To make this polyhedron, I started with the rhombicosidodecahedron, then applied the “morph duals by tilting to rectify” function in Stella 4d: Polyhedron Navigator — twice. If you’d like to try this program for yourself, there is a free trial download at http://www.software3d.com/Stella.php.
This is the thrid stellation of the rhombic dodecahedron. Its facelets are 24 rhombi and 24 “chevron” hexagons. Here’s another view, colored by individual face, with parallel faces having the same color.
Finally, here’s one in “rainbow color mode.”
I made these images using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
To make this using Stella 4d (available here), I applied the “morph duals by expansion” function to the great icosahedron.
This symmetrohedron has the six regular octagons, eight regular hexagons, and twelve squares of its “parent,” the great rhombicuboctahedron. It was modified by using the “morph duals at 50% by tilting to rectify” function, twice. This left the resulting polyhedron with additional faces: 72 trapezoids (24 each, of three types), and 48 scalene triangles. That’s 146 faces in all. I made it using Stella 4d, which you can try for yourself, free, at http://www.software3d.com/Stella.php.
This symmetrohedron has the twelve regular decagons, twenty regular hexagons, and thirty squares of its “parent,” the great rhombicosidodecahedron. It was modified by using the “morph duals at 50% by tilting to rectify” function, twice. This left the resulting polyhedron with additional faces: 180 trapezoids (60 each, of three types), and 120 scalene triangles. That’s 362 faces in all. I made it using Stella 4d, which you can try for yourself, free, at http://www.software3d.com/Stella.php.
This is a compound of left- and right-handed versions of the chiral Catalan solid known as the pentagonal hexecontahedron, which is the dual of the snub dodecahedron. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
This is a compound of left- and right-handed versions of the chiral Catalan solid known as the pentagonal icositetrahedron, which is the dual of the snub cube. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
I made this using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.
I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
The image above has faces colored by number of sides, while the one below is in “rainbow color mode.” I made these using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.
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