Hello MHF peeps,

I am new here so hello to you all

I am a not a mathematician, I program microprocessors and am interested in music and architecture.

My question (not sure if it fits here but I did look!) is about 3D symmetry.

I have been trying to build what is know as a Frabjous, it is a dodecahedron make from 30 identical pieces, it is made up of 4 pentagons:

multi-curve top on Flickr - Photo Sharing!

Each of the 20 corners has three individual pieces that connect together, and each of the individual pieces goes off to a different corner, so for example the corner 1 goes off to 13, 17 and 19, corner 2 goes to 14, 18 and 20.

I'm really sorry for being a nuisance, but how do I know for instance where the corners of 20 go off to, one part of 20 is made by 2 and 14 but then how do I work out the last part of the sequence?

If anyone would be so kind as to point out the logic or pattern behind this I would greatly appreciate it. This kind of 3D symmetry has really done a number on my head! Pardon the pun

This is the website that has helped me so far:

Making a Frabjous - Evil Mad Scientist Laboratories


Cut out the pieces