Acronym hi
Name hecatonicosachoron,
120-cell,
dodecacontachoron,
cosmochoron
 
Cross sections 
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Circumradius sqrt[7+3 sqrt(5)] = 3.702459
Inradius (7+3 sqrt(5))/4 = 3.427051
Vertex figure 
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Vertex layers
LayerSymmetrySubsymmetries
 o3o3o5o o3o3o . o3o . o o . o5o . o3o5o
1o3o3o5x o3o3o .
vertex first		 o3o . x
edge first		 o . o5x
{5} first		 . o3o5x
doe first
2 o3o3f .
vertex figure		 o3f . f f . o5f . o3o5f
3 o3f3x . o3F . o F . f5o . o3f5o
4a f3x3f . f3x . F x . o5F . f3x5o
4b X . x5o
5 F3f3o . f3F . o F . F5o . x3f5o
6 x3f3F . F3f . f f . f5f . f3o5f
7a f3o3X . X3o . x o . F5x . o3o5F
7b F3F3o . x3f . X Y . f5o
8a o3o3Y . x3X . o X . F5o . F3o5x
8b Y3o3o . f3o . Y
8c f3F3f .
9a o3X3x . F3F . F F . x5F . o3o5F
9b X3f3o . o3o . Z Z . o5f
10a F3o3X . f3F . X f . f5F . f3o5f
10b U . o5x
11a F3f3F . f3X . f o . X5o . x3f5o
11b Y3o . f
12a o3o3Z . o3X . X x . o5X . f3x5o
12b X3x3f . X . F5x
13a f3o3Y . X3f . F f . X5o . o3f5o
13b o3X3f . o3Y . F U . o5f
13c F3o . Z
14a f3F3F . Z3o . o Y . f5f . o3o5f
14b F3f . Y
15a o3Y3o . o3o . U f . o5X . o3o5x
opposite doe
15b x3f3X . U . f5o
15c X3f3x .
16a F3F3f . F3X . x x . X5o  
16b X3x . X X . x5F
17a Y3o3f . X3F . f o . o5X
17b f3X3o . f3o . U
18a Z3o3o . Y3f . o f . F5f
18b f3x3X . o3X . Y U . x5o
19a F3f3F . o3Z . F F . F5x
19b f3F . Z Z . f5o
20a X3o3F . f3Y . f X . o5F
20b x3f . U
21a x3X3o . X3f . X o . x5F
21b o3f3X . o3Y . X Y . o5f
22a o3o3Y . X3F . F f . f5f
22b Y3o3o .
22c f3F3f .
23a X3o3f . x3Z . o F . o5F
23b o3F3F . Z3x . o
23c F3F . Y
24a F3f3x . F3X . F x . F5o
24b X . o5x
25a o3f3F . f3X . X F . o5f
25b Y3o . X
26a f3x3f . Y3f . f f . f5o
26b f3x . U
27a x3f3o . Z3o . F o . x5o
opposite {5}
27b F3f . Z
28a f3o3o . f3Y . o  
28b X3o . Y
29a o3o3o .
opposite vertex		 F3X . f
29b o3f . U
30a   X3F . x
30b x3X . X
31 o3o . U
32a o3Z . o
32b f3F . Y
33a f3X . F
33b Y3o . F
33c o3F . Z
34 X3o . X
35a X3f . f
35b o3Y . f
36 F3f . X
37a F3F . F
37b o3o . Z
38a X3x . o
38b o3f . Y
39a o3X . x
39b f3x . X
40 f3F . f
41 F3f . o
42 x3f . F
43 F3o . o
44 f3o . f
45 o3o . x
opposite edge
(F=ff=x+f=2x+v, X=fff=F+f=3x+2v, Y=X+x=2F=4x+2v, Z=Y+v=4x+3v, U=FF=5x+3v)
Lace city
in approx. ASCII-art 
 ©  

