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.

A Polyhedron with Isosceles Trapezoids and Regular Pentagons as Faces

Posted on 16 January 2019 by RobertLovesPi

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

Seeing Red

Posted on 15 January 2019 by RobertLovesPi

These vandalized goggles were found in my science lab at school yesterday. When I tried them on, they literally had me seeing red.

A Non-Convex, Pyritohedral Dodecahedron with Non-Convex Pentagonal Faces

Posted on 13 January 2019 by RobertLovesPi

I created this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. Starting with the Platonic dodecahedron, I dropped the symmetry of the model down from icosahedral to tetrahedral, then stellated it six times. I also put the resulting polyhedron into “rainbow color mode” before making this .gif image.

Here’s a net for this solid. To build it, you’ll need six copies of this net.

My 2019 Birthday Star

Posted on 12 January 2019 by RobertLovesPi

I was born 51 years ago today. To mark the occasion, here’s a 51-pointed star. It’s made of {17/7} heptadecagrams repeated 3 times, and with their edges extended as lines, in three different colors. This works because 51 = (17)(3).

A 50-Faced Symmetrohedron with Cuboctahedral Symmetry

Posted on 6 January 2019 by RobertLovesPi

This image was created using Stella 4d, software you may try for yourself (for free) at http://www.software3d.com/Stella.php.

In this symmetrohedron, the red, blue, and green faces are regular polygons. Only the yellow isosceles trapezoids are irregular.

Zonohedra Based on the Pentagonal Dipyramid

Posted on 6 January 2019 by RobertLovesPi

Here’s a pentagonal dipyramid. It’s one of the Johnson solids.

The polyhedra-manipulation software I use, Stella 4d (available as a free trial download right here), lets the user make zonohedra from various “seed” polyhedra. When I made one with zones based on the vertices of the pentagonal dipyramid, a decagonal prism was the result. This surprised me; I wasn’t expecting to see a familiar polyhedron.

Other selections gave me the results I expected: polar zonohedra I had never seen before. Here’s the one based on the edges of the pentagonal dipyramid.

The next one is based on the pentagonal dipyramid’s faces.

Here’s one based on vertices and edges:

This next one is based on vertices and faces.

The next one is based on edges and faces.

Finally, here’s the last one, with zones based on the faces, edges, and vertices of a pentagonal dipyramid.

A Symmetrohedron with Tetrahedral Symmetry

Posted on 5 January 2019 by RobertLovesPi

Symmetrohedra are symmetrical, convex polyhedra which contain many faces (not necessarily all) which are regular polygons. In this symmetrohedron, the hexagons and triangles are regular, while the quadrilaterals are isosceles trapezoids. I made this symmetrohedron using Stella 4d, a program you can try for free at this website.

symmetrohedron featuring 10 reg hexagons and 4 eqtriangles and 12 isos traps

A Compound of a Slightly-Truncated Icosahedron and the Rhombic Triacontahedron

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41 Dodecahedra

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Created using *Stella 4d*, which can be tried for free at http://www.software3d.com/Stella.php.

Stellar Array

Posted on 2 January 2019 by RobertLovesPi

A great dodecahedron (red) sits in the middle of this polyhedral cluster. The polyhedra touching the one in the center are blue small stellated dodecahedra. Finally, there are yellow great stellated dodecahedra on the outside.

I assembled this polyhedral cluster using Stella 4d, which you can try for yourself at http://www.software3d.com/Stella.php.