I made this by faceting a great rhombicosidodecahedron, using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
A Compound of Ten Hexagonal Prisms
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Tessellation Featuring Regular Pentadecagons, Regular Hexagons of Two Sizes, Non-Convex Heptagons, and “Bowtie” Pairs of Isosceles Trapezoids
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Tessellation Featuring Regular Pentadecagons, Rhombi, Isosceles Triangles, and Six-Pointed Stars
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Two Symmetrohedra, Both of Which Feature Eight Regular Enneagons
The first of these, shown above, also includes six squares, 24 isosceles trapezoids, and twelve rectangles among its faces.
The second one, shown below, also includes among its faces six regular octagons, and twelve pairs of “bowtie” trapezoids.
I made both of these models using Stella 4d, which you can try for free here. The starting point for making them was the enneagonal-faced polyhedron found in this program’s built-in set of near-misses to the Johnson solids.
A Polyhedron Featuring Twenty Regular Enneagons and Sixty Kites
I made this using Stella 4d, which you can try for free at this website.
A Faceted Icosidodecahedron Featuring Golden Rectangles
This polyhedron has three face types. The blue triangles and the red star pentagons are easy to see, but it’s more challenging to see the yellow golden rectangles, since they are only partially visible. One of these golden rectangles is highlighted in the still image below, to make it easier to spot them.
I created these virtual models using Stella 4d: Polyhedron Navigator. This program may be tried out for free at http://www.software3d.com/Stella.php.
A Tessellation Featuring Regular Octagons, Squares, Rhombi, and Eight-Pointed Stars
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A Variant of the Familiar “Octagons and Squares” Tessellation
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A Compound of the Icosahedron and a Pyramid-Augmented Dodecahedron
Sharp-eyed polyhedronists may wonder about the dodecahedron augmented with pentagonal pyramids, because it closely resembles the pentakis dodecahedron, which is one of the Catalan solids. I checked, though, and the red triangles’ angles are not quite correct for that designation.
I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
A Compound of the Icosidodecahedron and the Triakis Icosahedron
I made this compound using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.
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