Mr. Trump, Please Get Some Sleep


Sleep is essential for good mental and physical health. It helps us heal when we need healing. I went to bed very early last night, and got all the sleep I need to do well at work today. I wish to suggest to our president that he do the same.

At least eight hours of sleep a night is healthy and helpful. Also, especially for a man in his seventies who is under a great deal of stress, long naps during the day can be a literal life-saver. In Mr. Trump’s case, the number of lives saved can be very large indeed.

To free up time for sleep, I have one more piece of advice for the president: limit yourself to one tweet per day.

A Tessellation Using Regular Pentagons and Hexagons, As Well As Two Types of Concave Polygon


Without even checking, I know that my automatic tweet about this post (as @RobertLovesPi) will be retweeted by the @HexagonBot on Twitter. Why? Because @HexagonBot retweets any tweet containing the word “hexagon,” or “hexagons.” I have absolutely no idea why other polygons lack their own Twitterbots, though.

Craters and Slopes Near the South Pole of the Moon Adorn the Faces of a Rhombic Enneacontahedron

Zonohedrified Dodeca

The images on the faces of this polyhedron are based on information sent from NASA’s Lunar Reconnaisance Orbiter, as seen at and tweeted by @LRO_NASA, which has been happily tweeting about its fifth anniversary in a polar lunar orbit recently. I have no idea whether this is actually an A.I. onboard the LRO, or simply someone at NASA getting paid to have fun on Twitter.

To get these images from near the Lunar South Pole onto the faces of a rhombic enneacontahedron, and then create this rotating image, I used Stella 4d:  Polyhedron Navigator. There is no better tool available for polyhedral research. To check this program out for yourself, simply visit

Thirty Flying Hexagons


Sixty Flying Hexagons

When I tweet a link to this blog-post as @robertlovespi, it will likely be quickly retweeted by @hexagonbot, simply because of the term “hexagon” being included in the tweet. What I don’t understand: Why do other polygons not have bots of their own?

I used Stella 4d to make this image, and you can find that program at

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


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

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.