This is the first stellation of the second polyhedron seen in the post just before this one, but with the color-scheme changed, on the grounds that I like blue. If you’d like to know more about how this polyhedron was created, I refer you to that post. Stella 4d was used to make these: software you can try right here.
To make this, I used the excavation-function of Stella 4d, set to remove pyramids with equal edge length from each face of an icosidodecahedron. You can try this program here.
The dual of this polyhedron is shown below.
This is the familiar dodecahedron/icosahedron compound, but with each face of both components of the compound altered by the excavation of an equal-edge-length pyramid. To make it, as well as the rotating image below, I used Stella 4d, which you can find here.
Also, here is the dual of the compound above:
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