Acronym	fix
Name	icosahedral hecatonicosachoron, faceted hexacosichoron
Cross sections	©
Circumradius	(1+sqrt(5))/2 = 1.618034
Inradius	(3+sqrt(5))/4 = 1.309017
Coordinates	(τ, 0, 0, 0)             & all permutations, all changes of sign (vertex inscribed f/q-hex) (τ/2, τ/2, τ/2, τ/2)   & all permutations, all changes of sign (vertex inscribed f-tes) (τ2/2, 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
Confer	Grünbaumian relatives: ex+fix   2fix   fix+gahi+120id   general polytopal classes: regular
External links

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.

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