Acronym gahi, apD Name grand hecatonicosachoron,aggrandized polydodecahedron Cross sections ` ©` Circumradius (1+sqrt(5))/2 = 1.618034 Inradius (1+sqrt(5))/4 = 0.809017 Density 20 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 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 Externallinks

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

snubbed forms: β5o3o5/2o
```

```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
```