Compound of great icosahedron and great stellated dodecahedron

15th stellation of icosidodecahedron
Type	stellation and compound
Convex hull	Rhombic triacontahedron
Polyhedra	1 great icosahedron 1 great stellated dodecahedron
Faces	20 triangles 12 pentagrams
Edges	60
Vertices	32
Symmetry group	icosahedral (Ih)

This polyhedron can be seen as either a polyhedral stellation or a compound.

As a compound

It can be seen as a polyhedron compound of a great icosahedron and great stellated dodecahedron. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual.

It has icosahedral symmetry (I_h) and it has the same vertex arrangement as a rhombic triacontahedron.

great icosahedron

great stellated dodecahedron

As a stellation

This polyhedron, is the 15th stellation of the icosidodecahedron, and given as Wenninger model index 61.

The stellation facets for construction are:

Facets from triangle

Facets from pentagon

References

• Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9. , p. 90.
• Wenninger, Magnus (1983). Dual Models. Cambridge University Press. ISBN 0-521-54325-8. , pp. 51-53.
• H. Cundy and A. Rollett Great Icosahedron Plus Great Stellated Dodecahedron. §3.10.4 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 132-133, 1989.

External links

• MathWorld Great Icosahedron -Great Stellated Dodecahedron Compound
• Great Stellated Dodecahedron plus Great Icosahedron - metallic paper model
• VRML George Hart: VRML transparent model

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