About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my own little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

Tetrahedrally-Symmetric Creatures with Polyhedral Legs

Posted on 23 November 2016 by RobertLovesPi

Each of these has a tetrahedron hidden from view in the center.

augmented-tetra

augmented-tetra-2

augmented-tetra-3

augmented-tetra-4

These were made using Stella 4d, which you may try for yourself here.

A Crinkled Octahedron

Posted on 22 November 2016 by RobertLovesPi

unnamedmnmn-octahedral

“Crinkled” is merely descriptive; I offer no mathematical definition of the term. This was a polyhedron I stumbled along while doing random-walk polyhedral manipulations with Stella 4d, available at this website.

The Compound of the Rhombic Dodecahedron and Its Own Third Stellation

Image

compound-of-rd-plus-stellation-of-rd

I used Stella 4d to make this polyhedral compound, and this program may be tried for free at this website.

Shield Mandala

Image

shield-mandala

The Dodecahedron, Made from Smaller Polyhedra

Posted on 14 November 2016 by RobertLovesPi

augmented-rhombic-triaconta-dodeca

The polyhedra at the vertices are rhombic triacontahedra, and the yellow edges are elongated rhombic prisms. This was made using Stella 4d, software you may try for free at this website.

An Icosahedron, Constructed from Smaller Polyhedra

Posted on 13 November 2016 by RobertLovesPi

Augmented Rhombic Triaconta.gif

The polyhedra at the vertices are rhombic triacontahedra, and the yellow edges are elongated rhombic prisms. This was made using Stella 4d, software you may try for free at this website.

Three Views of a Rotating Cluster of 33 Icosidodecahedra

Posted on 12 November 2016 by RobertLovesPi

33-icosidodeca

To make these three rotating cluster-polyhedra, I started with one icosidodecahedron in the center, then augmented each of its 32 faces with overlapping, additional icosidodecahedra, for a total of 33 icosidodecahedra per cluster. In the first image, only two colors are used: one for the triangular faces, and another for the pentagons. The second version, however, has the colors assigned by face-type, which is determined by each face’s placement in the overall cluster.

33-icosidodeca-ft

For the third version, I simply put Stella 4d (the program I use to make these images) into “rainbow color mode.” If you’d like to give Stella 4d a try, you can do so for free at this website.

33-icosidodeca-rc