The stelladodecahedron cone, or sadcone, is a nonconvex orbiform polyhedron and an edge-faceting of the small stellated dodecahedron. Its faces are 5 pentagrams and 5 triangles. It is named as such because the 5 pentagrams are arranged around one vertex similar to the configuration found in the small stellated dodecahedron.

Rank3
Notation
Elements
Faces5 triangles, 5 pentagrams
Edges5+5+10
Vertices1+5+5
Vertex figures1 pentagon, edge length (5–1)/2
5 butterflies, edge lengths 1 and (5–1)/2
5 isosceles triangles, edge lengths 1, (5–1)/2, (5–1)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Dihedral angles5/2–5/2: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
3–5/2 #1: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
3–5/2 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Related polytopes
ArmyGyepip, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
ConjugateGreat dodecahedron cone
Convex hullGyroelongated pentagonal pyramid
Abstract & topological properties
Flag count80
Euler characteristic1
OrientableNo
Genus1
Properties
SymmetryH2×I, order 10
ConvexNo
NatureTame

## Vertex coordinates

Its vertex coordinates are the same as those of the small stellated dodecahedron with any 1 vertex removed.