To make this polyhedron using Stella 4d (available here), I started with the dodecahedron, dropped the symmetry of the model down to tetrahedral, and then stellated it twice.
A Tetrahedral Stellation of the Dodecahedron
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The Compound of the Icosahedron and the Small Stellated Dodecahedron
I made this using Stella 4d, which you can try for free here.
An Unusual Eight-faced Polyhedron
This polyhedron has tetrahedral symmetry, and eight faces. Four of them are equilateral triangles, while the other four are 6/2-gons. I made it by modification of the truncated tetrahedron, using Stella 4d, which you can try for yourself, for free, at http://www.software3d.com/Stella.php.
A Tessellation of Kites and Regular Enneagons
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A Polyhedron With Eighteen Faces and Tetrahedral Symmetry
This polyhedron’s faces are six rhombi, and twelve kites. I came across it by modifying the truncated tetrahedron, using Stella 4d: Polyhedron Navigator. You can try this software for free at this website.
A Spiky Symmetrohedron
This was a normal symmetrohedron, until I augmented its trapezoidal faces with pyramids. I did this using Stella 4d: Polyhedron Navigator, which you can try out for free at http://www.software3d.com/Stella.php.
A Zonohedron Based on the Octahedron
To make this using Stella 4d (available here), I started with an octahedron, and then performed a face-based zonohedrification on it — six times.
A 56-Faced Polyhedron Featuring Eight Regular Heptagons
I made this using Stella 4d, which you can try for free right here.
A Zonish Rhombicosidodecahedron
This zonish polyhedron is based on the vertices of a rhombicosidodecahedron. I made it using Stella 4d, which you can try here.
A Zonish Dodecahedron
This zonish polyhedron has 162 faces, and is based on the faces and the vertices of a dodecahedron. I made it using Stella 4d, which you can try for free at this website.
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