rhombic patch

Sometimes reasoning about balloon twisting patterns can have interesting non-balloon results.  In this case, I was thinking about a rhombic triacontahedron--a ball that has a surface of 30 identical rhombi.  Doodling 3D things on paper can be tricky so I normally flatten them to 2D by distorting the shapes but keeping the connections (unlike a net this is like a stereographic projection putting usually one face as the perimeter of the rest: here the outer curvy lines represent one rhombus).   From a doodle in Notablity (I like this iPad app's grid), I  created some interesting incidental patterns that may suggest cubes etc.  Since I was in Kathmandu, where there are a lot of T-shirt embroidery folk, I got them to stitch this up for me for less than $10.  I really like the colouring of the regions.  I may give it some more thought but I'm happy for now.

The pattern that you can look for is the alternating of vertices with degree 5 and vertices with degree 3.  Precisely, every degree 3 vertex (where three black lines meet) is surrounded by degree 5 vertices and vice versa.

Perhaps, I'll post the original pattern as well.

BTW, here is an example of a rhombic triacontahedron:

Heptagons and Triangle mix

I have played with this style of pattern before.  It is reminiscent of "lots of legs".  This one is related to a triangular grid.  It's a bit convoluted connection though.  The purple triangles connected to three heptagons are what I focus on.  

I'm not sure if this pattern is worth putting some effort into....

Jazzing up old designs

I'm playing around with gimp (a photoshop-like tool) to add some fullness to my designs.  It's nice to have a better selection of colours and gradients. With the broccoli picture above, I like the way the curves lines contrast the hard edges of the pentagons. I need to update PolygonRnD to give me higher resolution on the small pentagons. Originally when I made the software, I did not allow for changing scale so there was no need to output more than 3 decimal places for the coordinates...now I have to go back and fix it.  I'll get around to it eventually.

Here, I just played with gradients and shading outside the pattern. I like the warm colours as well as the blending of the types of pentagons.  I posted paper versions of this in my office with the hopes of capturing some young minds in the patterns.

2 balloon decorative truncated tetrahedron

I've been playing around with a few balloon patterns that have odd degree vertices.  Lately, I revisited the doubling up the edges approach.  Here's my latest pattern.  The notation is a bit cryptic but. The pink strokes indicate where a connection has to be made. The big numbers mean  big bubbles and the small numbers mean 1 inch bubbles.

Probably this would make an OK flower vase--it has three points of contact which is good for balance. This is a view from the top. I'll probably make a youtube vid on this.

more flowers

Here's a simple pattern made with a 3 pentagon 2 square spacers.  Take away the spacers and you end up with a very dull triangular grid.  Since there is so much white space the bright colours seem to work without being over powering.

another bug

This pattern is a bit of a revisit of X bug from Jan 2008. I like the chevrons and the gear like aspect. Does seem a bit spread out though.  I'll play some more to see if there is something worth looking at.

Squared Triangle...

I liked this quote.


“Jokes of the proper kind, properly told, can do more to enlighten questions of politics, philosophy, and literature than any number of dull arguments.” 
― Isaac Asimov


I tried to come up with a polygon joke but this is the best I could come up with.  I guess I should stick with dull arguments.



It's not any funnier going the other way...