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.
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