Two Polyhedra Featuring Regular Pentadecagons

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.

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The Moon Unit Proposal

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.”

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Four Polyhedra Featuring Enneagons

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.

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Throwing Star Tessellation

throwing star tessellation

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Tessellation of Triangles and Pentagons

triangles and pentagons

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

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The C-320 Fullerene Polyhedron

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. Here is C-320 as a polyhedron.

C320 Dual of Geodesic Icosa

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

C320 ball and stick.gif

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

C320 space filling.gif

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.

 

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The Construction of a Zome Model of a 240-Atom Fullerene Molecule, In Seven Pictures

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You can buy your own Zome at http://www.zometool.com.

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