This solid has all the faces of the great rhombicosidodecahedron, plus 120 scalene triangles. I made it using Stella 4d, which you can try for free right here.
A Symmetrohedron Derived From the Great Rhombicosidodecahedron
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Tag Archives: Mathematics
Kepler’s “Stella Octangula,” With Ten Variants
Here’s Johonnes Kepler’s Stella Octangula — also known as the compound of two tetrahedra.
What follows are ten variants of this solid, all made using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
A 90-Faced Polyhedron
This polyhedron has sixty kite faces and thirty octagonal faces. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
A Polyhedron Featuring Twenty Regular Octadecagons and Twelve Regular Decagons
I made this using Stella 4d, which you can try for free right here.
Regular Octadecagons As Faces of Symmetrohedra
I tried to make a symmetrohedron using regular octadecagons and regular decagons, but that combination forces the octadecagons to overlap, and that causes the would-be symmetrohedron to be non-convex.
I tried to augment these octadecagons with antiprisms, and then form the convex hull of the result. Here’s what I found:
I made these using Stella 4d, which you can try for free right here.
A Face-Based Zonohedrified Rhombic Enneacontahedron
The decagons and octagons in this zonohedron are regular. The octadecagons are, sadly, only equilateral. I made this using Stella 4d, which you can try for free, right here.
A Face-Based Zonish Icosidodecahedron
I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
A Cube, Encased by the Apothems of Its Faces
I made this using Stella 4d, which you can try for free at this website.
An Agglomeration of Triangles and Six Oblique Heptagonal Prisms
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I made this using Stella 4d, which you can try for free right here.
A Polyhedron Featuring a Dozen Regular Heptagons and a Whole Mess of Quadrilaterals
There are four different shapes of quadrilaterals here, but they have one thing in common: there are twelve of each of them. Add those 48 quads to the twelve regular heptagons, and that gives a total of 60 faces. I found this polyhedron while playing with the snub dodecahedron, using Stella 4d: Polyhedron Navigator, a program you can try for free right here.
In the image below, each of the four types of quadrilateral appears with its own color.
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