Blog Archives

The Great Rhombcuboctahedron As a Building-Block

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The Great Rhombcuboctahedron As a Building-Block

This solid, also known as the great rhombicuboctahedron, and the truncated icosidodecahedron, can be used to build many other things. In addition to the elongated ring of eight above, for example, there’s this octagonal prism.

Augmented Trunc Cubocta2

Augmented Trunc Cubocta 2

Remember the elongated ring at the top of this post? This pic, directly above, is of a ring of four of those rings.

Augmented Trunc Cubocta3

And, yes, that’s a (non-great) rhombcuboctahedron made of great rhombcuboctahedra. Here it is again, with a different color-scheme.

Augmented Trunc Cubocta4

For the last of these constructions, eight more great rhombcuboctahedra are added to the figure in the two posts above, which is also returned to its original color-configuration. These eight new polyhedra have positions which correspond to the corners of a cube.

augmented rhombcuboctahedron made of great rhombcuboctahedra

Manipulating polyhedra in this manner is easy with Stella 4d, the program I used to do all of this. You may buy it, and/or try a free trial version first, at www.software3d.com/Stella.php.

My Students’ Painting of the Periodic Table of the Elements

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My Students' Painting of the Periodic Table of the Elements

This is my last year teaching at my current school — I’ll be transferring to another school in the same district in the Fall. To create a farewell gift to the school where I have taught for the last three years, I brought a lot of paint and other art supplies from home, bought more when they ran out, and let my students (who are enrolled in Chemistry and Physical Science) paint a large painting of the periodic table on two large wooden boards, each measuring 4′ by 6′. In the Fall, the plan is for the painting to be mounted on the wall of the science wing of my current school, in a location to be chosen by my current department chair, a personal friend of mine.

I think my students did a very good job — better than this picture I took with my cell phone reveals, just due to camera-quality. I am proud of them.

The Royal Octahedron, with Half-a-Dozen Crowns

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The Royal Octahedron, with Half-a-Dozen Crowns

Software credit: see http://www.software3d.com/Stella.php to check out Stella 4d, the program I used to make this. A free trial download is available.

Seventeen Truncated Tetrahedra Rotating in Symmetrical Formation

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Seventeen Truncated Tetrahedra in Symmetrical Formation

Software credit: you can try the free trial download of Stella 4d at http://www.software3d.com/Stella.php.

Eight Hexagons, Rotating with Six Tetrastars

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Eight Hexagons, Rotating with Six Tetrastars

Software credit:  see http://www.software3d.com/Stella.php for more information on Stella 4d, the program I used to make this. A free trial download is available.

Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons II

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← Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons II

Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

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Rippling Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

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Tessellation Using Squares, Regular Octagons, and Octaconcave, Equilateral Hexadecagons

Five Polyhedron-Inspired, Rotating Images of Many Colors

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Four Polyhedron-Inspired, Rotating Images of Many Colors

The three images below appear smaller than the one above, at first, but can be enlarged with a single click.

dual of Augmented Dodeca

These were all created using Stella 4d: Polyhedron Navigator. You can try or buy this software at http://www.software3d.com/Stella.php.

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In case you’re wondering, I’m simply calling these polyhedron-inspired images, rather than actual polyhedra, because of the holes in most of them. With the software I use to make these, creating these empty spaces is simply a matter of selecting faces, and then hiding them from view.

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For this last one, just for fun, I made the vertices visible — even those where hidden faces touch. The idea was to create a snow-like effect.

Zonohedrified Convex hull

Three Polyhedra Which Feature Regular Pentadecagons

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Some Polyhedra Which Feature Regular Pentadecagons

I haven’t encountered many polyhedra which feature regular pentadecagons, and geometry textbooks generally don’t even use that word, calling them “15-gons,” instead. The pentadecagon happens to be one of my favorite polygons, though, and has been ever since I independently figured out, a few years back, how to duplicate the ancient Greeks’ accomplishment of combining the Euclidean constructions for the regular pentagon and equilateral triangle, in order to construct a regular pentadecagon.

15Unnamed

The one above also includes regular decagons as faces — but I had to let the pentadecagons intersect each other to get that to work.

Co15nvex hull

This third polyhedron resembles a truncated icosahedron, but with pentadecagons replacing that solid’s twenty hexagons. The pentagons are still in place, with two types of trapezoid and some very thin rectangles needed to fill the gaps.

These images were all created using Stella 4d, software you may try or buy at http://www.software3d.com/Stella.php.