                 o3x o3F   x3V   F3F X3x   V3F       F3V   x3X F3F   V3x   F3o x3o                 
                                                                                                   
                                                                                                   
              x3f       F3F  fY3Xo      Z3o   F3X X3F   o3Z      Xo3fY  F3F       f3x              
                                                                                                   
            F3o F3f   X3x       o3Z   f3Y      Zx3xZ      Y3f   Z3o       x3X   f3F o3F            
                                                                                                   
                                                                                                   
         f3f       V3F   Z3o f3Y         U3o F3Y   Y3F o3U         Y3f o3Z   F3V       f3f         
                                                                                                   
                                                                                                   
      o3F             F3X       U3o             X3X             o3U       X3F             F3o      
                                                                                                   
    f3x f3F   F3V   X3F #     F3Y      VU3Yx  Z3F F3Z  Yx3VU      Y3F   #   F3X   V3F   F3f x3f    
                      (Zx3xZ)                                         (Zx3xZ)                      
                                                                                                   
 x3o       x3X   o3Z       Y3F   X3X Z3F                   F3Z X3X   F3Y       Z3o   X3x       o3x 
                                                                                                   
   F3o   F3F       Y3f   o3U       F3Z       U3f   f3U       Z3F       U3o   f3Y       F3F   o3F   
                                                                                                   
                                                                                                   
o3o   V3x   #   Z3o            Yx3VU      f3U  To3oT  U3f      VU3Yx            o3Z #     x3V   o3o
          (Xo3fY)                                                                 (fY3Xo)          
                                                                                                   
   F3o   F3F       Y3f   o3U       F3Z       U3f   f3U       Z3F       U3o   f3Y       F3F   o3F   
                                                                                                   
 x3o       x3X   o3Z       Y3F   X3X Z3F                   F3Z X3X   F3Y       Z3o   X3x       o3x 
                                                                                                   
                      (Zx3xZ)                                         (Zx3xZ)                      
    f3x f3F   F3V   X3F #     F3Y      VU3Yx  Z3F F3Z  Yx3VU      Y3F   #   F3X   V3F   F3f x3f    
                                                                                                   
      o3F             F3X       U3o             X3X             o3U       X3F             F3o      
                                                                                                   
                                                                                                   
         f3f       V3F   Z3o f3Y         U3o F3Y   Y3F o3U         Y3f o3Z   F3V       f3f         
                                                                                                   
                                                                                                   
            F3o F3f   X3x       o3Z   f3Y      Zx3xZ      Y3f   Z3o       x3X   f3F o3F            
                                                                                                   
              x3f       F3F  fY3Xo      Z3o   F3X X3F   o3Z      Xo3fY  F3F       f3x              
                                                                                                   
                                                                                                   
                 o3x o3F   x3V   F3F X3x   V3F       F3V   x3X F3F   V3x   F3o x3o                 
                                                                                                   
                                                                                                   
                        o3o   o3F       F3f             f3F       F3o   o3o                        
                                                                                                   
                                o3x   x3f F3o   f3f   o3F f3x   x3o
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: id tet tid
rahi 1206000
shinhi 1200120
fry 0600120
)
Confer
Grünbaumian relatives:
2rahi   2rahi+2400tet  
related CRFs:
id || f-doe || tid  
External
links 		hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope rahi is isomorphic to rigogishi, thereby replacing pentagons by pentagrams, resp. replacing id by gid.


