Acronym	sissid
TOCID symbol	D*
Name	small stellated dodecahedron
	© ©
Circumradius	sqrt[(5-sqrt(5))/8] = 0.587785
Inradius	sqrt[(5-sqrt(5))/40] = 0.262866
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
Confer	Grünbaumian relatives: 2sissid   gacid   sissid+2gike   2sissid+gike   sissid+3gike   3sissid+gike   2sissid+4gike   4sissid+2gike   compounds: passipsido   passipsi   general polytopal classes: regular
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As abstract polytope sissid is isomorphic to gad, thereby replacing facial pentagrams by pentagons and conversely vertex figure pentagons by corresponding pentagrams.

Incidence matrix according to Dynkin symbol

x5/2o5o

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

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