                                                  o5x                                                  
                                      o5f                     o5f                                      
                               f5o                                   f5o                               
                                                                                                       
                   x5o                     o5F           o5F                     x5o                   
                                                                                                       
                               F5o                                   F5o                               
                                      f5f                     f5f                                      
                                                                                                       
            f5o                                   F5x                                   f5o            
                   F5o                                                           F5o                   
                                                                                                       
       o5f                     x5F                                   x5F                     o5f       
                                                                                                       
                   f5f                                                           f5f                   
            o5F                                   F5f                                   o5F            
                                                                                                       
o5x                                   f5F                     f5F                                   o5x
                                                                                                       
                                                  X5o                                                  
                   F5x                     o5X           o5X                     F5x                   
                                                                                                       
       o5F                     F5f                                   F5f                     o5F       
o5f                                   X5o                     X5o                                   o5f
                                                                                                       
            f5f                                                                         f5f            
                                                                                                       
f5o                                   o5X                     o5X                                   f5o
       F5o                     f5F                                   f5F                     F5o       
                                                                                                       
                   x5F                     X5o           X5o                     x5F                   
                                                  o5X                                                  
                                                                                                       
x5o                                   F5f                     F5f                                   x5o
                                                                                                       
            F5o                                   f5F                                   F5o            
                   f5f                                                           f5f                   
                                                                                                       
       f5o                     F5x                                   F5x                     f5o       
                                                                                                       
                   o5F                                                           o5F                   
            o5f                                   x5F                                   o5f            
                                                                                                       
                                      f5f                     f5f                                      
                               o5F                                   o5F                               
                                                                                                       
                   o5x                     F5o           F5o                     o5x                   
                                                                                                       
                               o5f                                   o5f                               
                                      f5o                     f5o                                      
                                                  x5o                                                  

 ©  

                        o3o o3f   f3x       x3f   f3o o3o                        
                                                                                 
                                                                                 
               o3o   o3F       F3f             f3F       F3o   o3o               
                                                                                 
             o3f       f3F   X3o       F3F       o3X   F3f       f3o             
                                                                                 
                                                                                 
          f3x   F3f X3o   x3X      fY3Xo Xo3fY      X3x   o3X f3F   x3f          
                                                                                 
                                                                                 
                                                                                 
                                                                                 
     x3f       F3F  fY3Xo      Z3o   F3X X3F   o3Z      Xo3fY  F3F       f3x     
                                                                                 
                                                                                 
  f3o   f3F      Xo3fY      F3X   Y3f       f3Y   X3F      fY3Xo      F3f   o3f  
                                                                                 
o3o       o3X             X3F                       F3X             X3o       o3o
                                                                                 
                                                                                 
   F3o F3f   X3x       o3Z   f3Y      xZ3Zx      Y3f   Z3o       x3X   f3F o3F   
                                                                                 
                                                                                 
o3o       o3X             X3F                       F3X             X3o       o3o
                                                                                 
  f3o   f3F      Xo3fY      F3X   Y3f       f3Y   X3F      fY3Xo      F3f   o3f  
                                                                                 
                                                                                 
     x3f       F3F  fY3Xo      Z3o   F3X X3F   o3Z      Xo3fY  F3F       f3x     
                                                                                 
                                                                                 
                                                                                 
                                                                                 
          f3x   F3f X3o   x3X      fY3Xo Xo3fY      X3x   o3X f3F   x3f          
                                                                                 
                                                                                 
             o3f       f3F   X3o       F3F       o3X   F3f       f3o             
                                                                                 
               o3o   o3F       F3f             f3F       F3o   o3o               
                                                                                 
                                                                                 
                        o3o o3f   f3x       x3f   f3o o3o
Coordinates
  1. (τ2, τ2, 0, 0)                           all permutations, all changes of sign
  2. (sqrt(5) τ2/2, τ2/2, τ2/2, τ2/2) all permutations, all changes of sign
  3. (τ3/2, τ3/2, τ3/2, 1/2)              all permutations, all changes of sign
  4. (τ4/2, τ/2, τ/2, τ/2)                  all permutations, all changes of sign
  5. (τ4/2, τ2/2, 1/2, 0)                  all even permutations, all changes of sign
  6. (τ3/2, sqrt(5) τ2/2, 0, τ/2)      all even permutations, all changes of sign
  7. (τ3/2, τ2/2, τ2, τ/2)                  all even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: doe
hi 120
)
Dual ex
Confer
Grünbaumian relatives:
2hi  
general polytopal classes:
regular  
External
links 		hedrondude   wikipedia   WikiChoron   mathworld   quickfur

As abstract polytope hi is isomorphic to gogishi, thereby replacing pentagons by pentagrams resp. replacing doe by gissid.

