A Tessellation Featuring Regular Heptagons, Regular Hexagons, and Many Irregular Polygons

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If you’d like to see a larger version, simply click on the image.

The Twenty Triangles of an Icosidodecahedron

Posted on 19 March 2023 by RobertLovesPi

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

An Icosidodecahedron Variant

Posted on 19 March 2023 by RobertLovesPi

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

Three Views of a Modified Great Rhombicosidodecahedron

Posted on 18 March 2023 by RobertLovesPi

To make these using Stella 4d (available here), I started with the great rhombicosidodecahedron, then used the “morph duals by expansion” function on it — twice. Here’s the result, shown with coloring done by face type.

The next one has faces colored by number of sides.

Finally, here’s one shown in rainbow color mode.

A Faceted Version of the Great Rhombicosidodecahedron

Posted on 17 March 2023 by RobertLovesPi

I made this using Stella 4d, which is available here.

A Polyhedron Containing Twenty Regular Hexagons and Twenty-Four Convex Pentagons

Posted on 16 March 2023 by RobertLovesPi

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

A Symmetrohedron With 152 Faces

Posted on 15 March 2023 by RobertLovesPi

The 152 faces of this symmetrohedron include twelve regular decagons, twenty regular hexagons, and 120 irregular quadrilaterals arranged in thirty groups of four quads each. I made it using Stella 4d, which you can download here as a free trial version.

Two Polyhedral Compounds Derived From Catalan Solids

Posted on 14 March 2023 by RobertLovesPi

The second stellation of the dysdyakis triacontahedron, seen above, is an interesting two-part polyhedral compound. The dysdyakis triacontahedron is one of the Catalan solids, and is the dual of the great rhombicosidodecahedron.

There’s also a “little brother” to this first compound — it’s the second stellation of the dysdyakis dodecahedron, which is the dual of the great rhombicuboctahedron. Like its “big brother,” it’s a two-part compound. It is shown below.

Interestingly, the components of these two compounds are “stretched” versions of two other Catalan solids: the pentagonal hexecontahedron (dual of the snub dodecahedron), and the pentagonal icositetrahedron (dual of the snub cube).

I made these virtual models using Stella 4d, which you can download and try for free at http://www.software3d.com/Stella.php.

Two Symmetrohedra Featuring Regular Pentadecagonal Faces

Posted on 13 March 2023 by RobertLovesPi

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

Two Half-Visible Catalan Solids

Posted on 12 March 2023 by RobertLovesPi

The Catalan Solids shown here are the dysdyakis dodecahedron (dual of the great rhombicuboctahedron) and the dysdyakis triacontahedron (dual of the great rhombicosidodecahedron). In each one, all the faces are scalene triangles, and half of them have been rendered invisible, so that you can see the inside view of faces on the far side of each polyhedron. The remaining faces are shown in “rainbow color mode.”