A Truncation of the Small Stellated Dodecahedron

Posted on 17 February 2024 by RobertLovesPi

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

A Non-Convex Polyhedral Cluster Featuring Regular Heptagons, With a Puzzle

Posted on 10 February 2024 by RobertLovesPi

I stumbled upon this while playing with Stella 4d: Polyhedron Navigator, a program you can try for free at https://www.software3d.com/Stella.php. It’s difficult to herd regular heptagons.

There’s an obvious question raised by this image: what are the components of the polyhedral cluster, especially the one with heptagonal faces? Comments on this would be appreciated, especially ones with images of the components.

One Compound of Pyramids, and Another of Dipyramids

Posted on 21 January 2024 by RobertLovesPi

The compound above has eight components, each of which is a tall, triangular, and off-center pyramid. The one below has three co-centered components: elongated square dipyramids.

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

A Symmetrohedron With 62 Faces

Posted on 20 January 2024 by RobertLovesPi

In this solid, the quadrilaterals are all squares, and the red triangles are regular. The only irregular polygons are the dark blue triangles, which are obtuse and isosceles. I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

An Icosahedron, Augmented by Inverted Triangular Cupolae

Posted on 19 January 2024 by RobertLovesPi

I made this using Stella 4d: Polyhedron Navigator. For more about this software, including a free trial download of Stella, I refer you to http://www.software3d.com/Stella.php.

An Icosahedron, Built With Rhombic Triacontahedra and Elongated Prisms

Posted on 30 December 2023 by RobertLovesPi

I made these two versions of the icosahedron, using rhombic triacontahedra and elongated prisms, and a program called Stella 4d. You can try this program yourself, for free, at http://www.software3d.com/Stella.php.

Craters on the Near Side of the Moon, on the Faces of a Rhombic Enneacontahedron

Posted on 22 November 2023 by RobertLovesPi

Moon image from https://www.usgs.gov/news/national-news-release/usgs-releases-first-ever-comprehensive-geologic-map-moon. Polyhedron created using Stella 4d: Polyhedron Navigator, which you can try for free at this website.

The Five Platonic Solids, Each Surrounded by Rhombicosidodecahedra

Posted on 11 November 2023 by RobertLovesPi

First, the tetrahedron.

Next, the cube, with each square face augmented by a single rhombicosidodecahedron.

Next, this same operation is performed on an octahedron.

Next, the dodecahedron.

Finally, the last of the set, centered on an icosahedron. This one is my favorite.

I made these five models using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.

Clusters of Polyhedra Surrounding a Dodecahedron

Posted on 4 November 2023 by RobertLovesPi

The cluster below is formed by augmenting each face of the dodecahedron above with an icosidodecahedron.

Next, each triangular face is augmented with an icosahedron.

Now every pentagonal face is augmented with a dodecahedron.

Finally, the pentagonal faces in this cluster of polyhedra are augmented with icosidodecahedra. The resulting, new cluster has an overall icosahedral shape.