One Dozen Icosahedra

Posted on 13 October 2018 by RobertLovesPi

A dozen icosas

I made this using Stella 4d, software you can try for yourself right here.

Tessellation of Rhombi and Tetraconcave Octagons

Image

tessellation of rhombi and tetraconcave octagons

A Radial Tessellation Using Three Types of Rhombi

Posted on 13 October 2018 by RobertLovesPi

radial tessellation using three types of rhombi

The yellow rhombi have angles of 40 and 140 degrees, while the blue rhombi have angles of 80 and 100 degrees, just like in the last post here. However, that post did not include the red rhombi, which have angles of 60 and 120 degrees.

A Radial Tessellation Using Two Types of Rhombi

Posted on 13 October 2018 by RobertLovesPi

radial tessellation using two types of rhombi

The yellow rhombi have angles which measure 40 and 140 degrees, while the blue rhombi’s angles measure 80 and 100 degrees.

A Zonohedron with 1382 Faces, Based on the Rhombicosidodecahedron

Posted on 13 October 2018 by RobertLovesPi

This zonohedron was formed from zones based on the faces, edges, and vertices of a rhombicosidodecahedron. The first image shows it colored by face type.

The second image has the faces colored by number of sides.

Finally, here’s one in “rainbow color mode.”

These images were all formed using Stella 4d: Polyhedron Navigator, which you can try for free right here.

Four Different Faceted Versions of the Rhombicosidodecahedron

Posted on 7 October 2018 by RobertLovesPi

Faceted Rhombicosidodeca 2

Faceted Rhombicosidodeca 3

Faceted Rhombicosidodeca 4

Faceted Rhombicosidodeca

I made these using Stella 4d: Polyhedron Navigator, software you can try for yourself, free, right here.

Cluster of 31 Rhombic Triacontahedra

Posted on 6 October 2018 by RobertLovesPi

There’s one rhombic triacontahedron in the center of this cluster, with more attached to each of its thirty faces, one per face. In this one, the colors are chosen by the placement of the faces in the overall cluster.

Augmented Rhombic Triaconta

The one below is shown in “rainbow color mode.”

Augmented Rhombic Triaconta rainbow

Both of these images were created using Stella 4d: Polyhedron Navigator, software you may try for free right here.

A Compound of Three Trapezohedra

Posted on 30 September 2018 by RobertLovesPi

I came across this little beauty while exploring stellations of the triakis octahedron, which is the dual of the truncated cube. Its three components are each eight-faced trapezohedra, and it showed up as the sixth in that stellation-series.

compound of three trapezohedra.gif

Stella 4d: Polyhedron Navigator was used to make this rotating image. You may try it for free right here.

Space-Filling Truncated Octahedra in a Rhombic Dodecahedral Cluster

Posted on 30 September 2018 by RobertLovesPi

The truncated octahedron is well-known as the only Archimedean solid which can fill space, by itself, without leaving any gaps. The cluster below shows this, and has the overall shape of a rhombic dodecahedron.