The Fitful Flog

October 1, 2006

How to Make a Heptagon from a Circle

Heptagon from a Circle

So, I was after thinking, early one morning, that I had really ought to get back to that chrysanthemum model, being as there’s a big chysanthemum festival going on somewheres, but then I thought, it’s such a pain to make hexakaidecagons. What if I made them from squares and just folded the excess in? Hmm, I reflected, this would make the purists happy.

But you know, I can’t stand to make purists happy. Never could – sheer native cussedness. Melchior, the Oafish Brothercc of Casper the Friendly Ghost™ floated by around then and suggested that as the hexakaidecagon is almost a circle, I could just use a circle and really annoy the purists. Brilliant! I cried and immediately went on to do something else. (Did I mention my little problem with cussedness? Makes the bedstead psychomachia pale by comparison.)

First, I made pentagons from circles – puzzling at first, but then I remembered that anything that can be done with compass and straightedge can be done with paper. Bing, bang, badada, boom.

But heptagons, that was a challenge. They’re not constructible using traditional methods, though there are ways. Then, in the library, leafing through Miranda Lundy’s Sacred Geometry, I noticed she had a kickass method for estimating the angles. A little work and we were on our way to a seven pointed twist star that I thought very pretty.

Seven Pointed Twist Star

Here’s the sequenced crease pattern for making the heptagon and here’s an unimproved CP for making a seven pointed twist star. But just about anything you make out of a heptagon is going to be pretty.

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11 Responses to “How to Make a Heptagon from a Circle”

  1. 1
    Mélisande Says:

    At the Uffizi museum in Firenze there is a special exhibition about Leonardo da Vinci. I saw there a small video on the famous drawing of the vitruvian man in which they said the distance between the feet was the edge of a heptagon. But it wasn’t explained why.

    I wonder if your construction of heptagon, or the methods you read in the Sacred Geometry book, have some similarities with this drawing ?

  2. 2
    oschene Says:

    Ah, I thought you might be back – did you have a good time?

    From what I can read, Vitruvius left a list of proportions that the human body supposedly met, rule-of-thumb stuff you still hear in art classes. The heptagon fascinated people because it was so hard to construct, I think.

    There’s some nice reading on the subject here

  3. 3
    christine Says:

    Sickness. This has brought back a high school science fair project that brought me no distinction, but much disdain “Tiling a Plane With a Septagon and Polygons.” My project was exploratory and I created a whole bunch of tilings from septagons and polygons obtained from connecting the vertices and cutting out various shapes. Dang it I was a geek. No good answer to the question/statement “This project has no purpose does it?” My answer “If nothing else it would make a pretty bathroom floor.” Judges were clearly not interior designers.

  4. 4
    Rosemary Browne / Canada Says:

    Hello Phillip!

    I stumbled across your site today. In a word: WOW!!!! I love your motto: It is not origami until it is shared. Have you a book, particularily on boxes? I would like to attempt the Frangipani Box. Could you lend a little dialogue to get me going?

    Tnak you in advance for writing back.


  5. 5
    oschene Says:

    A pretty bathroom floor is not to be despised, Christine. Whereas, several of my high school and college instructors should be. My high school geometry teacher found my fascination with origami and polyhedra laughable. I see from his web page that he now uses both to teach with.

    Rosemary, I don’t have any books so far – much study is a weariness of the flesh. Though my friend, Eric, is having such a good time writing one that I’m giving the matter some thought. I will be diagramming a similar and simpler model this weekend, maybe, and this should get you started on the Frangipani box. It’s been pointed out to me, it’s not an easy model.

  6. 6
    Paul Says:

    you can’t do a heptagon like that. it’s wrong.. it’t not a heptagon..

  7. 7
    oschene Says:

    Indeed, sir, I can do anything I like.

    It is a heptagon — what it isn’t is totally accurate and the blog entry says so. It is, however, accurate enough for most applications. Try one and see.

  8. 8
    zografis Says:

    You ROCK — I’m not using it for origamy, but for another type of art project . . . but this it the best heptagon on the web!!! and I LOVE the 7-pointed twist star and it is giving me an awesmoe creative kick just looking at it. Thank you SO much!!!!!

  9. 9
    Roxanne Says:


    in your model on How to make a decagon, what is the size of the sheet you start with ? A A4 or a US size. Thank you!

  10. 10
    Rasmine Says:

    I never thought something like that method before..!! but i don’t know if my Mechanical Drafting will accept that kind of heptagon…. BUT IT’S REALLY HELPFUL..!! THANKS!

  11. 11
    Rasmine Says:

    i mean mechanical drafting teacher

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