The faces of this polyhedron all have the same tessellation projected on them, but with five different coloring schemes. These five different tessellations appear in non-moving form in the last post on this blog, and I used Geometer’s Sketchpad and MS-Paint to make them. Stella 4d, another program, was then used to put the whole thing together, and it may be tried for free at http://www.software3d.com/Stella.php.
I used four other color-schemes with this same tessellation, and those other images are shown below.
The icosahedron has twenty triangular faces. Truncate it once, and the triangles become hexagons, with pentagons appearing under the pyramids removed in the truncation. This is the “soccer ball” shape familiar to millions.
If you take this figure and truncate it again, the twenty hexagons become twenty dodecagons, the twelve pentagons each become decagons, and sixty isosceles triangles appear under the pyramids removed by this second truncation.
I made this image using Stella 4d, a program you can find at www.software3d.com/Stella.php. Also, just for fun, here’s a version of it with the colors switched around, and with a slight bounce as it rotates in the other direction.
The icosidodecahedron’s 24th stellation is above, and the 32nd, then the 36th, are below.
I made these images using Stella 4d, a program you can find at www.software3d.com/Stella.php.
Above is this polyhedral stellation in three colors. If every face is given its own color, though, except for parallel faces, it looks like this (click to enlarge):
I made both images using Stella 4d, a program you can find at http://www.software3d.com/Stella.php.
I stumbled upon this while using Stella 4d to modify existing polyhedra. You may find this program at http://www.software3d.com/Stella.php.
If the colors are inverted, but the background remains black, this is what it turns into:
Here’s what it looks like with different colors (click to enlarge it):
Pictured above is the most familiar hexagonal tessellation. I’ve found some additional tessellations which use equilateral (but non-equiangular) hexagons, and have radial symmetry. They appear, using various coloring-schemes, below.
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