Acronym srid
TOCID symbol rID
Name small rhombicosidodecahedron,
expanded icosahedron,
expanded dodecahedron

` © ©    ©`
Vertex figure [3,4,5,4] = xf&#q
Vertex layers
 Layer Symmetry Subsymmetries o3o5o o3o . o . o . o5o 1 x3o5x x3o .{3} first x . x{4} first . o5x{5} first 2 x3f . o . F . x5x 3a o3U . F . f . x5f 3b F3x . 4a f3F . A . o . F5o 4b f . V 5 V3x . V . F . o5F 6a x3V . x . B . f5x 6b B . x 7 F3f . F . A . x5x 8a U3o . x . B . x5oopposite {5} 8b x3F . B . x 9 f3x . V . F 10a o3x .opposite {3} A . o 10b f . V 11 F . f 12 o . F 13 x . xopposite {4}
(F=ff=f+x, V=2f, A=F+x=f+u=f+2x, B=V+x=2f+x)
Coordinates
1. 3/2, 1/2, 1/2)         & all permutations, all changes of sign
2. (τ, τ2/2, τ/2)             & even permutations, all changes of sign
3. 2/2, 1+τ/2, 0)        & 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: saddid   sird – other edge facetings)
Dihedral angles
• between {3} and {4}:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
• between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
Confer
Grünbaumian relatives:
2srid
related Johnson solids:
pecu   dirid   gyrid   pabidrid   mabidrid   pagydrid   magydrid   gybadrid   bagydrid   tagyrid   tedrid
facetings:
noble {9,3} modwrap
variations:
a3b5c   q3o5x   f3o5x   v3o5f
External

As abstract polytope srid is isomorphic to qrid, thereby replacing prograde pentagons by retrograde pentagrams.

The right image shows where the rhombi part of its name comes from: in fact it also can be seen as a rectified version of the rhombi-triacontahedron.

Note that srid can be thought of as the external blend of 1 cube + 8 peppies + 12 bilbiros + 6 G3s, cf. the Steward toroid E5 \ 6J91(P4).

