Tessellation of Equilateral, Concave Octagons

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A Fifty-Faced Polyhedron Featuring Eighteen Regular Octagons

Posted on 22 April 2022 by RobertLovesPi

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

Posted on 20 April 2022 by RobertLovesPi

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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A “Barrel” Polyhedron With Heptagonal Bases

Posted on 12 April 2022 by RobertLovesPi

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

Posted on 10 April 2022 by RobertLovesPi

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

Heptagonal/Hexagonal Mixed Antiprism

Posted on 9 April 2022 by RobertLovesPi

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

A Mandala Centered on a Regular Dodecagon

Posted on 5 April 2022 by RobertLovesPi

In addition to the central dodecagon, this mandala has two rings of squares, one of equilateral triangles, a ring of rhombi, another of regular hexagons, and, finally, a ring of equilateral decagons.