The faces of this polyhedron are twelve regular pentagons, thirty golden rectangles, and twenty equilateral triangles. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
This particular faceting is made of six square faces, and eight {6/2} hexagons.
Here it is again, in “rainbow color mode”:
I made these models using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
I made this faceted truncated octahedron using Stella 4d, which you can try right here. It has twenty faces: six large squares, six small squares, and eight {6/2} hexagons.
I made these compounds using Stella 4d, which you can try for free at http;//www.software3d.com/Stella.php.
I made this with Stella 4d: Polyhedron Navigator, a program you can try for free at http://www.software3d.com/Stella.php.
I stumbled upon this while playing with Stella 4d: Polyhedron Navigator, a program you can try for free at https://www.software3d.com/Stella.php. It’s difficult to herd regular heptagons.
There’s an obvious question raised by this image: what are the components of the polyhedral cluster, especially the one with heptagonal faces? Comments on this would be appreciated, especially ones with images of the components.
The compound above has eight components, each of which is a tall, triangular, and off-center pyramid. The one below has three co-centered components: elongated square dipyramids.
I made these using Stella 4d: Polyhedron Navigatgor, which you can try for free at http://www.software3d.com/Stella.php.
In this solid, the quadrilaterals are all squares, and the red triangles are regular. The only irregular polygons are the dark blue triangles, which are obtuse and isosceles. I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
I made this using Stella 4d: Polyhedron Navigator. For more about this software, including a free trial download of Stella, I refer you to http://www.software3d.com/Stella.php.
I’ve been making and blogging these birthday stars for well over a decade, and see no reason to stop any time soon. This one is made of four {7/3} heptagrams, shown in blue, with four {7/2} heptagrams shown in yellow. The area of intersection of these two types of star polygon is shown in green. This works to yield a 56-pointed star because (7)(4) + (7)(4) = 28 + 28 = 56.
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