I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my own little slice of the Internet.
The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.
The black polygons in this radial tessellation are regular decagons. The red figures are hourglass-shaped equilateral hexagons, which remind me of the distinctive red markings found on many black widow spiders.
Heptagons only appear infrequently in interesting polyhedra. I recently found a few that I like.
To form the first of these solids, shown above, I started with the icosidodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, and then stellated it twice using Stella 4d (available here). To obtain the model shown below, which also features heptagons and triangles, I stellated it once more. Both of these polyhedra have pyritohedral symmetry.
To form the next model shown, I began with an rhombicosidodecahedron, set it to tetrahedral symmetry, and stellated it eight times. This produces a chiral solid with tetrahedral symmetry.
For the last of these four polyhedra featuring heptagons, I began with the snub dodecahedron, dropped the symmetry of the model down from icosahedral to tetrahedral, and then stellated it sixty-one times. The resulting solid is chiral, with tetrahedral symmetry.
To make this polyhedron using Stella 4d (available here), I began with the dodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, and then stellated it thirteen times.
This stellated polyhedron has pyritohedral symmetry, but this is easier to see in its convex hull:
The eight blue triangles in this convex hull are equilateral, while the twelve yellow ones are golden isosceles triangles.
To make this polyhedron using Stella 4d (available here), one starts with the icosahedron, drops the symmetry of the model down from icosahedral to tetrahedral, and then stellates it once. The result is a chiral solid featuring four triangular faces and twelve kites:
The dual of this polyhedron, which is also chiral, has four triangular faces, and twelve faces which are isosceles trapezoids. It is a type of faceted dodecahedron — a partial faceting, meaning it is made without using all of the dodecahedron’s vertices.
I’d like to thank Richard, athttps://photosociology.wordpress.com/, for nominating me for the Liebster Award for blogging. It’s an honor to simply have someone choose to follow my blog, and I feel grateful every time I get a new follower, but this takes that feeling of being honored to a whole new level.
These are the guidelines for the 2018 Liebster award:
• Thank the person who nominated you • Display the award on your post • Write a small post about what makes you passionate about blogging • Provide 10 random facts about yourself • Answer the questions given to you • Nominate 5-11 other blogs for this award • Ask them creative and unique questions of your own • List the rules and inform your nominees of the award
What makes me passionate about blogging? Well, for as long as I can remember, I have been passionate about mathematics, to the point of obsession. Blogging gives me a way to record and share the results of that obsession. My blog isn’t 100% math, but mathematics-related posts outnumber everything else here by a wide margin, and it is my love of mathematics that keeps this blog going.
On to the ten random facts about myself . . .
I have Aspergers Syndrome, now officially known in the USA as high-functioning autism. I didn’t discover this until I was already in my 40s (I’m now 50), though, for which I am grateful. I see being an “Aspie” as a difference, not a disease, nor a disability.
I’m married to a wonderful woman; we celebrate our 4th wedding anniversary soon.
I’m a high school teacher. Next year will be my 24th year in the classroom. I mostly teach mathematics and the “mathy” sciences. My wife is a teacher as well; she teaches mathematics.
Strangely enough, both of my college degrees are in history. This generally puzzles people, but it’s easy enough to explain: I chose to major in something I didn’t yet know much about, and about which I was (and still am) curious. My experiences in elementary, junior high, and high school math classes were abysmal, and I didn’t care to continue that experience.
I’m not religious. The label I prefer is not “atheist” nor “agnostic,” though, but simply “skeptic.” This reflects the fact that I have two primary methods for determining what I consider to be true: mathematical proof, and the scientific method. Skepticism is essential for both.
I see my brain as an organic computer, and frequently work on re-writing my own software, usually while asleep. This is something I’ve blogged about before, as are most of the things in this list.
I started blogging on Tumblr, and came to WordPress a few years later, in 2012, to escape what I call Tumblr’s “reblogging-virus.”
My political orientation has changed over the years, and is now best captured by the term “anti-Trumpism.” I’ve also been known to call myself a “neo-Jeffersonian.”
I’m LGBTQ-friendly.
I’ve seen the fantastic band Murder By Death seven times. Here is a sample of their music, from one of their older albums. You can find much more about them athttp://www.murderbydeath.com.
Now I need to answer the questions which Richard has posed for me. I have a hunch my “Aspieness” will come out in some of these answers.
1. How straight is straight?
“For any two points, there is exactly one line which contains them.” This is a fundamental postulate of Euclidean geometry. Straightness is a characteristic of such lines.
2. What would you think I was referring to if I told you to ‘put it down’?
The contents of my hand(s), of course. If I wasn’t holding anything, I’d simply be confused, and would ask for clarification.
3. Why are swans graceful?
Swans have the characteristics they have because they evolved that way. It is human beings who have chosen to label some of those characteristics as “gracefulness.”
4. Would you be a superhero or a sidekick, and what would your name be?
I would do neither, for I have at times suffered from delusions that I had superpowers. I don’t want my mind to go there again. One example of this was a belief, years ago at a time of ridiculously high stress, that my emotional state could control the weather. If I start thinking I have superpowers again, I’ll immediately take the medication prescribed by my psychiatrist for just such an eventuality.
5. If you could remove one letter from the English alphabet, what would it be, and what consequences do you see coming from it?
I suppose I would choose the letter “c,” for the soft “c” can be replaced by the letter “s,” and the hard “c” by the letter “k.” I’m not sure what we’d do for the “ch” sound, though.
6. What was the last thing you lost and never found? What do you imagine has happened to it?
That’s my Social Security card, which I need to get replaced soon. I don’t have a clue what happened to it.
7. What significance does the number seven have to you? What memories do you associate with it?
I’ve blogged about the significance of the number seven, so I refer you to that post for the answer to this question. The only memory of the number seven I recall is when a friend of mine named Tony explained to me the ideas which later inspired that blog-post.
8. Young and completely broke or old and disgustingly rich?
Neither, by the standards of where I live (the USA). We’re middle-class. We live comfortably, but not extravagantly.
9. If a giant squirrel had commandeered your mode of transportation, whether car, moped, bike etc., and seemed to know how to make it work, what would you do to stop him?
I would assume this was a hallucination, and I would immediately take the medication I mentioned when I answered question #4, above.
10. If you had your own coat of arms, what would I expect to find on them to describe you/ your family?
Some of my ancestors were Scottish, and their clan already has a coat of arms, so I’d simply use it.
Next, here are my nominees for this award. These are all blogs I find interesting. I also deliberately chose blogs which are radically different from my own.
Now I need some questions for these fine bloggers to answer:
Do you see the current occupant of the White House as a problem? If so, what, if anything, are you doing about it?
How strong a role does mathematics play in your life?
Which of the sciences do you find most interesting, and why?
Of all the posts on your blog, which one do you think is your best work?
What food(s), if any, could you absolutely not give up for the rest of your life, even for $100,000?
What do you think of astrology?
That’s it! Thanks again to Richard for nominating me; I’m glad I took the time to write this acceptance-post. Also, congratulations to the five new nominees!
RobertLovesPi.net 