Incidence matrix according to Dynkin symbol

```x3o5x

. . . | 60 |  2  2 |  1  2  1
------+----+-------+---------
x . . |  2 | 60  * |  1  1  0
. . x |  2 |  * 60 |  0  1  1
------+----+-------+---------
x3o . |  3 |  3  0 | 20  *  *
x . x |  4 |  2  2 |  * 30  *
. o5x |  5 |  0  5 |  *  * 12

snubbed forms: β3o5x, x3o5β, β3o5β
```

```x5/4o3/2x

.   .   . | 60 |  2  2 |  1  2  1
----------+----+-------+---------
x   .   . |  2 | 60  * |  1  1  0
.   .   x |  2 |  * 60 |  0  1  1
----------+----+-------+---------
x5/4o   . |  5 |  5  0 | 12  *  *
x   .   x |  4 |  2  2 |  * 30  *
.   o3/2x |  3 |  0  3 |  *  * 20
```

```oxxFofxx5xxfoFxxo&#xt   → height(1,2) = height(3,4) = height(5,6) = height(7,8) = sqrt[(5-sqrt(5))/10] = 0.525731
height(2,3) = height(6,7) = sqrt[(5+sqrt(5))/10] = 0.850651
height(4,5) = sqrt[(5-2 sqrt(5))/5] = 0.324920

o.......5o.......     | 5  *  * * *  *  * * | 2  2 0 0  0 0  0  0  0  0 0  0 0 0  0 0 | 1 1 2 0 0 0  0 0 0 0 0 0 0
.o......5.o......     | * 10  * * *  *  * * | 0  1 1 1  1 0  0  0  0  0 0  0 0 0  0 0 | 0 1 1 1 1 0  0 0 0 0 0 0 0
..o.....5..o.....     | *  * 10 * *  *  * * | 0  0 0 0  1 1  1  1  0  0 0  0 0 0  0 0 | 0 0 0 1 1 1  1 0 0 0 0 0 0
...o....5...o....     | *  *  * 5 *  *  * * | 0  0 0 0  0 0  2  0  2  0 0  0 0 0  0 0 | 0 0 0 0 1 0  2 1 0 0 0 0 0
....o...5....o...     | *  *  * * 5  *  * * | 0  0 0 0  0 0  0  2  0  2 0  0 0 0  0 0 | 0 0 0 0 0 1  2 0 1 0 0 0 0
.....o..5.....o..     | *  *  * * * 10  * * | 0  0 0 0  0 0  0  0  1  1 1  1 0 0  0 0 | 0 0 0 0 0 0  1 1 1 1 0 0 0
......o.5......o.     | *  *  * * *  * 10 * | 0  0 0 0  0 0  0  0  0  0 0  1 1 1  1 0 | 0 0 0 0 0 0  0 0 1 1 1 1 0
.......o5.......o     | *  *  * * *  *  * 5 | 0  0 0 0  0 0  0  0  0  0 0  0 0 0  2 2 | 0 0 0 0 0 0  0 0 0 0 2 1 1
----------------------+---------------------+-----------------------------------------+---------------------------
........ x.......     | 2  0  0 0 0  0  0 0 | 5  * * *  * *  *  *  *  * *  * * *  * * | 1 0 1 0 0 0  0 0 0 0 0 0 0
oo......5oo......&#x  | 1  1  0 0 0  0  0 0 | * 10 * *  * *  *  *  *  * *  * * *  * * | 0 1 1 0 0 0  0 0 0 0 0 0 0
.x...... ........     | 0  2  0 0 0  0  0 0 | *  * 5 *  * *  *  *  *  * *  * * *  * * | 0 1 0 1 0 0  0 0 0 0 0 0 0
........ .x......     | 0  2  0 0 0  0  0 0 | *  * * 5  * *  *  *  *  * *  * * *  * * | 0 0 1 0 1 0  0 0 0 0 0 0 0
.oo.....5.oo.....&#x  | 0  1  1 0 0  0  0 0 | *  * * * 10 *  *  *  *  * *  * * *  * * | 0 0 0 1 1 0  0 0 0 0 0 0 0
..x..... ........     | 0  0  2 0 0  0  0 0 | *  * * *  * 5  *  *  *  * *  * * *  * * | 0 0 0 1 0 1  0 0 0 0 0 0 0
..oo....5..oo....&#x  | 0  0  1 1 0  0  0 0 | *  * * *  * * 10  *  *  * *  * * *  * * | 0 0 0 0 1 0  1 0 0 0 0 0 0
..o.o...5..o.o...&#x  | 0  0  1 0 1  0  0 0 | *  * * *  * *  * 10  *  * *  * * *  * * | 0 0 0 0 0 1  1 0 0 0 0 0 0
...o.o..5...o.o..&#x  | 0  0  0 1 0  1  0 0 | *  * * *  * *  *  * 10  * *  * * *  * * | 0 0 0 0 0 0  1 1 0 0 0 0 0
....oo..5....oo..&#x  | 0  0  0 0 1  1  0 0 | *  * * *  * *  *  *  * 10 *  * * *  * * | 0 0 0 0 0 0  1 0 1 0 0 0 0
........ .....x..     | 0  0  0 0 0  2  0 0 | *  * * *  * *  *  *  *  * 5  * * *  * * | 0 0 0 0 0 0  0 1 0 1 0 0 0
.....oo.5.....oo.&#x  | 0  0  0 0 0  1  1 0 | *  * * *  * *  *  *  *  * * 10 * *  * * | 0 0 0 0 0 0  0 0 1 1 0 0 0
......x. ........     | 0  0  0 0 0  0  2 0 | *  * * *  * *  *  *  *  * *  * 5 *  * * | 0 0 0 0 0 0  0 0 1 0 1 0 0
........ ......x.     | 0  0  0 0 0  0  2 0 | *  * * *  * *  *  *  *  * *  * * 5  * * | 0 0 0 0 0 0  0 0 0 1 0 1 0
......oo5......oo&#x  | 0  0  0 0 0  0  1 1 | *  * * *  * *  *  *  *  * *  * * * 10 * | 0 0 0 0 0 0  0 0 0 0 1 1 0
