Hexagons have six sides

First off, I have to say how disappointed I’m feeling about this Cycle365 group and it’s questionable arithmetic skills.  I was sure that someone would point out that the feature photo of my latest post, A Pair of Pentagons, was actually a trapezoid, a four sided figure.  I knew this of course – five is one of the easier numbers to count up to, if you have human hands – but posted it as a test.  You all failed, and will have to skip recess for the next week to attend Integers 101.

Try to do better this time.  The featured photo, from our ride to Elgin, includes both pentagons and hexagons.  See if you can tell which is which!  Also, extra credit if anyone knows the name for the spherical object itself.

This is just a placeholder for now. I’ll add a real description when I get more time.

6 response to "Hexagons have six sides"

  1. By: NancyG Posted: January 9, 2021

    I don’t want to do math — I just want to ride my bike and take pictures.

  2. By: Rich-Illinois Posted: January 9, 2021

    Math? I printed up some 18 dollars bills and went to change them at the bank — they asked if I preferred 3 6’s or 2 9’s.

  3. By: The Navigator Posted: January 9, 2021

    I am totally with Nancy. I have to think too much at work so don’t want to think at all when it’s related to the bike!

  4. By: BobinVT Posted: January 10, 2021

    Scott, we trust you! We all just took you at your word. As to the shape in this post, I knew it was a thing, but I did have to look up the name, so no extra credit for me. Can I say it? Icosahedron.

  5. By: gregblood Posted: January 10, 2021

    I’m having a hard time counting all the sides so I’d just call it many-sided die. An expert in geometry, however, would study that structure for hours. Perhaps he would count 32 sides and proclaim it to be “the dreaded triacontadihedron.”

    • By: Scooter Posted: January 10, 2021

      Thanks! I’d forgotten the word for 3-D structures like this – polyhedrons. I looked up polyhedrons with both hexagons and pentagons, and see that there’s a whole family of these shapes, called ‘Goldberg polyhedrons’. The soccer ball is a rounded instance of these.

      Here’s a video discussing them: https://amara.org/en/videos/iG21idzX6cxS/en/2234272/. They’re interesting – regardless of how many surfaces there are in total, there are always exactly 8 pentagons. I think this is a ‘1-1’ Goldberg polyhedron, which has 42 faces.

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