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Sorry, there was a logical error there, which I found by adding more examples. This now seems to work fine though, but it still doesn't like it:
when A>=B+C or B>A+C or C>=A+B then 'Not a triangle'
when A=B and B=C then 'Equilateral'
when (A=B and B!=C) or (A=C and C!=B) or (B=C and C!=A) then 'Isosceles'
when A!=B and B!=C and A!=C then 'Scalene'
else 'Balls Up'
end as Type