Amazing Geometric Origami


Considering the links between origami and geometry, there are precious few books that are dedicated to attractive, elegant designs demonstrating principles whilst stressing the artistic aspect as well. This has been a dream project, not least because the publishers also requested a DVD of all the models in the book, and wanted me to produce the complete package, including the DVD interface!

I've made many videos in the past, but this scale of project was new to me and has proved an interesting challenge as well as a steep learning curve! I invested in a set of studio lighting and some decent editing software and set off. Editing was time-consuming, but the biggest issue was unexpected - as the videos were transcode into DVD format, they all went very dark - in the end I had to deliberately lighten every video to allow for this, which took a lot of trial and error! Creating the DVD interface (using DVDstyler, a superb freeware package) also involved a lot of new skills, but thankfully the product is now complete.

I'm well aware of the exacting standards mathematicians apply to products like this and will no doubt get a flood of corrections, but the maths has been checked by a teacher of the subject and two highly experienced geometric enthusiasts and it should pass muster. It's not intended to be a definitive guide to the subject, more of an introduction to some of the key principles and demonstrations of their use.

Obviously, there were a wealth of models from which to choose, but I've focussed on the platonic solids, some dissections and other interesting designs, with a small amount of maths to accompany each.

Models: Reptile / Tetrahedron / Triangular Antiprism / Twisted Tube / Dubai Unit / Octagon Dissection / Dodecagon Dissection / Octahedron / Penrose Triangle - Nick Robinson / Pentagonal Ring / Icosahedron - Rob Foord / 60 degree Star -  David Petty / Rhombicuboctahedron / Penultimate Unit - Robert Neale / Pythagoras - Leong Cheng Chit / Robin Star - Maria Sinayskaya / Windmill cube / Chambered Cuboctahedron - Francis Ow / XYZ Planar / Joe Power / Hexagonally Bisected Cube - Thoki Yenn

Reptile by Nick Robinson
page 10 (from Square)

Tetrahedron by Nick Robinson
page 12 (from Square)

Triangular Antiprism by Nick Robinson
page 14 (from Square)

Pentagonal Ring by Robert Foord
page 16 (from Square)

Twisted Tube by Nick Robinson
page 20 (from Square)

Octagon Dissection by Nick Robinson
page 22 (from Square)

Dubai Unit by Nick Robinson
page 26 (from Square)

Dodecagon Dissection by Nick Robinson
page 30 (from Square)

Octahedron by Nick Robinson
page 34 (from Square)

60 degree Star by David Petty
page 36 (from Square)

Rhombicuboctahedron by Robert Neale
page 40 (from Square)

Proving Pythagoras by Leong Cheng Chit
page 42 (from Square)

Robin Star by Maria Sinayskaya
page 46 (from Square)

Windmill Cube by Robert Foord
page 50 (from Square)

Chambered Octahedron by Francis Ow
page 54 (from Square)

Icosahedron by Robert Foord
page 58 (from Square)

Skeletal Dodecahedron by Robert Neale
page 60 (from Square)

XYZ Planar by Joe Power
page 66 (from Square)

Hexagonally Bisected Cube by Thoki Yenn
page 70 (from Square)

Penrose Triangle by Nick Robinson
page 74 (from 4x1)

Images have been sourced from the web or the author. If you want an image removing (or have a better one!) please get in touch.