Acronym gahi
Name grand hecatonicosachoron
Cross sections
 ©
Circumradius (1+sqrt(5))/2 = 1.618034
Inradius (1+sqrt(5))/4 = 0.809017
Coordinates
  1. (τ, 0, 0, 0)             & all permutations, all changes of sign
    (vertex inscribed f/q-hex)
  2. (τ/2, τ/2, τ/2, τ/2)   & all permutations, all changes of sign
    (vertex inscribed f-tes)
  3. 2/2, τ/2, 1/2, 0)   & even permutations, all changes of sign
    (vertex inscribed sadi)
where τ = (1+sqrt(5))/2 (a. and b. together define a vertex inscribed f-ico)
General of army ex
Colonel of regiment ex
Dual gishi
Dihedral angles
  • at {5} between doe and doe:   72°
Confer
Grünbaumian relatives:
fix+gahi+120id   gahi+gohi   2gahi  
general polytopal classes:
regular   noble polytopes  
External
links
hedrondude   wikipedia   WikiChoron   nan ma

As abstract polytope gahi is isomorphic to gishi, thereby replacing doe by gissid, resp. replacing pentagonal faces by pentagrammal ones, resp. replacing pentagrammal edge figures each by pentagonal ones, resp. replacing gike vertex figures by ike ones. – As such gahi is a lieutenant.


Incidence matrix according to Dynkin symbol

x5o3o5/2o

. . .   . | 120   12 |  30 |  20
----------+-----+-----+-----+----
x . .   . |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
x5o .   . |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
x5o3o   .   20 |  30 |  12 | 120

x5o3o5/3o

. . .   . | 120   12 |  30 |  20
----------+-----+-----+-----+----
x . .   . |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
x5o .   . |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
x5o3o   .   20 |  30 |  12 | 120

x5o3/2o5/2o

. .   .   . | 120   12 |  30 |  20
------------+-----+-----+-----+----
x .   .   . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5o   .   . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5o3/2o   .   20 |  30 |  12 | 120

x5o3/2o5/3o

. .   .   . | 120   12 |  30 |  20
------------+-----+-----+-----+----
x .   .   . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5o   .   . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5o3/2o   .   20 |  30 |  12 | 120

x5/4o3o5/2o

.   . .   . | 120   12 |  30 |  20
------------+-----+-----+-----+----
x   . .   . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5/4o .   . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5/4o3o   .   20 |  30 |  12 | 120

x5/4o3o5/3o

.   . .   . | 120   12 |  30 |  20
------------+-----+-----+-----+----
x   . .   . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5/4o .   . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5/4o3o   .   20 |  30 |  12 | 120

x5/4o3/2o5/2o

.   .   .   . | 120   12 |  30 |  20
--------------+-----+-----+-----+----
x   .   .   . |   2 | 720 |   5 |   5
--------------+-----+-----+-----+----
x5/4o   .   . |   5 |   5 | 720 |   2
--------------+-----+-----+-----+----
x5/4o3/2o   .   20 |  30 |  12 | 120

x5/4o3/2o5/3o

.   .   .   . | 120   12 |  30 |  20
--------------+-----+-----+-----+----
x   .   .   . |   2 | 720 |   5 |   5
--------------+-----+-----+-----+----
x5/4o   .   . |   5 |   5 | 720 |   2
--------------+-----+-----+-----+----
x5/4o3/2o   .   20 |  30 |  12 | 120

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