The Great Icosidodecahedron and Its Dual, the Great Rhombic Triacontahedron

Posted on 1 January 2020 by RobertLovesPi

The great icosidodecahedron is one of the uniform polyhedra, which I do not know well. I stumbled across it while creating facetings of the (lesser) icosidodecahedron. This solid has two face-types, there are red pentagrams and yellow equilateral triangles, as seen in the next two pictures.

The dual of this solid is the great rhombic triacontahedron. Its faces are thirty interpenetrating rhombi.

I used Stella 4d to create these images. You may try this program for free at http://www.software3d.com/Stella.php.

Four Rhombicosidodecahedra Surrounding a Tetrahedron

Posted on 31 December 2019 by RobertLovesPi

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

Simulated Geomag Rhombicosidodecahedron

Posted on 24 December 2019 by RobertLovesPi

This rhombicosidodecahedron appears to be made from Geomag pieces, but, in reality, it was made virtually using a program called Stella 4d. You may try Stella, for free, at http://www.software3d.com/Stella.php.

A Symmetrohedron with 122 Faces

Posted on 23 December 2019 by RobertLovesPi

In this symmetrohedron, all faces are regular, except for the green isosceles triangles. If these triangles were a little closer to being regular, this would be a near-miss to the Johnson solids, but that is not the case. I made this (starting with the last polyhedron in the post right before this one) using Stella 4d: Polyhedron Navigator, a program you can try for free at http://www.software3d.com/Stella.php.

A Blend of the Icosahedron and the Rhombic Enneacontahedron

Posted on 22 December 2019 by RobertLovesPi

This is the icosahedron, one of the Platonic solids. It has twenty faces.

The polyhedron below is the rhombic enneacontahedron, a well-known zonohedron with ninety faces.

Finally, here is a polyhedron which blends these two. It has 20 + 90 = 110 faces.

I used Stella 4d: Polyhedron Navigator to make these images. You can try this program for free at http://www.software3d.com/Stella.php.

Fifty Faces Each in Two Polyhedra

Posted on 18 December 2019 by RobertLovesPi

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

A Twice-Zonohedrified Dodecahedron

Posted on 10 December 2019 by RobertLovesPi

If one starts with a dodecahedron, and then creates a zonohedron based on that solid’s vertices, the result is a rhombic enneacontahedron.

If, in turn, one then creates a new zonohedron based on the vertices of this rhombic enneacontahedron, the result is this 1230-faced polyhedron — a twice-zonohedrified dodecahedron. Included in its faces are thirty dodecagons, sixty hexagons, and sixty octagons, all of them equilateral.

Stella 4d: Polyhedron Navigator was used to perform these transformations, and to create the rotating images above. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.

Two Views of a Zonohedron with 3690 Faces

Posted on 8 December 2019 by RobertLovesPi

I used Stella 4d to make these images. You can try this program as a free trial download at http://www.software3d.com/Stella.php.

Six Rotating Polyhedra, in Christmas Colors, from the Stellation-Series of the Icosahedron/Dodecahedron Compound

Posted on 8 December 2019 by RobertLovesPi

These .gifs were made using Stella 4d: Polyhedron Navigator, software you can try for free right here.

Two Symmetrohedra Featuring Decagons

Posted on 7 December 2019 by RobertLovesPi

Symmetrohedra are polyhedra which have some form of polyhedral symmetry, as well as having regular polygons for many (not necessarily all) of their faces. I found these two symmetrohedra while playing around with Stella 4d: Polyhedron Navigator — a program you can try for free at this website. Each of these symmetrohedra have 74 faces, with twelve of them being regular decagons.