Making Maths

This is the Broken Square Cube by David Mitchell Folding instructions are here . This doesn't feel as though it is going to hold together well until the last piece goes in.  Now it is pretty stable. Folded from 6 squares of paper.  Blue on one side, white on the other.

This is a nice one.  Kusudama Starsea by Tomoko Fuse Video instructions here  https://www.youtube.com/watch?v=u-71U6rs9Vg There is even this video  here  that puts a light inside and makes it a lamp.  Looks nice.

 I have been interested in something that seems to be called IQ puzzle lamps. They are made by fitting together pieces of translucent plastic and placing a bulb inside. A while back I found a template and some translucent plastic sheets and tried some out.  This would be less time consuming with a laser cutter but armed with a pair of scissors and a craft knife was all that was available to me. This site  has instructions and a template to use. The model I made pictured above is 120 modules. Instructions for construction are  here . It uses the module in both it's backward and forward orientation.  Using a non transparent plastic I recently made these 30 unit pieces. Where all the modules are orientated the same way round. Pictured here is one where the pieces are 'forward' and one where the pieces are 'backward' so on one model the pieces rotate clockwise and the other model is anticlockwise.  Instructions for these 30 unit models are here Another model I ...

 This lovely piece is by Dave Brill.  It uses 30 modules made from squares.  He has diagrams of his work  here .  After completing my model I found a video which is a bit easier to follow  here  which coincidentally also shows a gold model. Video by Origami y Matemáticas - Jaime Niño Bernal  I used squares of side length 6cm, which I think is probably a bit too small. Also I had to use glue to keep it together. The video above  shows how to do it with no glue but uses little pegs to hold it together during construction. I reckon larger modules will be easier to put together. 

I cannot believe that I have never seen this varient before. Simple but very effective.  I found the instructions here . Diagrams and also instruction diagram on how to colour with three colours so that no two colours touch.   I think it would look interesting in monochrome.  Here's a model with fewer pieces in some paper I wanted to use up. 

  A quick make for Ramadan. The star instructions are here  folded from a 14cm square and I used the Moon instructions from here , and used a piece of card but converted to cm using 9cm radius, 6.75cm radius and 7.5 cm radius. There's a nice opportunity for construction/loci to find the centre of the crease circle when doing the moon.  In creating a star, you first fold to make and cut a pentagon.