The 120 does could be divided into 12 cycles of 10. Any 2 of those stacked does are separated by special pentagons with a-type edges only. All non-polar pentagons of each doe belong to a second class. There will be a chiral subset of 5 tropal edges of each doe, which is of that type too, then. I.e. at that tropal edge there will be incident, as third pentagon, one such cycle dividing one again. That is, the non-polar pentagons would have the edge sequence a-b-a-b-b. Further it will turn out that those cycle dividing pentagons are completely separated from each other, i.e. there is incident just one such pentagon at any vertex of hi.


Incidence matrix according to Dynkin symbol

o3o3o5x

. . . . | 600 ♦    4 |   6 |   4
--------+-----+------+-----+----
. . . x |   2 | 1200 |   3 |   3
--------+-----+------+-----+----
. . o5x |   5 |    5 | 720 |   2
--------+-----+------+-----+----
. o3o5x ♦  20 |   30 |  12 | 120


o3o3o5/4x

. . .   . | 600 ♦    4 |   6 |   4
----------+-----+------+-----+----
. . .   x |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
. . o5/4x |   5 |    5 | 720 |   2
----------+-----+------+-----+----
. o3o5/4x ♦  20 |   30 |  12 | 120


o3o3/2o5x

. .   . . | 600 ♦    4 |   6 |   4
----------+-----+------+-----+----
. .   . x |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
. .   o5x |   5 |    5 | 720 |   2
----------+-----+------+-----+----
. o3/2o5x ♦  20 |   30 |  12 | 120


o3o3/2o5/4x

. .   .   . | 600 ♦    4 |   6 |   4
------------+-----+------+-----+----
. .   .   x |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
. .   o5/4x |   5 |    5 | 720 |   2
------------+-----+------+-----+----
. o3/2o5/4x ♦  20 |   30 |  12 | 120


o3/2o3o5x

.   . . . | 600 ♦    4 |   6 |   4
----------+-----+------+-----+----
.   . . x |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
.   . o5x |   5 |    5 | 720 |   2
----------+-----+------+-----+----
.   o3o5x ♦  20 |   30 |  12 | 120


o3/2o3o5/4x

.   . .   . | 600 ♦    4 |   6 |   4
------------+-----+------+-----+----
.   . .   x |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
.   . o5/4x |   5 |    5 | 720 |   2
------------+-----+------+-----+----
.   o3o5/4x ♦  20 |   30 |  12 | 120


o3/2o3/2o5x

.   .   . . | 600 ♦    4 |   6 |   4
------------+-----+------+-----+----
.   .   . x |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
.   .   o5x |   5 |    5 | 720 |   2
------------+-----+------+-----+----
.   o3/2o5x ♦  20 |   30 |  12 | 120


o3/2o3/2o5/4x

.   .   .   . | 600 ♦    4 |   6 |   4
--------------+-----+------+-----+----
.   .   .   x |   2 | 1200 |   3 |   3
--------------+-----+------+-----+----
.   .   o5/4x |   5 |    5 | 720 |   2
--------------+-----+------+-----+----
.   o3/2o5/4x ♦  20 |   30 |  12 | 120


acc. to swirl subsymmetry:

600 |   2   2 |   1   5 |   4
----+---------+---------+----
  2 | 600   * |   1   2 |   3  a
  2 |   * 600 |   0   3 |   3  b
----+---------+---------+----
  5 |   5   0 | 120   * |   2  aaaaa
  5 |   2   3 |   * 600 |   2  ababb
----+---------+---------+----
 20 |  15  15 |   2  10 | 120

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