Folding optimal 5/6 polygons

I have looked at various ways of folding the “optimal” pentagon & hexagon (the largest regular hexagon within a square of paper). Additive constraints are a mathematically exact construction, a finite number of operations (no iterative method) and, of course, a folding sequence as simple as possible.

Hexagon

  1. The corner B comes in B’ on the medium vertical line. This allows us to built the intersection F of the fold AE with the diagonal BD. Reverse the model.
  2. Fold D onto F.
  3. Resuming the construction to get the optimal hexagon is also easy.

Pentagon

The goal is now to fold a regular pentagon, as large as possible, within a square of paper. In origami geometry, there exists a lot of techniques to fold an approximate pentagon. Much less are concerned with exact pentagon, and only one about optimal pentagon: R. Morassi, The elusive pentagon, in the proceedings of the First International Meeting of Origami Science and Technology, H. Huzita, editor, Ferrara, pp. 27- 37, 1989. The one proposed herein is much simple.

  1. fold AD onto AB where D is the middle of the edge in order to build C.

   is the golden ratio.

2) bring C on the horizontal mid-crease.
3) bisect the complementary angle.
4) bisect again and mark the diagonal BE.
5) bisect again. I goes on J.
6) half way: B goes on J. Unfold.
7)& 8 complete the stellated pentagon.

David Dureisseix

Share
Facebook
Twitter
LinkedIn
Pinterest
More resources
Traditional Bench

Simple Models

Get started on your origami journey by heading over to our simple models page where you can learn to fold from our diagram resources.

Color Tree

The official suppliers for the British Origami Society. We provide our range of arts and craft papers to customers all over the UK and around the world!

News

Check out the latest British Origami news and happenings

Charitable Donations

The BOS are delighted to accept donations to our general funds.

Join Our Volunteers

No matter what your skills and abilities, we will find some way you can help us!

Something Wrong?

Please provide details below of any issues you may have encountered. Thank you

Rabbit by Stephen O'Hanlon