The dodecahedron-small triambic icosahedron compound is a stellated form of a truncated icosahedron, but a different truncation than in the truncated icosahedron Archimedean solid. It contains curious but attractive patterns of raised regular pentagrams and irregular hexagrams.
The interior is the hull of a small ditrigonal icosidodecahedron and the convex hull has the connectivity of the pentakis dodecahedron.
The compound is implemented in the Wolfram Language as PolyhedronData["DodecahedronSmallTriambicIcosahedronCompound"] and its hull as PolyhedronData["DodecahedronSmallTriambicIcosahedronCompoundHull"].
For a compound hull constructed from a small triambic icosahedron with longest edge length equal to unity, the solid has lengths
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(1)
|
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(2)
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(3)
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(4)
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The dodecahedron component has circumradius
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(5)
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The surface area is given by the smallest positive root of
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(6)
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approximately equal to 
, and the volume is given
by
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(7)
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