Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this complex of octahedra. If you’d like to try this software for yourself, there is a free trial version available at http://www.software3d.com/Stella.php.
Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this complex of tetrahedra. If you’d like to try this software for yourself, there is a free trial version available at http://www.software3d.com/Stella.php.
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.
Created using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
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.
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.
I made this faceting of the rhombicosidodecahedron using Stella 4d: Polyhedron Navigator. You can try this program out, for free, at http://www.software3d.com/Stella.php.
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.
RobertLovesPi.net 