Squares, Stars, and Icosagons

On the creative front, I've come up with some holiday patterns in InkScape to use as backgrounds for when I'm telecommuting to work or holiday events.  I started with a square, then I duplicated them so I had five, then rotated them 72 degrees and grouped them into star patterns.  The star groups are either pointed upward or downward.  

Pentagonal designs tend to fall into two categories:  five or ten rays radiating from a central point, or rings of alternating units.  

The first design I came up with starts with a upward pointing star group; each of its five edges are joined with the edges of a downward pointing star group, which forms a ring around the center; each of the ten free edges on the downward pointing star groups are joined with an upward star, forming another ring, and the whole design keeps repeating that way.  What's interesting to me is way almond-shaped gaps open up in the network of star groups.

For the second design I wanted more complete circles (actually bevelled decagons or icosagons).  The decagons can only hold three star groups at most, with the result that a decagon can only overlap with at most only two other decagons.   In addition to the almond-shaped gaps, packing the decagons together creates a boat- or T-shaped gap and also a star-shaped gap in the arrangement of star groups--I arranged star groups in a way that would favor the creation of complete decagons and star gaps. 

The third design is the second one, only zoomed out a little.  Since this is all done with pentagonal symmetry, the designs end up looking like zilij or Penrose tilings.  I suppose I should go back into InkScape and change the colors; red and green are traditional for the winter holidays, but a number of people have commented that the contrasting hues make them dizzy.