Compound of great icosahedron and great stellated dodecahedron

Compound of great icosahedron and great stellated dodecahedron
15th stellation of icosidodecahedron
Compound of great icosahedron and stellated dodecahedron.png
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.

Contents

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 (Ih) and it has the same vertex arrangement as a rhombic triacontahedron.

Great icosahedron.png
great icosahedron
Great stellated dodecahedron.png
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:

Second compound stellation of icosidecahedron facets.png
Facets from triangle
Second compound stellation of icosidecahedron pentfacets.png
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