Hi Robert,

> Could this be a case where both are in common usage, but both are not
> quite official...

My Cambridge dictionary reports:

tessellate
    US ALSO tesselate

tessellation
    US ALSO tesselation

There is no "tessellator" but I think the word building pattern is pretty
clear. The double 'l' seems to be valid in both US and UK English.

Cheers,
Marco

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