Acronym gohi, gpD
Name great hecatonicosachoron,
greatened polydodecahedron
Cross sections
 ©
Circumradius (1+sqrt(5))/2 = 1.618034
Inradius (3+sqrt(5))/4 = 1.309017
Density 6
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 (selfdual)
Dihedral angles
  • at {5} between gad and gad:   144°
Confer
Grünbaumian relatives:
gahi+gohi   ex+gohi+120id   2gohi  
related segmentochora:
sissidpy  
general polytopal classes:
regular   noble polytopes  
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   nan ma

As abstract polytope gohi is isomorphic to gashi, thereby replacing gad by sissid, resp. replacing pentagonal faces and edge figures each by pentagrammal ones, resp. replacing sissid vertex figures by gad ones.

Its vertex pyramid is an f-scaled sissidpy.


Incidence matrix according to Dynkin symbol

x5o5/2o5o

. .   . . | 120   12 |  30 |  12
----------+-----+-----+-----+----
x .   . . |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
x5o   . . |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
x5o5/2o .   12 |  30 |  12 | 120

snubbed forms: β5o5/2o5o

x5o5/2o5/4o

. .   .   . | 120   12 |  30 |  12
------------+-----+-----+-----+----
x .   .   . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5o   .   . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5o5/2o   .   12 |  30 |  12 | 120

x5o5/3o5o

. .   . . | 120   12 |  30 |  12
----------+-----+-----+-----+----
x .   . . |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
x5o   . . |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
x5o5/3o .   12 |  30 |  12 | 120

x5o5/3o5/4o

. .   .   . | 120   12 |  30 |  12
------------+-----+-----+-----+----
x .   .   . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5o   .   . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5o5/3o   .   12 |  30 |  12 | 120

x5/4o5/2o5o

.   .   . . | 120   12 |  30 |  12
------------+-----+-----+-----+----
x   .   . . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5/4o   . . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5/4o5/2o .   12 |  30 |  12 | 120

x5/4o5/2o5/4o

.   .   .   . | 120   12 |  30 |  12
--------------+-----+-----+-----+----
x   .   .   . |   2 | 720 |   5 |   5
--------------+-----+-----+-----+----
x5/4o   .   . |   5 |   5 | 720 |   2
--------------+-----+-----+-----+----
x5/4o5/2o   .   12 |  30 |  12 | 120

x5/4o5/3o5o

.   .   . . | 120   12 |  30 |  12
------------+-----+-----+-----+----
x   .   . . |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
x5/4o   . . |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
x5/4o5/3o .   12 |  30 |  12 | 120

x5/4o5/3o5/4o

.   .   .   . | 120   12 |  30 |  12
--------------+-----+-----+-----+----
x   .   .   . |   2 | 720 |   5 |   5
--------------+-----+-----+-----+----
x5/4o   .   . |   5 |   5 | 720 |   2
--------------+-----+-----+-----+----
x5/4o5/3o   .   12 |  30 |  12 | 120

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