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.

Circles and Lines

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circles and lines

Two Lines and Many Circles

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op art

Seven Rainbow Polyhedra

Posted on 22 October 2017 by RobertLovesPi

These were made using Stella 4d, which may be tried for free at http://www.software3d.com/Stella.php.

Two Polyhedra Featuring Regular Pentadecagons

Posted on 21 October 2017 by RobertLovesPi

42.5 vertex angles in yellow triangles

This polyhedron has 92 faces: twelve regular pentadecagons, twenty equilateral triangles, and sixty isosceles triangles, each with a vertex angle of ~42.5°. Its first stellation appears below.

yellow triangle vertex angle is 42p5 degrees stellation 1

Both models were created using Stella 4d, software you can try for yourself at http://www.software3d.com/Stella.php.

The Moon Unit Proposal

Posted on 19 October 2017 by RobertLovesPi

moon unit

I propose that 384,400 km (238,855 miles), the average distance from the Earth to the Moon, be called a “moon unit.” Example: “The mileage of my car is over one moon unit.”

Four Polyhedra Featuring Enneagons

Posted on 17 October 2017 by RobertLovesPi

enneagons and octagons

enneagons and kites

octagons enneagons bowtie trapezoids

Dual of Convex hull

Enneagons are also called nonagons; they are polygons with nine sides. I used Stella 4d to make these four rotating polyhedra, and you may try this program for yourself at http://www.software3d.com/Stella.php.

Throwing Star Tessellation

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Tessellation of Blue Triangles and Yellow Concave Pentagons

Posted on 8 October 2017 by RobertLovesPi

triangles and pentagons

Alternately, this can be seen as a tessellation of blue diconcave hexagons and yellow triconcave enneagons. Which do you see?

The C-320 Fullerene Polyhedron

Posted on 7 October 2017 by RobertLovesPi

The duals of the geodesic domes are polyhedra with hexagonal and pentagonal faces. This particular one has 320 vertices, with those vertices representing carbon atoms in the molecular version of this solid. Here is C₃₂₀ as a polyhedron.

The next image shows this molecule as a ball-and-stick model.

Finally, here it is as a space-filling molecular model.

All three images were created with Stella 4d: Polyhedron Navigator. This is the page to visit if you want to try Stella for yourself: http://www.software3d.com/Stella.php.