# A Euclidean Construction of a Regular Triacontagon

Steps of this construction:

1. Use the green circles and blue lines to construct the yellow pentagon, along with its green inscribed pentagram.
2. Construct the equilateral triangle shown in gray. This is needed to obtain a twelve degree angle. The triangle is needed for its sixty degree angle, because 72 – 60 = 12. (The 72 degree angle is found inside the pentagon.)
3. Identify the twelve degree angle shown in bold. A twelve degree angle is needed because 360 / 30 = 12.
4. Use the red circles to complete the thirty sides of the regular triacontagon, which is shown with bold black segments, inscribed inside a large, bold, red circle.

## Tessellation Using Regular Triacontagons, Isosceles Triangles, Equiangular Triangles, and Isosceles Trapezoids

### Image

Little blurbs about posts on this blog get auto-tweeted on my Twitter, @RobertLovesPi. There’s also an A.I. on Twitter, @Hexagonbot, who retweeted my last two tweets about blog-posts here, but will not be retweeting the tweet about this one.

Why is this? Simple: @Hexagonbot is programmed to retweet any tweet which contains the word “hexagon,” which was in the titles of the last two posts here (also tessellations). This tessellation has no hexagons, though, and so the @Hexagonbot will not find it worthy of attention.

I cannot explain why hexagons get their own bot on Twitter, but other polygons do not have such bots. It’s simply one of the mysteries of the Internet.