Acronym sirsid TOCID symbol s*IID* Name small (inverted) retrosnub icosicosidodecahedron,retrosnub disicosidodecahedron,yog sothoth ` © ©` Circumradius sqrt[13+3 sqrt(5)-sqrt[102+46 sqrt(5)]]/4 = 0.580695 Coordinates ([-1/τ-sqrt(3τ-2)]/4, 0, [3-τ sqrt(3τ-2)]/4)         & even permutations, all changes of sign ([1/τ-sqrt(3τ-2)]/4, 1, [1+2/τ-τ sqrt(3τ-2)]/4)   & even permutations, all changes of sign ([τ2-sqrt(3τ-2)]/4, 1/2τ, [1-τ sqrt(3τ-2)]/4)       & even permutations, all changes of sign where τ = (1+sqrt(5))/2 Vertex figure [3/2,3,3/2,3,5/2,3] Colonel of regiment (is itself not locally convex, but no other uniform polyhedral members) Externallinks

As abstract polytope sirsid is isomorphic to seside, thereby replacing retrograde icosahedral triangles by prograde ones. – As such sirsid is a lieutenant.

As mere alternated faceting the 2{3}-compound is regular, for sure. It is by the afterwards to be applied step back to equally sized edges that those compounds become non-regular.

Incidence matrix according to Dynkin symbol

```s3/2s3/2s5/2*a

demi( .   .   .      ) | 60 |  2  2  2 |  1  1  1  3
-----------------------+----+----------+------------
sefa( s3/2s   .      ) |  2 | 60  *  * |  1  0  0  1
sefa( s   .   s5/2*a ) |  2 |  * 60  * |  0  1  0  1
sefa( .   s3/2s      ) |  2 |  *  * 60 |  0  0  1  1
-----------------------+----+----------+------------
s3/2s   .        ♦  3 |  3  0  0 | 20  *  *  *
s   .   s5/2*a   ♦  5 |  0  5  0 |  * 12  *  *
.   s3/2s        ♦  3 |  0  0  3 |  *  * 20  *
sefa( s3/2s3/2s5/2*a ) |  3 |  1  1  1 |  *  *  * 60
```

```β3/2β5o

both( .   . . ) | 60 |   4  2 |  2  1  3
----------------+----+--------+---------
sefa( s3/2s . ) |  2 | 120  * |  1  0  1
sefa( .   β5o ) |  2 |   * 60 |  0  1  1
----------------+----+--------+---------
both( s3/2s . ) ♦  3 |   3  0 | 40  *  *  as coplanar pair of {3}
.   β5o   ♦  5 |   0  5 |  * 12  *
sefa( β3/2β5o ) |  3 |   2  1 |  *  * 60

or
both( .   . . ) | 60 |   4  2 |  2  1  3
----------------+----+--------+---------
sefa( s3/2s . ) |  2 | 120  * |  1  0  1
sefa( .   β5o ) |  2 |   * 60 |  0  1  1
----------------+----+--------+---------
both( s3/2s . ) ♦  6 |   6  0 | 20  *  *  as non-regular compound of 2{3}
.   β5o   ♦  5 |   0  5 |  * 12  *
sefa( β3/2β5o ) |  3 |   2  1 |  *  * 60
```