mathematical art | RobertLovesPi.net

Pulsating Cuboctahedron, Featuring Enneagrammic Mandalas

The enneagramic mandalas on the square faces of this cuboctahedron are from the last post, with inverted-color, smaller versions of the same image on the triangular faces. These mandalas were created using Geometer’s Sketchpad and MS-Paint. Projecting them onto the faces of the cuboctahedron, and then creating this rotating, pulsating .gif image, however, took a third program: Stella 4d, which you can buy, or try for free, at http://www.software3d.com/Stella.php.

Ten Enneagrams

Image

These enneagrams are of the {9/3} variety, which means each one is made of three concentric, equilateral triangles. One of these enneagrams is at the center; the other nine surround it.

Various Colorings of a Enneagon-Centered Mandala

Image

Various Colorings of a Enneagon-Centered Mandala

The rest will each get bigger if you click on them.

A Rhombic Dodecahedron, Decorated with Rippled Tessellations

Image

A Rhombic Dodecahedron, Decorated with Rippled Tessellations

The decorations on each face were created using the design, made using Geometer’s Sketchpad and MS_Paint, shown here. I then used Stella 4d, available at this website, to project this flat image onto each face of this polyhedron, and make this rotating image.

A Pentagonal Icositetrahedron, Decorated with Rippled Tessellations, Along with Its Compound with Its Own Mirror-Image

Image

A Pentagonal Icositetrahedron, Decorated with Rippled Tessellations

The decorations on each face were created using the design, made using Geometer’s Sketchpad and MS_Paint, from this post: https://robertlovespi.wordpress.com/2014/05/28/rippling-tessellation-using-squares-regular-octagons-and-octaconcave-equilateral-hexadecagons/. I then used Stella 4d, available at http://www.software3d.com/Stella.php, to project this flat image onto each face of this chiral polyhedron, the dual of the snub cube, and make this rotating image.

Next, I used Stella to add this figure to its own mirror-image, to make a compound — something that is always possible with chiral polyhedra. Here is the result.