A Chiral Tessellation of the Plane Using Regular Hexagons and Parallelograms
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Author Archives: RobertLovesPi
A Tessellation of the Plane Using Concave Octagons and Regular Hexagons
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A Polyhedron Featuring Sixty Regular Heptagons
In addition to the sixty heptagons, there are twelve regular pentagons and sixty quadrilaterals in this polyhedron, along with 380 triangles of various shapes and sizes. That’s 512 faces in all.
I used Stella 4d: Polyhedron Navigator to make this. You may try this program, for free, at http://www.software3d.com/Stella.php.
Golden Kite Tessellation
The blue kites have sides which are in the golden ratio (~1.618:1), while the yellow kites’ sides are in a ratio equaling the square of that number, or approximately ~2.618:1.
Another Tessellation of Concave Octagons
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Tessellation of Equilateral, Concave Octagons
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A Fifty-Faced Polyhedron Featuring Eighteen Regular Octagons
In addition to the eighteen regular octagons, this polyhedron also has eight equiangular hexagons and twenty-four isosceles trapezoids among its fifty faces. I made it using Stella 4d, which you can try, for free, right here.
Repeated Augmentations of a Dodecahedron With More and More Dodecahedra
Here’s a single dodecahedron.
A new “cluster polyhedron” can be made by augmenting each pentagonal face with another dodecahedron.
If you can do it once, you can do it again, augmenting each pentagon with a new dodecahedron.
Once more.
I made these polyhedral clusters using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
Tessellation of Regular Pentagons and Rhombi
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RobertLovesPi.net 