120 Flying Kites #1

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120 Flying Kites #1

Created with software you can try and/or buy at http://www.software3d.com.Stella.php.

Sunrise 2014

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Sunrise 2014

Drawn with Geometer’s Sketchpad, and based on the numbers four and seven.

150 Irregular Hexagons, Rotating About a Common Axis

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150 Irregular Hexagons, Rotating About a Common Axis

There are sixty of the irregaular, pentagonal gaps. Also, the hexagons themselves are of three types, two of which are sixty in number, and one of which is thirty in number.

If the gaps are filled, and the color scheme changed to make each of the four polygon-types into its own color-group, this looks, instead, like this (click on it if you wish to see it enlarged). It has 210 faces.

60pentagons and 60and60and30hexagons total faces 210

(Images created with Stella 4d — software you can try yourself at http://www.software3d.com/Stella.php.)

Spin

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Spin

Kryptonite

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Kryptonite

Software credit: see http://www.software3d.com/stella.php

My Wikipedia Userboxen Collection, Part V

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My Wikipedia Userboxen Collection, Part V

Finally: the last installment!

Triangles and Circles

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Triangles and Circles

Mostly Empty Space

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Mostly Empty Space

Ask any chemist or physicist, and they’ll verify that ordinary matter is mostly empty space. (The physicist may then go on to confuse you by explaining how that “empty” space isn’t really empty,  if inspected closely enough, but that’s not my subject here.)

This image, geometrically created, is also mostly empty space. To make it, I started with the polyhedron seen in the last post — itself created by stellation of the post before it — and continued stellating, many more times. By doing so, I stumbled across a polyhedron with these “X” shapes included, plus some other stuff. To finish making this, I simply rendered everything except the “X” shapes invisible, then changed the coloring scheme of the result.

Stella 4d was used to create this image, and you may try it for free at http://www.software3d.com/stella.php.

Concentric Pentagons, Pentagrams, and Circles

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Concentric Pentagons, Pentagrams, and Circles

Star 46

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Star 46

I started a personal tradition 43 years ago, on the day I turned three years old, of associating stars with my birthday. On that day, I looked up in the sky, and saw the three stars of Orion’s Belt: Alnitak, Alnilam, and Mintaka. Given that these three stars were bright, and formed a fairly straight line, and given that I was turning three that day, it seemed perfectly obvious that those three stars had been placed there, in the sky, specifically for me — and so, that day, I claimed them as my personal property. (No one has ever accused me of lacking ego, nor self-confidence.)

As a young child, the science that most fascinated me was astronomy. In more recent years, my interest in stars has become more focused on the geometrical figures called stars, or star polygons — and so, now, rather than looking for my birthday stars in the sky, I always use geometry to construct some star, or starlike pattern, based on the number of years I have survived, to date. This is the one for the number 46, my age as of today.