I stumbled upon these while playing with tetrahedral-symmetry alterations of a great rhombicuboctahedron, using Stella 4d. You can try this program for free at http://www.software3d.com/Stella.php.
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Tessellation Featuring Regular Octagons, Squares, Isosceles Trapezoids, and Thin Crosses
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A Tessellation Featuring Regular Hexagons, Squares, Equilateral Triangles, and Isosceles Trapezoids
A Tessellation Featuring Regular Hexagons, Isosceles Triangles, and Squares in Two Sizes
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A Tessellation Featuring Regular and Irregular Hexagons, Regular and Irregular Pentagons, Rectangles, Six-Pointed Stars, Equilateral Triangles, and Isosceles Triangles
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A Symmetrohedron Featuring Twelve Regular Pentadecagons and Sixty Kites
I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
A Curvy Tessellation #5
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A Curvy Tessellation #4
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An Excavated Truncated Icosahedron
In this polyhedron, the twenty hexagonal faces have had triangular cupolae removed from the inside of the solid. I did this with Stella 4d, which you can find at http://www.software3d.com/Stella.php.
A 72-Faced Faceted Rhombicosidodecahedron
Twelve of the faces of this polyhedron are star pentagons, and they are easy to spot. The other sixty faces are isosceles trapezoids, and they’re harder to find because parts of them are hidden inside in the solid. The image below shows where these trapezoids can be found.
I made this using Stella 4d: Polyhedron Navigator, a program you can try for free at http://www.software3d.com/Stella.php.












