The Fitful Flog

July 4, 2006

How to Make A Regular Decagon (or Pentagon, Whatever) from a Square

Pentagonal Waterbomb

Both Eric and Eduardo were asking, how do you make accurate decagons out of a square?

Well, when I’m after accuracy, I draw a decagon in my creaking, ancient CorelDraw 8 install and print it out. But this lacks…authenticity. I’m way big on authenticity.

The method for making a decagon from a square is not difficult and is easily memorized. It is derived, I believe, from an old Japanese method, developed for a folk art called monkiri or crest-cutting. Monkiri involves folding paper in various ways and then cutting out designs in it. When unfolded, the cut paper reveals a surprising image, like an idealized cherry blossom or waves on water. American children do similar things to create snowflakes and paper dolls. The great folder, Bob Neale, once gave me a fascinating kid’s book on monkiri. It’s around here, somewhere.

Of course, once you have trapped the wily and elusive regular decagon, what do you do with it? Well, you could do something simple, like the above waterbomb – you-all know how to make a waterbomb, don’t you? Or, you could get all jiggy with it and make a Puff Star. Kind of up to you, the faithful reader.

The How to Make a Regular Decagon (or Pentagon, Whatever) from a Square file.

Later on — some more on monkiri

Whenever I use Google Language Tools on a Japanese site, I sing this Red Housepainters’ song,

it’s not that simple
this dictionary never has a word
for the way i’m feeling
it’s nothing plain for me
of a different god and moral
what if i laid my head down on your stomach
or put my mouth to your hand
i cannot translate
japanese to english
or english to japanese

Don’t get me wrong – Google provides me with that middle voice feeling, that sense of being on the wrong side of my brain, that I’ve come to expect from trying to put Japanese concepts into the American mind. It’s all good. Check it out:

The crest ardently the place

9 Responses to “How to Make A Regular Decagon (or Pentagon, Whatever) from a Square”

  1. 1
    Origami Tessellations - Decagon (or pentagon) creation instructions for origami folders Says:

    […] You can get the diagram instructions from his website. (As he pushes the limits of sane blog header lengths in the process. What a URL!) […]

  2. 2
    Lorenzo Marchi Says:

    Thank you for sharing this method, I’ve found also useful this method from Darren Abbey to n-sect a square that is a common thing in your designs!

  3. 3
    oschene Says:

    N-secting can be fun! Especially when you broaden the idea to rectangles.

    You also might want to check out:
    and Robert Lang’s excellent article:

  4. 4
    Mélisande Says:

    About later on :

    Google Translate et Babelfish sont peut-être les poètes surréalistes de notre temps.
    Chaque siècle a ce qu’il mérite…

  5. 5
    oschene Says:

    Hmm, that suggests that if we feed in Rimbaud, Google Translate and Babelfish would turn his work into symbolic logic of striking clarity.

    With black, E white, I red, U green, O blue: vowels,
    I will say some day your births latent:
    With, black hairy corset of the bright flies
    Who bombinent around the cruel stinks,
    Gulfs of shade; E, franknesses of the vapors and the tents,
    Lances of the proud glaciers, kings white, shivers the ombelles ones;
    I, crimsons, spit blood, laughter of the beautiful lips
    In penitent anger or intoxications;
    U, cycles, vibrements divine of the verdant seas,
    Peace of the sown rough grazings of animals, peace of the wrinkles
    That alchemy prints with the great studious faces;
    O, supreme Bugle full with the strange strideurs,
    Silences crossed of [Worlds and of the Angels]:
    – O the Omega, purple ray of [Its] Eyes! purple ray of [Its] Eyes!

  6. 6
    Mélisande Says:

    I’m not able to decide if it is more clear in english…
    I prefer the french original.
    Cultural bias, indeed.

    Since childhood, I see vowels in color when I’m reading, but not the same as above :
    A blue, E grey, I yellow, O red and U green.

  7. 7
    oschene Says:

    I have a similar feeling with certain songs – some sequences of harmonies taste like tangerine juice to me. I noticed this around age 4 and I still get it, time to time.

    Today, I saw this on Solresol.

  8. 8
    The Fitful Flog -- 10 Pointed Twist Star Says:

    […] No? Okay, newbie – here?s how to make a decagon. […]

  9. 9
    Emma Says:

    How happy I am to find your blog!
    I was completely intrigued with monkiri, bought a “kit” here in France (via the internet), it is completely in Japanese and… sadly, I don’t speak it, or read it.

    I had trouble finding links about it, and you have helped me tremendously!
    Thank you!

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