Compound of dodecahedron and icosahedron

It can be seen as the compound of an icosahedron and 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 the same vertex arrangement as a rhombic triacontahedron.

This can be seen as the three-dimensional equivalent of the compound of two pentagons ({10/2} "decagram"); this series continues into the fourth dimension as the compound of 120-cell and 600-cell and into higher dimensions as compounds of hyperbolic tilings.

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| image2 = Polyhedron pair 12-20 from blue.png |width2=1|height2=1

| image3 = Polyhedron pair 12-20 from yellow.png |width3=1|height3=1

| image4 = Polyhedron pair 12-20 from red.png |width4=1|height4=1

| footer = Seen from 2-fold, 3-fold and 5-fold symmetry axes
The decagon on the right is the Petrie polygon of both solids.

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| image2 = Polyhedron pair 12-20 big.png |width2=1|height2=1

| image3 = Polyhedron small rhombi 12-20 dual max.png |width3=1|height3=1

| footer = If the edge crossings were vertices, the mapping on a sphere would be the same as that of a deltoidal hexecontahedron.

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This polyhedron is the first stellation of the icosidodecahedron, and given as Wenninger model index 47.

The stellation facets for construction are:

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The compound of a Dodecahedron and an Icosahedron shares the same vertices as a list of other polyhedra, including the Rhombic triacontahedron and the Small triambic icosahedron.

In the film Tron (1982), the character Bit took this shape when not speaking.

In the cartoon series Steven Universe (2013-2019), Steven's shield bubble, briefly used in the episode Change Your Mind, had this shape.

• Compound of two tetrahedra
• Compound of cube and octahedron
• Compound of small stellated dodecahedron and great dodecahedron
• Compound of great stellated dodecahedron and great icosahedron

• {{cite book | first=Magnus | last=Wenninger | authorlink=Magnus Wenninger | title=Polyhedron Models | publisher=Cambridge University Press | year=1974 | isbn=0-521-09859-9 }}

• {{mathworld |urlname=Dodecahedron-IcosahedronCompound |title=Dodecahedron-Icosahedron Compound}}

Category:Polyhedral stellation

Category:Polyhedral compounds