Acronym gaghi, gapD Name great grand hecatonicosachoron,greatened aggrandized polydodecahedron Cross sections ` ©` Circumradius 1 Inradius (sqrt(5)-1)/4 = 0.309017 Density 76 Coordinates (1, 0, 0, 0)                                         & all permutations, all changes of sign (vertex inscribed q-hex) (1/2, 1/2, 1/2, 1/2)                             & all permutations, all changes of sign (vertex inscribed tes) ((1+sqrt(5))/4, (sqrt(5)-1)/4, 1/4, 0)   & all even permutations, all changes of sign (vertex inscribed v-sadi) General of army ex Colonel of regiment sishi Dual gofix Dihedral angles at {5} between gad and gad:   72° Confer Grünbaumian relatives: gaghi+didhi   gaghi+idhi   gaghi+paphacki+sridaphi   gaghi+sridixhi   2gaghi   2gaghi+2paphacki   sishi+gaghi+idhi   decompositions: pt || gaghi   general polytopal classes: regular   noble polytopes Externallinks

As abstract polytope gaghi is isomorphic to sishi, thereby replacing pentagons by pentagrams, resp. gad by sissid, resp. replacing gissid vertex figures by doe ones. – As such gaghi is a lieutenant.

If considered with according densities, then gaghi can be thought of as the external blend of 120 gadpies. This decomposition is described as the degenerate segmentoteron ox5oo5/2oo3oo&#x.

Incidence matrix according to Dynkin symbol

```x5o5/2o3o

. .   . . | 120 ♦   20 |  30 |  12
----------+-----+------+-----+----
x .   . . |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
x5o   . . |   5 |    5 | 720 |   2
----------+-----+------+-----+----
x5o5/2o . ♦  12 |   30 |  12 | 120
```

```x5o5/2o3/2o

. .   .   . | 120 ♦   20 |  30 |  12
------------+-----+------+-----+----
x .   .   . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5o   .   . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5o5/2o   . ♦  12 |   30 |  12 | 120
```

```x5o5/3o3o

. .   . . | 120 ♦   20 |  30 |  12
----------+-----+------+-----+----
x .   . . |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
x5o   . . |   5 |    5 | 720 |   2
----------+-----+------+-----+----
x5o5/3o . ♦  12 |   30 |  12 | 120
```

```x5o5/3o3/2o

. .   .   . | 120 ♦   20 |  30 |  12
------------+-----+------+-----+----
x .   .   . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5o   .   . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5o5/3o   . ♦  12 |   30 |  12 | 120
```

```x5/4o5/2o3o

.   .   . . | 120 ♦   20 |  30 |  12
------------+-----+------+-----+----
x   .   . . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5/4o   . . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5/4o5/2o . ♦  12 |   30 |  12 | 120
```

```x5/4o5/2o3/2o

.   .   .   . | 120 ♦   20 |  30 |  12
--------------+-----+------+-----+----
x   .   .   . |   2 | 1200 |   3 |   3
--------------+-----+------+-----+----
x5/4o   .   . |   5 |    5 | 720 |   2
--------------+-----+------+-----+----
x5/4o5/2o   . ♦  12 |   30 |  12 | 120
```

```x5/4o5/3o3o

.   .   . . | 120 ♦   20 |  30 |  12
------------+-----+------+-----+----
x   .   . . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5/4o   . . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5/4o5/3o . ♦  12 |   30 |  12 | 120
```

```x5/4o5/3o3/2o

.   .   .   . | 120 ♦   20 |  30 |  12
--------------+-----+------+-----+----
x   .   .   . |   2 | 1200 |   3 |   3
--------------+-----+------+-----+----
x5/4o   .   . |   5 |    5 | 720 |   2
--------------+-----+------+-----+----
x5/4o5/3o   . ♦  12 |   30 |  12 | 120
```

 © 2004-2021 top of page