Incidence matrix according to Dynkin symbol

o3o3x5o

. . . . | 1200 ♦    6 |    6   3 |   2   3
--------+------+------+----------+--------
. . x . |    2 | 3600 |    2   1 |   1   2
--------+------+------+----------+--------
. o3x . |    3 |    3 | 2400   * |   1   1
. . x5o |    5 |    5 |    * 720 |   0   2
--------+------+------+----------+--------
o3o3x . ♦    4 |    6 |    4   0 | 600   *
. o3x5o ♦   30 |   60 |   20  12 |   * 120


o3o3x5/4o

. . .   . | 1200 ♦    6 |    6   3 |   2   3
----------+------+------+----------+--------
. . x   . |    2 | 3600 |    2   1 |   1   2
----------+------+------+----------+--------
. o3x   . |    3 |    3 | 2400   * |   1   1
. . x5/4o |    5 |    5 |    * 720 |   0   2
----------+------+------+----------+--------
o3o3x   . ♦    4 |    6 |    4   0 | 600   *
. o3x5/4o ♦   30 |   60 |   20  12 |   * 120


o3o3/2x5o

. .   . . | 1200 ♦    6 |    6   3 |   2   3
----------+------+------+----------+--------
. .   x . |    2 | 3600 |    2   1 |   1   2
----------+------+------+----------+--------
. o3/2x . |    3 |    3 | 2400   * |   1   1
. .   x5o |    5 |    5 |    * 720 |   0   2
----------+------+------+----------+--------
o3o3/2x . ♦    4 |    6 |    4   0 | 600   *
. o3/2x5o ♦   30 |   60 |   20  12 |   * 120


o3o3/2x5/4o

. .   .   . | 1200 ♦    6 |    6   3 |   2   3
------------+------+------+----------+--------
. .   x   . |    2 | 3600 |    2   1 |   1   2
------------+------+------+----------+--------
. o3/2x   . |    3 |    3 | 2400   * |   1   1
. .   x5/4o |    5 |    5 |    * 720 |   0   2
------------+------+------+----------+--------
o3o3/2x   . ♦    4 |    6 |    4   0 | 600   *
. o3/2x5/4o ♦   30 |   60 |   20  12 |   * 120


o3/2o3x5o

.   . . . | 1200 ♦    6 |    6   3 |   2   3
----------+------+------+----------+--------
.   . x . |    2 | 3600 |    2   1 |   1   2
----------+------+------+----------+--------
.   o3x . |    3 |    3 | 2400   * |   1   1
.   . x5o |    5 |    5 |    * 720 |   0   2
----------+------+------+----------+--------
o3/2o3x . ♦    4 |    6 |    4   0 | 600   *
.   o3x5o ♦   30 |   60 |   20  12 |   * 120


o3/2o3x5/4o

.   . .   . | 1200 ♦    6 |    6   3 |   2   3
------------+------+------+----------+--------
.   . x   . |    2 | 3600 |    2   1 |   1   2
------------+------+------+----------+--------
.   o3x   . |    3 |    3 | 2400   * |   1   1
.   . x5/4o |    5 |    5 |    * 720 |   0   2
------------+------+------+----------+--------
o3/2o3x   . ♦    4 |    6 |    4   0 | 600   *
.   o3x5/4o ♦   30 |   60 |   20  12 |   * 120


o3/2o3/2x5o

.   .   . . | 1200 ♦    6 |    6   3 |   2   3
------------+------+------+----------+--------
.   .   x . |    2 | 3600 |    2   1 |   1   2
------------+------+------+----------+--------
.   o3/2x . |    3 |    3 | 2400   * |   1   1
.   .   x5o |    5 |    5 |    * 720 |   0   2
------------+------+------+----------+--------
o3/2o3/2x . ♦    4 |    6 |    4   0 | 600   *
.   o3/2x5o ♦   30 |   60 |   20  12 |   * 120


o3/2o3/2x5/4o

.   .   .   . | 1200 ♦    6 |    6   3 |   2   3
--------------+------+------+----------+--------
.   .   x   . |    2 | 3600 |    2   1 |   1   2
--------------+------+------+----------+--------
.   o3/2x   . |    3 |    3 | 2400   * |   1   1
.   .   x5/4o |    5 |    5 |    * 720 |   0   2
--------------+------+------+----------+--------
o3/2o3/2x   . ♦    4 |    6 |    4   0 | 600   *
.   o3/2x5/4o ♦   30 |   60 |   20  12 |   * 120

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