This pattern applies the concept of a five point star to heptagons. The five point star
can be constructed with a pentagon path that alternates a small turns to the right followed by a larger turns to the left. For heptagons, there are fourteen polygons instead ten. As well, the purple triangles and pentagons are added to the loop fourteen heptagons for decoration. I think that these extra polygons help bring out the symmetry.

Here's another unravelled loop. A graphical representation of the process of creation is below. A pentagon loop (two partial stars) is combined with two loops of six triangles. The two gaps between the adjacent red pentagons are not filled with triangles (notice that there was originally fourteen gaps in the original loop and only twelve triangles)--these gaps are filled with squares and that are decorated with purple pentagons to maintain the alternating colours.

* = ...

This one began as a simple loop of six pentagons that was turned inside-out using two loops of three pentagons. Afterwards to link those inside-out loops (which look perhaps like a toothy mouth) another loop was used--the original simple loop of six pentagons was elaborated with interlacing hexagon spacers (these loops inner hole look like the outlines of eights with a vertical javelin through it). Below, I included a wallpaper version of the pattern.

Sometimes it's the missing tiles that make things interesting. Here there are a number of missing heptagons. A missing heptagon makes each of the gentler curve between the three triangles. Including the heptagons would lead to many overlapping polygons. Perhaps there is an artful inclusion of a selection of the heptagons...

This is constructed by interleaving a loop of fourteen orange heptagons with a straight line of olive triangles. As well fourteen additional triangles decorate the inside and outside of the new loop.

Large symmetrical loops made with pentagons make this pattern interesting. In the inner loop, there are ten pentagons with ten square spacers that outline a twenty-sided regular (all angles and sides are the same) polygon. In the outer loop, there is a thirty-sided regular polygon which can be seen as the diagonals of the grey triangular pairs.

Some more play. This is based on a checker board design. The colours are not probably the best but the gaps are interesting. Like many patterns, this one started as a Tileland doodle and was later turned into a PolygonR&D program. Below I have included a larger section of the pattern to more easily see how the pattern repeats. The olive/brown polygon loop shows the basic unit for the pattern.