Acronym sissid
TOCID symbol D*
Name small stellated dodecahedron,
vertex figure of gofix
 
 © ©    ©
Circumradius sqrt[(5-sqrt(5))/8] = 0.587785
Inradius sqrt[(5-sqrt(5))/40] = 0.262866
Density 3
Vertex figure [(5/2)5]
Vertex layers
LayerSymmetrySubsymmetries
 o5/2o5oo5/2o .o   . o.   o5o
1x5/2o5oo5/2o .v   . o.   o5o
vertex first
2x5/2o .
{5/2} first
o   . x
edge first
.   o5v
3o5/2x .
opposite {5/2}
x   . v.   v5o
vertex figure
4o5/2o .o   . x
opposite edge
.   o5o
opposite vertex
5 v   . o 
Lace city
in approx. ASCII-art
 o   o 
   x   
v     v
   x   
 o   o 
Coordinates (1/2, 1/2τ, 0)   & even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army ike
Colonel of regiment (is itself locally convex – other uniform polyhedral member: gike – other edge facetings)
Dual gad
Dihedral angles
  • between {5/2} and {5/2}:   arccos(-1/sqrt(5)) = 116.565051°
Confer
Grünbaumian relatives:
2sissid   gacid   sissid+2gike   2sissid+gike   sissid+3gike   3sissid+gike   2sissid+4gike   4sissid+2gike  
compounds:
passipsido   passipsi  
facetings:
scufgi   targi  
general polytopal classes:
regular   noble polytopes  
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   mathworld   Polyedergarten   nan ma

As abstract polytope sissid is isomorphic to gad, thereby replacing facial pentagrams by pentagons and conversely vertex figure pentagons by corresponding pentagrams. Both sissid and gad can be seen as different realizations of the same self-dual regular abstract polyhedron {5,5}6 (where the index just denotes the size of the corresponding Petrie polygon).


Incidence matrix according to Dynkin symbol

x5/2o5o

.   . . | 12 |  5 |  5
--------+----+----+---
x   . . |  2 | 30 |  2
--------+----+----+---
x5/2o . |  5 |  5 | 12

snubbed forms: β5/2o5o

x5/3o5o

.   . . | 12 |  5 |  5
--------+----+----+---
x   . . |  2 | 30 |  2
--------+----+----+---
x5/3o . |  5 |  5 | 12

o5/4o5/2x

.   .   . | 12 |  5 |  5
----------+----+----+---
.   .   x |  2 | 30 |  2
----------+----+----+---
.   o5/2x |  5 |  5 | 12

o5/4o5/3x

.   .   . | 12 |  5 |  5
----------+----+----+---
.   .   x |  2 | 30 |  2
----------+----+----+---
.   o5/3x |  5 |  5 | 12

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