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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Two Views of a Heptagrammic Dipyramid

I made these using Stella 4d, which you can try for free right here.

A “Barrel” Polyhedron With Heptagonal Bases

Here is this polyhedron’s dual.

I made these using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

Octagonal/Heptagonal Mixed Antiprism

I made this using Stella 4d, which you can try for free at this website.

Heptagonal/Hexagonal Mixed Antiprism

I made this using Stella 4d, which you can try for free right here.