Bent Pent

This is a beautiful and interesting shape, reminiscent of a piece of jewellery:

Pentagons in a ring


I came across it in this tricky little word-puzzle:

Word puzzle using pentagon-ring


Here’s a printable version of the puzzle:

Printable puzzle


Let’s try placing some other regular polygons with s sides around regular polygons with s*2 sides:

Hexagonal ring of triangles


Octagonal ring of squares


Decagonal ring of pentagons


Dodecagonal ring of hexagons


Only regular pentagons fit perfectly, edge-to-edge, around a regular decagon. But all these polygonal-rings can be used to create interesting and beautiful fractals, as I hope to show in a future post.

The Hex Fractor

A regular hexagon can be divided into six equilateral triangles. An equilateral triangle can be divided into three more equilateral triangles and a regular hexagon. If you discard the three triangles and repeat, you create a fractal, like this:

hexring
Adjusting the sides of the internal hexagon creates new fractals:
hexring2
hexring1
Discarding a hexagon after each subdivision creates new shapes:

hexring4
hexring5
hexring6
And you can start with another regular polygon, divide it into triangles, then proceed with the hexagons:
hexring3