Acronym sissid
TOCID symbol D*
Name small stellated dodecahedron,
penta-stellahedron,
vertex figure of gofix

` © ©    ©`
Density 3
Vertex figure [(5/2)5]
Vertex layers
 Layer Symmetry Subsymmetries o5/2o5o o5/2o . o   . o .   o5o 1 x5/2o5o o5/2o . v   . o .   o5overtex first 2 x5/2o .{5/2} first o   . xedge first .   o5v 3 o5/2x .opposite {5/2} x   . v .   v5overtex figure 4 o5/2o . o   . xopposite edge .   o5oopposite 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)
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

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
```