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 (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 (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 Externallinks

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
```