Square and Triangle Sunburst

I was attracted to this pattern because it's simple shapes lead to an interesting structure.  Like similar patterns, this one can be constructed with easily understandable wedges.  In this case, there are 12 wedges that are connected to the central dodecagon (comprised of the hexagon, 6 triangles, and 6 squares).  Each narrow wedge is constructed from alternating layers of triangles and squares.  One way to spot a wedge is to look for the squares with the same orientation.  I chose to include the layer with 4 squares to make the wedge construction clearer.

Perhaps, it best as a polygon doodle (in Tileland).  Breaking the patterns can be as much fun as making them...

Paths of Heptagons and Triangles

Here's some paths that have alternating heptagons and triangles. It's related to heptagon flowers. It looks a lot more jumbled than these flowers. This is probably due to the rotational symmetry that seems more arbitrary.

There are three local patterns that are replicated again and again with the same orientation: the large pin-wheel, the three chevrons cluster, and the propeller that has mirror symmetry.  By focusing on each of these local patterns, you can see that each pattern is arranged in a triangular lattice with a two neighbouring triangles forming pattern's fundamental region--the smallest region that can be replicated by affine transformations to recreate the whole pattern.

It's a bit mesmerising. 

heptagons bugging out

Lots of twists with this pattern of heptagons and squares.  There are two squares that ended up having to be removed since they were overlapping but you may still be able to spot the 90 degree angles.

The bug pattern is new.  I had a bug pattern a while ago that used 6 heptagons but this one is very different.  One easy way to see the difference is that the bug is surrounded by 8 heptagons.  The other one also used triangles.

Maybe it would better viewed from the side...

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.