.......x ........     | 0  0  0 0 0  0  0 2 | *  * * *  * *  *  *  *  * *  * * *  * 5 | 0 0 0 0 0 0  0 0 0 0 1 0 1
----------------------+---------------------+-----------------------------------------+---------------------------
o.......5x.......     | 5  0  0 0 0  0  0 0 | 5  0 0 0  0 0  0  0  0  0 0  0 0 0  0 0 | 1 * * * * *  * * * * * * *
ox...... ........&#x  | 1  2  0 0 0  0  0 0 | 0  2 1 0  0 0  0  0  0  0 0  0 0 0  0 0 | * 5 * * * *  * * * * * * *
........ xx......&#x  | 2  2  0 0 0  0  0 0 | 1  2 0 1  0 0  0  0  0  0 0  0 0 0  0 0 | * * 5 * * *  * * * * * * *
.xx..... ........&#x  | 0  2  2 0 0  0  0 0 | 0  0 1 0  2 1  0  0  0  0 0  0 0 0  0 0 | * * * 5 * *  * * * * * * *
........ .xfo....&#xt | 0  2  2 1 0  0  0 0 | 0  0 0 1  2 0  2  0  0  0 0  0 0 0  0 0 | * * * * 5 *  * * * * * * *
..x.o... ........&#x  | 0  0  2 0 1  0  0 0 | 0  0 0 0  0 1  0  2  0  0 0  0 0 0  0 0 | * * * * * 5  * * * * * * *
..oooo..5..oooo..&#xr | 0  0  1 1 1  1  0 0 | 0  0 0 0  0 0  1  1  1  1 0  0 0 0  0 0 | * * * * * * 10 * * * * * *  cycle(BCED)
........ ...o.x..&#x  | 0  0  0 1 0  2  0 0 | 0  0 0 0  0 0  0  0  2  0 1  0 0 0  0 0 | * * * * * *  * 5 * * * * *
....ofx. ........&#xt | 0  0  0 0 1  2  2 0 | 0  0 0 0  0 0  0  0  0  2 0  2 1 0  0 0 | * * * * * *  * * 5 * * * *
........ .....xx.&#x  | 0  0  0 0 0  2  2 0 | 0  0 0 0  0 0  0  0  0  0 1  2 0 1  0 0 | * * * * * *  * * * 5 * * *
......xx ........&#x  | 0  0  0 0 0  0  2 2 | 0  0 0 0  0 0  0  0  0  0 0  0 1 0  2 1 | * * * * * *  * * * * 5 * *
........ ......xo&#x  | 0  0  0 0 0  0  2 1 | 0  0 0 0  0 0  0  0  0  0 0  0 0 1  2 0 | * * * * * *  * * * * * 5 *
.......x5.......o     | 0  0  0 0 0  0  0 5 | 0  0 0 0  0 0  0  0  0  0 0  0 0 0  0 5 | * * * * * *  * * * * * * 1
```
```or
o.......5o.......     & | 10  *  *  * |  2  2  0  0  0  0  0  0 | 1  1  2  0  0  0  0
.o......5.o......     & |  * 20  *  * |  0  1  1  1  1  0  0  0 | 0  1  1  1  1  0  0
..o.....5..o.....     & |  *  * 20  * |  0  0  0  0  1  1  1  1 | 0  0  0  1  1  1  1
...o....5...o....     & |  *  *  * 10 |  0  0  0  0  0  0  2  2 | 0  0  0  0  1  1  2
------------------------+-------------+-------------------------+--------------------
........ x.......     & |  2  0  0  0 | 10  *  *  *  *  *  *  * | 1  0  1  0  0  0  0
oo......5oo......&#x  & |  1  1  0  0 |  * 20  *  *  *  *  *  * | 0  1  1  0  0  0  0
.x...... ........     & |  0  2  0  0 |  *  * 10  *  *  *  *  * | 0  1  0  1  0  0  0
........ .x......     & |  0  2  0  0 |  *  *  * 10  *  *  *  * | 0  0  1  0  1  0  0
.oo.....5.oo.....&#x  & |  0  1  1  0 |  *  *  *  * 20  *  *  * | 0  0  0  1  1  0  0
..x..... ........     & |  0  0  2  0 |  *  *  *  *  * 10  *  * | 0  0  0  1  0  1  0
..oo....5..oo....&#x  & |  0  0  1  1 |  *  *  *  *  *  * 20  * | 0  0  0  0  1  0  1
..o.o...5..o.o...&#x  & |  0  0  1  1 |  *  *  *  *  *  *  * 20 | 0  0  0  0  0  1  1
------------------------+-------------+-------------------------+--------------------
o.......5x.......     & |  5  0  0  0 |  5  0  0  0  0  0  0  0 | 2  *  *  *  *  *  *
ox...... ........&#x  & |  1  2  0  0 |  0  2  1  0  0  0  0  0 | * 10  *  *  *  *  *
........ xx......&#x  & |  2  2  0  0 |  1  2  0  1  0  0  0  0 | *  * 10  *  *  *  *
.xx..... ........&#x  & |  0  2  2  0 |  0  0  1  0  2  1  0  0 | *  *  * 10  *  *  *
........ .xfo....&#xt & |  0  2  2  1 |  0  0  0  1  2  0  2  0 | *  *  *  * 10  *  *
..x.o... ........&#x  & |  0  0  2  1 |  0  0  0  0  0  1  0  2 | *  *  *  *  * 10  *
..oooo..5..oooo..&#xr   |  0  0  2  2 |  0  0  0  0  0  0  2  2 | *  *  *  *  *  * 10  cycle(BCED)
```