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.
I made these two versions of the icosahedron, using rhombic triacontahedra and elongated prisms, and a program called Stella 4d. You can try this program yourself, for free, at http://www.software3d.com/Stella.php.
Moon image from https://www.usgs.gov/news/national-news-release/usgs-releases-first-ever-comprehensive-geologic-map-moon. Polyhedron created using Stella 4d: Polyhedron Navigator, which you can try for free at this website.
First, the tetrahedron.
Next, the cube, with each square face augmented by a single rhombicosidodecahedron.
Next, this same operation is performed on an octahedron.
Next, the dodecahedron.
Finally, the last of the set, centered on an icosahedron. This one is my favorite.
I made these five models using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
The cluster below is formed by augmenting each face of the dodecahedron above with an icosidodecahedron.
Next, each triangular face is augmented with an icosahedron.
Now every pentagonal face is augmented with a dodecahedron.
Finally, the pentagonal faces in this cluster of polyhedra are augmented with icosidodecahedra. The resulting, new cluster has an overall icosahedral shape.
I did all of this using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
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