Acronym snid
TOCID symbol sID
Name snub dodecahedron,
snub icosidodecahedron
 
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Circumradius sqrt[162+42 sqrt(5)+6 cbrt[20448+9140 sqrt(5)+12 sqrt(7137+3192 sqrt(5))]+6 cbrt[20448+9140 sqrt(5)-12 sqrt(7137+3192 sqrt(5))]]/12 = 2.155837
Vertex figure [34,5]
Snub derivation
General of army (is itself convex)
Colonel of regiment (is itself locally convex – no other uniform polyhedral members)
Dihedral angles
  • between {3} and {3}:   arccos([cbrt(u+v)+cbrt(u-v)+1/3]/3) = 164.175366°
  • between {3} and {5}:   ≈152.930°
where
u = -2 (49+27 sqrt(5))/27 v = 2 sqrt[2 (93+49 sqrt(5))/3]/3
Confer
compounds:
dissid  
External
links
hedrondude   wikipedia   mathworld   quickfur

As abstract polytope snid is isomorphic to gosid, gisid, and girsid, thereby replacing prograde icosahedral triangles and pentagons respectively by prograde icosahedral triangles and (prograde) pentagrams, by prograde icosahedral triangles and retrograde pentagrams, by retrrograde icosahedral triangles and retrograde pentagrams.


Incidence matrix according to Dynkin symbol

s3s5s

demi( . . . ) | 60 |  1  2  2 |  1  1  3
--------------+----+----------+---------
      s 2 s     2 | 30  *  * |  0  0  2
sefa( s3s . ) |  2 |  * 60  * |  1  0  1
sefa( . s5s ) |  2 |  *  * 60 |  0  1  1
--------------+----+----------+---------
      s3s .     3 |  0  3  0 | 20  *  *
      . s5s     5 |  0  0  5 |  * 12  *
sefa( s3s5s ) |  3 |  1  1  1 |  *  * 60

starting figure: x3x5x

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