A number of attractive 10-compounds of the regular icosahedron can be constructed.

The compound illustrated above is implemented in the Wolfram Language as `PolyhedronData`[`"IcosahedronTenCompound"`,
1].

This icosahedron 10-compound is illustrated above together with its dodecahedron 10-compound dual and common midsphere.

The common solid and convex hull are illustrated above.