About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my own little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

Two Symmetrohedra

Posted on 29 July 2021 by RobertLovesPi

Symmetrohedra are symmetric polyhedra with many faces regular, but not necessarily all of them. The symmetrohedron shown above is the dual of the convex hull of the compound of the great rhombicosidodecahedron and its dual, the disdyakis triacontahedron. All of its faces are regular, except for the triangles, which are scalene.

The second symmetrohedron shown here is the dual of the convex hull of the great rhombcuboctahedron and its dual, the disdyakis dodecahedron. Like its “big brother” above, all of this symmetrohedron’s faces are regular, except for the scalene triangles.

These polyhedra were made using Stella 4d, a program you can try for free at this website.

A Curvy Tessellation #3

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A Curvy Tessellation #2

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A Cluster of Twelve Rhombic Triacontahedra

Posted on 29 July 2021 by RobertLovesPi

To make this, I started with the rhombic hexecontahedron (shown in this post), and then I augmented its twelve indentations with rhombic triacontahedra. I did this using Stella 4d, which you can try for free right here.

The Rhombic Hexecontahedron

Posted on 29 July 2021 by RobertLovesPi

This is the rhombic hexecontahedron. Its faces are 60 rhombi with diagonals in the golden ratio. I made it by starting with a rhombic triacontahedron, then stellating it 26 times. This was done using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

This non-convex polyhedron can also be made using Zome, available at http://www.zometool.com, using all red struts of the same length. This was the reason I made the edges red, and the vertices white (like Zomeballs).

An Aperiodic Tessellation Featuring Regular Decagons and Regular Pentagons, Along With Concave Pentagons and a Few Rhombi

Posted on 28 July 2021 by RobertLovesPi

It is not possible to tessellate a plane using only regular pentagons and decagons, but that doesn’t stop me from trying. To get this to work, I had to add rhombi and concave pentagons — but even then, it’s an aperiodic tessellation.