16 | June | 2014 | RobertLovesPi.net

Three Similar Tessellations

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Three Similar Tessellations

You can click on the smaller ones, if you wish, to make them larger.

My New Spider Tattoo

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My New Spider Tattoo

I just got a new tattoo on my right wrist, and got it as the Golden Lotus Tattoo Shop in Sherwood, Arkansas. Kendal Harkey is the tattoo artist who created this tattoo.

Since this was cover-work, I simply asked Kendal to do a Google-image-search for “spider,” then pick which one would best work best for that purpose. Here’s what he selected:

I’m now left with a puzzle: I tried to find this same image with Google, but couldn’t . . . and I want to know what kind of spider this is! If you recognize it, or find it on-line, please leave its scientific name in a comment here.

[Update: I found the source on Google, at http://coloringhub.com/dangerous-spider-coloring-pages/spider-picture/ — but it’s a drawing, not a photograph, and so it may or not be a drawing of a real spider species . . . so I still need assistance, if anyone else knows more details.]

Tetrakaiicosagon with Diagonals

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Tetrakaiicosagon with Diagonals

How many diagonals does a polygon with 24 sides have?

First, consider that there are 24 vertices for diagonals to come from, and they each have 21 places to go, since they can’t go to themselves, or to the adjacent vertices. (24)(21) therefore equals twice the number of diagonals, since I just counted each one twice (once per endpoint). There are therefore (24)(21)/2 = 252 diagonals.

A Rhombic Triacontahedron with Tessellated Faces

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A Rhombic Triacontahedron with Tessellated Faces

The faces of this polyhedron all have the same tessellation projected on them, but with five different coloring schemes. These five different tessellations appear in non-moving form in the last post on this blog, and I used Geometer’s Sketchpad and MS-Paint to make them. Stella 4d, another program, was then used to put the whole thing together, and it may be tried for free at http://www.software3d.com/Stella.php.

Five Versions of a Tessellation Using Squares and Equilateral Triangles

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Tessellation Using Squares and Triangles

I used four other color-schemes with this same tessellation, and those other images are shown below.

The Truncated Truncated Icosahedron

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The Truncated Truncated Icosahedron

The icosahedron has twenty triangular faces. Truncate it once, and the triangles become hexagons, with pentagons appearing under the pyramids removed in the truncation. This is the “soccer ball” shape familiar to millions.

If you take this figure and truncate it again, the twenty hexagons become twenty dodecagons, the twelve pentagons each become decagons, and sixty isosceles triangles appear under the pyramids removed by this second truncation.

I made this image using Stella 4d, a program you can find at www.software3d.com/Stella.php. Also, just for fun, here’s a version of it with the colors switched around, and with a slight bounce as it rotates in the other direction.

Three Stellations of the Icosidodecahedron

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Three Stellations of the Icosidodecahedron

The icosidodecahedron’s 24th stellation is above, and the 32nd, then the 36th, are below.

I made these images using Stella 4d, a program you can find at www.software3d.com/Stella.php.

The Rhombic Dodecahedron’s Third Stellation

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The Rhombic Dodecahedron's Third Stellation

Above is this polyhedral stellation in three colors. If every face is given its own color, though, except for parallel faces, it looks like this (click to enlarge):