# DeePolygons!!

Geometry always fascinates me!

When I was in school, my Math (Geometry) teacher taught us to draw a circle around triangle, square, pentagon, hexagon, heptagon and octagon. Initially, I found it’s difficult to draw an odd no. sides shapes, but practice made me achieve. But I had a curiosity of these shapes; there will be infinite sides in the polygons till it becomes a circle. The teacher taught us that circle is not a polygon, It is made up of infinite sides and it has no corners (I never got a straight answer on it).

I sketched a circle around an equilateral triangle, then square around it, circle-pentagon, circle-hexagon, circle-heptagon, octagon,… till sept-decagon (all intersecting each other). I found an interesting pattern out of it which gives a visibility of a sphere. I cloned it and rotated upside down.

After intersecting these equilateral polygons ‘Hexagram’ formed in the center. But, what if I do it either way around. I placed circles and polygons inside this triangle one by one same as above. (see below figure)

Hexagram is called as a ‘Mandala’/ ‘Sadkona Yantra’ found on ancient South Indian Hindu temples. It symbolizes ‘Nar-narayana’ or perfect meditative state of balance achieved between Man and God.

“The downward triangle symbolizes Shakti, the sacred embodiment of femininity, and the upward triangle symbolizes Shiva, or Agni-tattva, representing the focused aspects of masculinity. The mystical union of the two triangles represents Creation, occurring through the divine union of male and female. The two locked triangles are also known as ‘Shanmukha’ — the six-faced, representing the six faces of Shiva & Shakti’s progeny Karthikeya. This symbol is also a part of several yantras and has deep significance in Hindu ritual worship and history.” (courtesy: Wikipedia, Hindu-temples)

I started exploring polygons, like.. variations in geometry, by seeing them in nature, drawing patterns, their applications design etc. There are lots of types of polygons & characterized by regular, simple, convex, concave, equilateral, equiangular, etc.

(Below drawings to understand variety)

But, what if I start creating patterns on my own. Even if many people have worked on it, still more work has to be done. Because there are infinite possibilities to explore polygons. Followings are my practices & efforts of making patterns out of them. Trying to achieve a balance between complexity and the simplicity.

I’m also understanding 3-dimensional forms of polygons, called as ‘Polyhydrons’, below is the one which I explored in a paper.

More work is to be done & I’m willing to do intricate and detailed formations. (Check my work on www.deeyaa.com).