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# Geometry Weekend 2023

## Introduction

A good overview of the origins of modular origami is at The Public Paperfolding History Project: Modular Origami: http://www.origamiheaven.com/historyofmodularorigami.htm

The same site also has the Modular Origami Design Encyclopaedia.

## Origami to make

Here is a selection of modular origami to make. How could you develop your own ideas from these?

Curler Unit by Herman Van Goubergen

https://www.britishorigami.org/cp-resource/curler-units/

Dodecahedron (Penultimate Unit) by Robert Neale
https://web.eecs.utk.edu/~jplank/plank/origami/penultimate/pentagon.html

Meditations on a Waterbomb (1977) contains classic modular origami by Kenneth Kawamura and Joe Power:
http://www.origamiheaven.com/pdfs/meditations.pdf

Five Intersecting Tetrahedra by Tom Hull and Francis Ow
http://origametry.net/fit.html

The website of the late Francis Ow has many diagrams of his excellent work, including his 120 degree unit.

Waterbomb Corrugation: start with the simple two by two version and then try doubling the frequency for the harder four by four version. A video tutorial may help:

When creasing large paper or a large number of squares, you can score the crosses with a ruler and a tool like a ballpoint pen that has run out of ink.

## Books and resources to read

As well as my own origami books, including Origami from Surface to Form (read online in full at Wooden Books), here are some others that are well worth reading:

David Brill. Brilliant Origami: A Collection of Original Design. Japan Publications, 1996.

Kunihiko Kasahara and Toshie Takahama. Origami for the Connoisseur. Japan Publications, 1988.

Kunihiko Kasahara. Origami Omnibus: Paper-Folding for Everybody. Japan Publications, 1988.

Jun Maekawa. The Art & Science of Geometric Origami: Create Spectacular Paper Polyhedra, Waves, Spirals, Fractals and More! Tuttle Publishing, 2022.

David Mitchell. Mathematical Origami: Geometrical Shapes by Paper Folding, Second edition. Tarquin Publications, 2020.

David Petty. Planar Modular Origami. British Origami Society, 2013. https://www.colortreelimited.co.uk/product/65-planar-modular-origami-david-petty/

These three non-origami books are good sources of inspiration and reference data for polyhedra:

Peter Cromwell. Shapes in Space: Convex Polyhedra with Regular Faces. Association of Teachers of Mathematics. 2004.

H.M. Cundy and A.P. Rollett. Mathematical Models. 3rd edition. Tarquin Publications, 1981.

Amy C. Edmondson. A Fuller explanation: the synergetic geometry of R. Buckminster Fuller. Birkhäuser (Design science collection), 1987.

This resource can help if you want to colour the edges of an icosahedron or a dodecahedron so that the same colour does not meet at a vertex (except for the icosahedron in three colours where the same colour does meet at vertex, but not on the same face).

## Software to use

Dynamic geometry software Geogebra is free to use and allows you do geometry (2D and 3D) in a empirical way. Use and experiment some of my Geogebra resources.

Play the computer game Elite at https://archive.org/details/Elite_1985_Firebird_Software_ZX_Spectrum
(quick start: press 1 to launch; space/right shift to +/- velocity; cursor keys or S/X/N/M to climb/dive/roll)

## Films to watch

These are some relevant films:

PLAITED POLYHEDRA (1960) Three-dimensional geometric paper shapes made without using glue by Robert Pargeter https://www.britishpathe.com/asset/36828/

The Ron Resch Paper & Stick Film http://www.ronresch.org/ronresch/gallery/paper-and-stick-film/

NOVA “The Origami Revolution.” https://archive.org/details/TheOrigamiRevolution