Acronym fix, pI Name icosahedral hecatonicosachoron,faceted hexacosichoron,polyicosahedron Cross sections ` ©` Circumradius (1+sqrt(5))/2 = 1.618034 Inradius (3+sqrt(5))/4 = 1.309017 Density 4 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 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 Externallinks

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
```