An enneacontahedron is a polyhedron with ninety faces. There are many such polyhedra. This particular one has sixty hexagonal faces, and thirty rhombic faces. I made it using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.
This is the day I turn 52 years old, and I’m marking the occasion with a 52-pointed star. This particular star is a compound of four thirteen-pointed stars, each shown in a different color. This works because (4)(13) = 52.
The sky bursting full of rapid and illuminated clouds, rushing bright blue against an indigo background, made me feel I was looking up at the planet Neptune, stretching from one horizon to the other. I went inside, to get my phone, to snap a picture, but, when I got back out, the eighth planet above had been replaced — by a stormy-but-normal third-planet sky. I came back inside with no images, except in memory.
(Image source: NASA / JPL / Voyager 2 / this website.)
I made these using Stella 4d, a program you can try as a free trial download at http://www.software3d.com/Stella.php.
The great icosidodecahedron is one of the uniform polyhedra, which I do not know well. I stumbled across it while creating facetings of the (lesser) icosidodecahedron. This solid has two face-types, there are red pentagrams and yellow equilateral triangles, as seen in the next two pictures.
The dual of this solid is the great rhombic triacontahedron. Its faces are thirty interpenetrating rhombi.
I used Stella 4d to create these images. You may try this program 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.
I made this duoprism, a four-dimensional polytope, using Stella 4d. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.
There are six regular, convex four-dimensional polytopes. Five of them correspond on a 1:1 basis with the Platonic solids (as the tesseract corresponds to the cube), leaving one four-dimensional polytope without a three-dimensional analogue among the Platonics. That polychoron is the icositetrachoron, also named the 24-cell and made of 24 octahedral cells. It also happens to be self-dual.
If, in hyperspace, the corners are cut off just right, new cells are created with 24 cubic cells created at the corners, with 24 truncated octahedral cells remaining from the original polychoron. This is the truncated icositetrachoron:
4-dimensional polytopes have 3-dimensional nets. These nets are shown below — first for the icositetrachoron, and then for the truncated icositetrachoron.
I used Stella 4d to create these images. You can try Stella for free at http://www.software3d.com/Stella.php.
This rhombicosidodecahedron appears to be made from Geomag pieces, but, in reality, it was made virtually using a program called Stella 4d. You may try Stella, for free, at http://www.software3d.com/Stella.php.
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