This collection of curves was built around a tessellation of the plane using regular hexagons. To make the second version, I inverted the colors, except for the black circles and arcs.
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Tag Archives: Mathematics
A Picture of Five
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A Dozen Dodecahedra, Surrounding an Icosahedron
I made these virtual models using Stella 4d: Polyhedron Navigator. If you’d like to try this program for yourself — free — the website to visit is http://www.software3d.com/Stella.php.
A Parallelogram-Expanded Snub Dodecahedron
The snub dodecahedron may be thought of as a dozen regular pentagons, surrounded and separated by a sea of triangles. In this expansion of that Archimedean solid, thirty parallelograms are added to the mix, also surrounded by triangles. In the image above, coloring is by face type — for example, the yellow triangles are those triangles which share an edge with a pentagon. Other triangles have other colors.
The image shown below is of the same polyhedron, but with a different coloring-scheme. In it, all triangles are given the same color, even when their shapes are slightly different.
This polyhedron has an interesting all-pentagon dual, which is shown below. This dual has sixty each of both the small and large pentagons, for a total of 120 faces.
I used Stella 4d: Polyhedron Navigator to create these polyhedra, and to make these rotating images. This program may be tried for free at http://www.software3d.com/Stella.php.
An Embellished Icosahedron
Created using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
A Compound of Six Pentadecagonal Prisms
This chiral polyhedral compound was generated from a partial faceting of the polyhedron shown in the last post here, using Stella 4d‘s faceting function, plus its “try to make faces regular” operation afterwards. Making the six-prism compound in the first place was suggested by Tony Hartley, on Facebook, where I posted a link to that last post in a mathematical group for discussion. Thanks, Tony!
If you’d like to try Stella for yourself, the site to visit for a free trial download is http://www.software3d.com/Stella.php.
An Unusual Polyhedron with 200 Faces
This polyhedron was made from the faceted rhombicosidodecahedron in the post immediately before this one, by stellating it a few times. Its 200 faces include twenty equilateral triangles (yellow), sixty irregular decagons (green), and two sets of sixty trapezoids each (red and blue). I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
