On 13.01.2024 14:29, jr wrote:
>
> I have no idea (yet) what "C3" and "C4" symmetries
> might be
> regards, jr.
> 

C3 is triangle tiling ("parquet"), while C4 is square parquet. It's easy 
to visualize bitmap image as square pixel parquet and, therefore, turn 
it into C4 tiling of some 3D objects, having the same step distance 
along both x and y axes. With C3, however, step along one axis (in my 
version, x) is equal to triangle side (which, in my case, is 
2*sphere_radius), while step along the other (in my version, y) is equal 
to triangle height (which would be sqrt(3)*sphere_radius). As a result, 
if you compare my s4zaika and s3zaika programs, both have just two 
nested loops along y and x, across the image, but s4zaika have a normal

for y in range(0, Y, 1):

loop, while s3zaika have some weird

triangleheight = 0.5 * 1.7320508075688773
Ycount = int(Y/triangleheight)
for y in range(0, Ycount, 1):

loop, where 0.5 is the sphere radius; and apparently reads source PNG 
pixels with non-integer coordinates; all this requires some work from my 
rusty more than 0.5*century old encephalon :-)

So, now I have C2 (hidden inside C4 sourcecodes), C3 and C4; C5 does not 
exist, as do not C7 and above; so I have only C6 ("honeycomb") remain 
uncovered. But it need remembering some more school math...

Ilya

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