Acronym id
TOCID symbol ID
Name icosidodecahedron

` © ©`
Vertex figure [(3,5)2] = x f
Vertex layers
 Layer Symmetry Subsymmetries o3o5o o3o . o . o . o5o 1 o3x5o o3x .{3} first o . overtex first . x5o{5} first 2 x3f . x . fvertex figure . o5f 3 F3o . F . x . x5x 4 f3f . f . F . f5o 5a o3F . o . X . o5xopposite {5} 5b X . o 6 f3x . f . F 7 x3o .opposite {3} F . x 8 x . f 9 o . oopposite vertex
(F=ff=x+f=2x+v=x(10,3), X=F+v=2f=2x+2v=x(10,5))
Coordinates
1. (τ, 0, 0)   & all permutations, all changes of sign
(vertex inscribed fq-oct)
2. 2/2, τ/2, 1/2)   & even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army (is itself convex)
Colonel of regiment (is itself locally convex – other uniform polyhedral members: sidhid   seihid – other edge facetings)
Dual rhote
Confer
Grünbaumian relatives:
2id   2id+40{3}   id+seihid+sidhid
related Johnson solids:
pero   pobro   epgybro
External

As abstract polytope id is isomorphic to gid, thereby replacing pentagons by pentagrams.

Incidence matrix according to Dynkin symbol

```o3x5o

. . . | 30 |  4 |  2  2
------+----+----+------
. x . |  2 | 60 |  1  1
------+----+----+------
o3x . |  3 |  3 | 20  *
. x5o |  5 |  5 |  * 12
```

```o3/2x5o

.   . . | 30 |  4 |  2  2
--------+----+----+------
.   x . |  2 | 60 |  1  1
--------+----+----+------
o3/2x . |  3 |  3 | 20  *
.   x5o |  5 |  5 |  * 12
```

```o5/4x3o

.   . . | 30 |  4 |  2  2
--------+----+----+------
.   x . |  2 | 60 |  1  1
--------+----+----+------
o5/4x . |  5 |  5 | 12  *
.   x3o |  3 |  3 |  * 20
```

```o5/4x3/2o

.   .   . | 30 |  4 |  2  2
----------+----+----+------
.   x   . |  2 | 60 |  1  1
----------+----+----+------
o5/4x   . |  5 |  5 | 12  *
.   x3/2o |  3 |  3 |  * 20
```

```xoxfo5ofxox&#xt   → outer heights = sqrt[(5-sqrt(5))/10] = 0.525731
inner heights = sqrt[(5+sqrt(5))/10] = 0.850651
({5} || pseudo dual f-{5} || pseudo {10} || pseudo f-{5} || dual {5})

o....5o....     | 5 *  * * * | 2  2  0 0 0  0  0 0 | 1 2 1 0 0 0 0 0
.o...5.o...     | * 5  * * * | 0  2  2 0 0  0  0 0 | 0 1 2 1 0 0 0 0
..o..5..o..     | * * 10 * * | 0  0  1 1 1  1  0 0 | 0 0 1 1 1 1 0 0
...o.5...o.     | * *  * 5 * | 0  0  0 0 0  2  2 0 | 0 0 0 0 2 1 1 0
....o5....o     | * *  * * 5 | 0  0  0 0 0  0  2 2 | 0 0 0 0 1 0 2 1
----------------+------------+---------------------+----------------
x.... .....     | 2 0  0 0 0 | 5  *  * * *  *  * * | 1 1 0 0 0 0 0 0
oo...5oo...&#x  | 1 1  0 0 0 | * 10  * * *  *  * * | 0 1 1 0 0 0 0 0
.oo..5.oo..&#x  | 0 1  1 0 0 | *  * 10 * *  *  * * | 0 0 1 1 0 0 0 0
..x.. .....     | 0 0  2 0 0 | *  *  * 5 *  *  * * | 0 0 0 1 1 0 0 0
..... ..x..     | 0 0  2 0 0 | *  *  * * 5  *  * * | 0 0 1 0 0 1 0 0
..oo.5..oo.&#x  | 0 0  1 1 0 | *  *  * * * 10  * * | 0 0 0 0 1 1 0 0
...oo5...oo&#x  | 0 0  0 1 1 | *  *  * * *  * 10 * | 0 0 0 0 1 0 1 0
..... ....x     | 0 0  0 0 2 | *  *  * * *  *  * 5 | 0 0 0 0 0 0 1 1
----------------+------------+---------------------+----------------
x....5o....     | 5 0  0 0 0 | 5  0  0 0 0  0  0 0 | 1 * * * * * * *
xo... .....&#x  | 2 1  0 0 0 | 1  2  0 0 0  0  0 0 | * 5 * * * * * *
..... ofx..&#xt | 1 2  2 0 0 | 0  2  2 0 1  0  0 0 | * * 5 * * * * *
.ox.. .....&#x  | 0 1  2 0 0 | 0  0  2 1 0  0  0 0 | * * * 5 * * * *
..xfo .....&#xt | 0 0  2 2 1 | 0  0  0 1 0  2  2 0 | * * * * 5 * * *
..... ..xo.&#x  | 0 0  2 1 0 | 0  0  0 0 1  2  0 0 | * * * * * 5 * *
..... ...ox&#x  | 0 0  0 1 2 | 0  0  0 0 0  0  2 1 | * * * * * * 5 *
....o5....x     | 0 0  0 0 5 | 0  0  0 0 0  0  0 5 | * * * * * * * 1

or
o....5o....      & | 10  *  * |  2  2  0  0 | 1  2  1  0
.o...5.o...      & |  * 10  * |  0  2  2  0 | 0  1  2  1
..o..5..o..        |  *  * 10 |  0  0  2  2 | 0  0  2  2
-------------------+----------+-------------+-----------
x.... .....      & |  2  0  0 | 10  *  *  * | 1  1  0  0
oo...5oo...&#x   & |  1  1  0 |  * 20  *  * | 0  1  1  0
.oo..5.oo..&#x   & |  0  1  1 |  *  * 20  * | 0  0  1  1
..x.. .....      & |  0  0  2 |  *  *  * 10 | 0  0  1  1
-------------------+----------+-------------+-----------
x....5o....      & |  5  0  0 |  5  0  0  0 | 2  *  *  *
xo... .....&#x   & |  2  1  0 |  1  2  0  0 | * 10  *  *
..... ofx..&#xt  & |  1  2  2 |  0  2  2  1 | *  * 10  *
.ox.. .....&#x   & |  0  1  2 |  0  0  2  1 | *  *  * 10
```