Acronym	sissid
TOCID symbol	D*
Name	small stellated dodecahedron, penta-stellahedron, vertex figure of gofix
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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	Layer Symmetry Subsymmetries   o5/2o5o o5/2o . o   . o .   o5o 1 x5/2o5o o5/2o . v   . o .   o5o vertex first 2 x5/2o . {5/2} first o   . x edge first .   o5v 3 o5/2x . opposite {5/2} x   . v .   v5o vertex figure 4 o5/2o . 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°
Face vector	12, 30, 12
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: Wythoffian polyhedra   regular   noble polytopes
External links

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