Acronym fix
Name icosahedral hecatonicosachoron,
faceted hexacosichoron
Cross sections
 ©
Circumradius (1+sqrt(5))/2 = 1.618034
Inradius (3+sqrt(5))/4 = 1.309017
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 sishi
Dihedral angles
  • at {3} between ike and ike:   120°
Confer
Grünbaumian relatives:
ex+fix   2ex+fix   3ex+fix   3ex+2fix+gaghi   fix+gahi+120id   2fix  
decompositions:
sishi || fix  
general polytopal classes:
regular   noble polytopes  
External
links
hedrondude   wikipedia   WikiChoron  

As abstract polytope fix is isomorphic to gofix, thereby replacing ike by gike, resp. replacing pentagrammal edge figures by pentagonal ones, resp. replacing gad vertex figures by sissid ones.

If considered with according densities, then fix can be thought of as the external blend of 1 sishi + 120 sissidpies + 720 stascs + 1200 pens + 120 ikepies. This decomposition is described as the degenerate segmentoteron xo5/2oo5oo3ox&#x.


Incidence matrix according to Dynkin symbol

x3o5o5/2o

. . .   . | 120   12 |   30 |  12
----------+-----+-----+------+----
x . .   . |   2 | 720 |    5 |   5
----------+-----+-----+------+----
x3o .   . |   3 |   3 | 1200 |   2
----------+-----+-----+------+----
x3o5o   .   12 |  30 |   20 | 120

x3o5o5/3o

. . .   . | 120   12 |   30 |  12
----------+-----+-----+------+----
x . .   . |   2 | 720 |    5 |   5
----------+-----+-----+------+----
x3o .   . |   3 |   3 | 1200 |   2
----------+-----+-----+------+----
x3o5o   .   12 |  30 |   20 | 120

x3o5/4o5/2o

. .   .   . | 120   12 |   30 |  12
------------+-----+-----+------+----
x .   .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3o   .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3o5/4o   .   12 |  30 |   20 | 120

x3o5/4o5/3o

. .   .   . | 120   12 |   30 |  12
------------+-----+-----+------+----
x .   .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3o   .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3o5/4o   .   12 |  30 |   20 | 120

x3/2o5o5/2o

.   . .   . | 120   12 |   30 |  12
------------+-----+-----+------+----
x   . .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3/2o .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3/2o5o   .   12 |  30 |   20 | 120

x3/2o5o5/3o

.   . .   . | 120   12 |   30 |  12
------------+-----+-----+------+----
x   . .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3/2o .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3/2o5o   .   12 |  30 |   20 | 120

x3/2o5/4o5/2o

.   .   .   . | 120   12 |   30 |  12
--------------+-----+-----+------+----
x   .   .   . |   2 | 720 |    5 |   5
--------------+-----+-----+------+----
x3/2o   .   . |   3 |   3 | 1200 |   2
--------------+-----+-----+------+----
x3/2o5/4o   .   12 |  30 |   20 | 120

x3/2o5/4o5/3o

.   .   .   . | 120   12 |   30 |  12
--------------+-----+-----+------+----
x   .   .   . |   2 | 720 |    5 |   5
--------------+-----+-----+------+----
x3/2o   .   . |   3 |   3 | 1200 |   2
--------------+-----+-----+------+----
x3/2o5/4o   .   12 |  30 |   20 | 120

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