Acronym	seside
TOCID symbol	sIID*, ssI
Name	small snub icosicosidodecahedron, snub disicosidodecahedron, holosnub icosahedron, hastur
VRML	⭳ ©
Circumradius	sqrt[13+3 sqrt(5)+sqrt[102+46 sqrt(5)]]/4 = 1.458190
Vertex figure	[5/2,35]
Colonel of regiment	(is itself locally convex – no other uniform polyhedral members)
Snub derivation / VRML	⭳
Face vector	60, 180, 112
External links

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

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

     s    
  3 / \ 3 
   s---s  
    5/2   

s5/2s3s3*a

demi( .   . .    ) | 60 |  2  2  2 |  1  1  1  3
-------------------+----+----------+------------
sefa( s5/2s .    ) |  2 | 60  *  * |  1  0  0  1
sefa( s   . s3*a ) |  2 |  * 60  * |  0  1  0  1
sefa( .   s3s    ) |  2 |  *  * 60 |  0  0  1  1
-------------------+----+----------+------------
      s5/2s .      ♦  5 |  5  0  0 | 12  *  *  *
      s   . s3*a   ♦  3 |  0  3  0 |  * 20  *  *
      .   s3s      ♦  3 |  0  0  3 |  *  * 20  *
sefa( s5/2s3s3*a ) |  3 |  1  1  1 |  *  *  * 60

or
demi( .   . .    )    | 60 |  2   4 |  1  2  3
----------------------+----+--------+---------
sefa( s5/2s .    )    |  2 | 60   * |  1  0  1
sefa( s   . s3*a )  & |  2 |  * 120 |  0  1  1
----------------------+----+--------+---------
      s5/2s .         ♦  5 |  5   0 | 12  *  *
      s   . s3*a    & ♦  3 |  0   3 |  * 40  *
sefa( s5/2s3s3*a )    |  3 |  1   2 |  *  * 60

starting figure: x5/2x3x3*a

β3β5o

both( . . .    ) | 60 |  2  2  2 |  1  1  1  3
-----------------+----+----------+------------
sefa( s3s . (r)) |  2 | 60  *  * |  1  0  0  1
sefa( s3s . (l)) |  2 |  * 60  * |  0  1  0  1
sefa( . β5o    ) |  2 |  *  * 60 |  0  0  1  1
-----------------+----+----------+------------
      s3s . (r)  ♦  3 |  3  0  0 | 20  *  *  *
      s3s . (l)  ♦  3 |  0  3  0 |  * 20  *  *
      . β5o      ♦  5 |  0  0  5 |  *  * 12  *
sefa( β3β5o    ) |  3 |  1  1  1 |  *  *  * 60

or
both( . . . ) | 60 |   4  2 |  2  1  3
--------------+----+--------+---------
sefa( s3s . ) |  2 | 120  * |  1  0  1
sefa( . β5o ) |  2 |   * 60 |  0  1  1
--------------+----+--------+---------
both( s3s . ) ♦  3 |   3  0 | 40  *  *  as coplanar pair of {3}
      . β5o   ♦  5 |   0  5 |  * 12  *
sefa( β3β5o ) |  3 |   2  1 |  *  * 60

or
both( . . . ) | 60 |   4  2 |  2  1  3
--------------+----+--------+---------
sefa( s3s . ) |  2 | 120  * |  1  0  1
sefa( . β5o ) |  2 |   * 60 |  0  1  1
--------------+----+--------+---------
both( s3s . ) ♦  6 |   6  0 | 20  *  *  as non-regular compound of 2{3}
      . β5o   ♦  5 |   0  5 |  * 12  *
sefa( β3β5o ) |  3 |   2  1 |  *  * 60

starting figure: x3x5o