Any of these rotating polyhedra may be made larger with a click. I created them using Stella 4d, a program you may try (as a free trial download) at http://www.software3d.com/Stella.php.
Any of these rotating polyhedra may be made larger with a single click. All were created using Stella 4d, a program you may try for free at this website: http://www.software3d.com/Stella.php.
Symmetrohedra have many regular faces, but irregular faces are allowed in them as well. The octagons, hexagons, and squares in this polyhedron are regular, but the 48 triangles are scalene. Here’s what it looks like with these triangles rendered invisible:
Stella 4d was used to make these images; it may be tried for free at this website: http://www.software3d.com/Stella.php.
I used Stella 4d to make this zonohedron. This program may be tried for free at http://www.software3d.com/Stella.php.
From the center to the outside, this cluster contains one icosahedron, twenty octahedra, twenty icosidodecahedra, twenty more octahedra, and, finally, twenty rhombicosidodecahedra.
All three of the images here were created using Stella 4d, a program you may try, free, at this website.
This is what you get if you start with an icosahedron, augment each of its faces with tetrahedra, and then augment the tetrahedral faces with octahedra. I made it using Stella 4d, a program you may try for free at http://www.software3d.com/Stella.php.
This was created using Stella 4d, a program you can buy, or try for free, at http://www.software3d.com/Stella.php.
The great icosahedron, one of the Kepler-Poinsot solids, is hidden from view at the center of this cluster. Each of its faces is augmented with a Platonic icosahedron, producing what you see here. Stella 4d is the software I used; more information about that program may be found here.
This is a pentagonal hexacontahedron, the dual of the snub dodecahedron. It’s decorated with mandalas of the the type I blogged here, two posts ago. The mandalas do interesting things when this polyhedron is stellated, as you can see below.
That was the first stellation, and here is the second:
The sixth stellation was the last one I found interesting enough to post.
All four polyhedral images above were created using Stella 4d: Polyhedron Navigator, software you may buy, or try for free, at this website.
The snub dodecahedron, one of the Archimedean solids, has eighty faces which are triangles, and twelve pentagonal faces as well. In the view above, the pentagons are rendered invisible, allowing the interior to be viewed as the solid rotates.
The eighty triangles are of two types: the sixty yellow ones share an edge with a pentagon, and the twenty blue ones do not. If the blue triangles are also hidden, the “transparency” of this solid becomes even greater, as seen below.
Both of these images were created using Stella 4d, software you may try for free at this website.
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