A Polyhedron Featuring Twenty Regular Enneagons and Sixty Kites

Posted on 29 September 2024 by RobertLovesPi

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

A Faceted Icosidodecahedron Featuring Golden Rectangles

Posted on 28 September 2024 by RobertLovesPi

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

Posted on 27 September 2024 by RobertLovesPi

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

Posted on 26 September 2024 by RobertLovesPi

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

A Tessellation Featuring Regular Enneagons, Regular Hexagons, Equilateral Triangles, and Kites

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An Untidy Faceting of the Icosidodecahedron

Posted on 25 September 2024 by RobertLovesPi

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. Untidy facetings are like normal ones, except they do not use all the vertices of the “seed” polyhedron.

Two Views of a Faceted Great Rhombicosidodecahedron

Posted on 9 August 2024 by RobertLovesPi

This was the initial image that Stella 4d (free trial here) gave me when I first created this faceting. Every face type — and there are many — has a different color in this image.

It’s a little easier on the eyes to see this faceting if the face types are grouped into just three colors, as seen below.

The Medial Rhombic Triacontahedron, Rendered in Zome

Posted on 13 July 2024 by RobertLovesPi

This is the medial rhombic triacontahedron, constructed using Zometools. It is the dual of the uniform polyhedron known as the dodecadodecahedron.

If you’d like to have Zome for your home or classroom, the website to visit to get it is http://www.zometool.com. I give it an enthusiastic “two thumbs up.”