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 2015-03-24 

Tube map stellated rhombicuboctahedron

This is the fourth post in a series of posts about tube map folding.
A while ago, I made this (a stellated rhombicuboctahedron):
Here are some hastily typed instructions for Matt Parker, who is making one at this month's Maths Jam. Other people are welcome to follow these instructions too.

You will need

Making a module

First, take a tube map and fold the cover over. This will ensure that your shape will have tube (map and not index) on the outside and you will have pages to tuck your tabs between later.
Now fold one corner diagonally across to another corner. It does not matter which diagonal you chose for the first piece but after this all following pieces must be the same as the first.
Now fold the overlapping bit back over the top.
Turn it over and fold this overlap over too.
You have made one module.
You will need 48 of these and some glue.

Putting it together

By slotting three or four of these modules together, you can make a pyramid with a triangle or square as its base.
A stellated rhombicuboctahedron is a rhombicuboctahedron with a pyramid, or stellation on each face. In other words, you now need to build a rhombicuboctahedron with the bases of pyramids like these. A rhombicuboctahedron looks like this:
en.wiki User Cyp, CC BY-SA 3.0
More usefully, its net looks like this:
To build a stellated rhombicuboctahedron, make this net, but with each shape as the base of a pyramid. This is what it will look like 6/48 tube maps in:
If you make on of these, please tweet me a photo so I can see it!
Edit: Proof that these instructions can be followed:
Previous post in series
Tube map Platonic solids, pt. 3
This is the fourth post in a series of posts about tube map folding.
Next post in series
Tube map kaleidocycles

Similar posts

Tube map Platonic solids, pt. 2
Tube map kaleidocycles
Tube map Platonic solids, pt. 3
Electromagnetic Field talk

Comments

Comments in green were written by me. Comments in blue were not written by me.
 2017-10-14 
I wish you'd make the final stellation of the rhombicuboctahedron! And show us! I know the shapes of the faces but have been stuck two years on the assembly!
Reply
Roberts, David
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