Goldgerg Poly {5+, 3} 12,0

[Bryan L]

Maybe I have too much time on my hands or am just a bit cuckoo, but I enjoy modelling so much that I had to try a 12,0. 

There are 7 free vertices and even with some help from a spreadsheet it is just too finicky where a small change will have an amplified effect later on.

What I need is paramaterized modelling software where the effects can be immediately visualised.

I had just given up when I happened to look at my 6,0 version. It looked too familiar so I decided to overlay it on the 12,0. Some key vertices were off a bit and I wondered if using the 6,0 vertices might help - but I was going to have to go back and change the spreadsheet and by this time I was running low on energy / positivity.

Then the idea came to just make half sized hexes inside the 6,0 ones. Because I had maintained as much radial symmetry as possible in the 6,0 it fell into place more than I could have imagined. The intermediate hexes between the light red, yellow and blue half hexes required no adjustment at all. I just had to connect the dots between the 6,0 vertices and the half sized ones. The green ones had to be recreated but the existing geometry forced everything (as far as I can remember - there might have been one free vertex in there). Then the next two hexes between the blue and the apex were free and a bit of adjustment evened out the distortions...

Instead of colouring all the hexes I coloured the spokes between which still shows individual hexes. Although I didn't colour the green spokes, they are for all intents and purposes the same, differing just a little in the 4th significant digit - but enough to be beyond the sketchup plane tolerance...

[Bryan L]

For anyone wanting to model this, the 6,0 has equal arcs between the light red centres, their vertices and the edge between the two yellows. That is a third of the arc between the icosa mid edge and face centre. The yellow free vertex adjoining the blue and green hexes is 59.3111241505373 degrees from the centre and the blue yellow / yellow vertex. Geometry will force everything else.

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