nice! i did a mobius strip thing as well, and used it to understand the rotation / angles of three quarks, spin-half. during the opposing spin you move to the other side, which is a really nice way to comprehend spin half. i then stacked the 3 "quarks" one on top of the other, with the middle one's "phase" rotated by 90 degrees to the other (took a while to twist them about so as to line up). turns out that phase-shifting of 90 degrees is what allows the quarks to superimpose in a non-destructive fashion (see wikipedia "Phasor Arithmetic" https://en.wikipedia.org/wiki/Phasor)

... and it was just a piece of paper, a pen and some sellotape that allowed me to intuitively grasp it very very quickly no "maths" involved!

to make the dodecahedron i made one 5-sided cardboard piece (tried paper... it's really awkward, keeps collapsing) then used that as a template to cut out 11 more. you have to put sellotape on both sides of the faces, otherwise it falls apart very quickly, but try to keep the corners free of tape so that you can poke a needle in to "reinflate" the thing as it will collapse on you quite easily if you put too much pressure on. start by putting 5 around one, that at least gives a stable base, then put the next 5 on. you can still, without too much difficulty, keep adding tape on both sides up until about face 10 or 11. face 12 - the last one - you simply can't put tape on both sides (duuh), unless you use the needle to poke around and push tape against the last face from the inside.

i ended up changing the numbering pattern on the dodecahedron a number of times. the idea is, to put numbers on each face of the dodecahedron, and match incremental jumps in those numbers (2->6->10->2) onto poincare sphere (theta, phi) matrix operations of a line from the centre of the sphere through the centre of the face. as a general rule i'm making sure that increments of 6 are a very very simple operation.

i'm looking for the right "pattern"... ahh... what's the mathematical word... the right... sequence of numbers on faces (1,7,2,8,3,9....) which match easiest with the matrix transformations *but* also match intuitively with left/right-handed quarks and so on, i.e. i expect the left-handed quarks, when you look at the equivalent poincare matrix operations, to be *mirror* operations compared to the use of their right-handed equivalents. so not all possible permutations (ah! that's the word i was looking for) of the 12 numbers are candidates. you can't just slap numbers on faces randomly and go "yeahhh we're done"