Columbus cubes

by maggie

For someone who only got a D in their applied Maths A-level I’ve always been fascinated by geometry, topology and mathematical curiosites.

This little pamphlet from part of a Tarquin publications book is all that remains of my first foray into the world of rotating rings and hypercubes.
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magic cubes, flexisquares, spherical geometry

Eventually i found modular origami, because there are only so many cranes one can make
The most straightforward modular piece is a cube, and a columbus cube is a cube with a corner caved in.
you can stand even it on the flat triangle

you can stand even it on the flat triangle

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You can join them at the corner

 

stack them high

stack them high – using opposite corners

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Joining corners oposite on the same face. If you have 20 of them you can make a big ball

or run rings around them

or run rings around them

I’ve finally got the last of my stuff out of storage and before it gets refiled in the attic, I’ve been revising some of the projects that have been on hold for a while. (some of my notes are dated 2008.)
As I said last week I’m not starting anything new, just sorting out where my interests really lie…
All these paper models are interesting enough, but when the sit around gathering dust one should really do something with them.
There is a point to this story.
Ply spliting.
This technique makes fairly robust  shapes and there is  a puzzle to solve in how make it.
cotton cords starting at the base in a square and spiralling up then over the top

cotton cords starting at the base in a square and spiralling up then over the top

This piece is ancient but demonstrates how plain geometric shapes get warped by the cords. The dark ‘ear holes’ at the top hide the ends of the cords.
I’ve been thinking of the columbus cube constructs in terms of paths sets of cords would follow. For anything more than a cube these are complex and I’m not sure whether it’s possible to make the structure as pure as possible. Where do the cords start and finish? etc. lots of questions still.
Right: woven cube showing 'paths' going round four faces Centre: skeletal cube showing one set of 'paths'. collapsed corner in centre. Left: columbus cube. yellow paths are continuous and would fill up gaps in Centre structure

Right: woven cube showing ‘paths’ going round four faces Centre: skeletal cube showing one set of ‘paths’. collapsed corner in centre. Left: columbus cube. yellow paths are continuous and would fill up gaps in Centre structure

 

However this is yet another big open ended project and I mustn’t be distracted any further by the shiny. And I’m not trying to write a text book here either.
MER
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