Acronym sirsid
TOCID symbol s*IID*
Name small (inverted) retrosnub icosicosidodecahedron,
retrosnub disicosidodecahedron,
yog sothoth
 
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Circumradius sqrt[13+3 sqrt(5)-sqrt[102+46 sqrt(5)]]/4 = 0.580695
Coordinates
  1. ([-1/τ-sqrt(3τ-2)]/4, 0, [3-τ sqrt(3τ-2)]/4)         & even permutations, all changes of sign
  2. ([1/τ-sqrt(3τ-2)]/4, 1, [1+2/τ-τ sqrt(3τ-2)]/4)   & even permutations, all changes of sign
  3. ([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)
External
links
hedrondude   wikipedia   WikiChoron   mathworld

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

starting figure: x3/2x3/2x5/2*a

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

starting figure: x3/2x5o
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

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