= Complete three-ray toric surfaces with at most one singular point
{title2=$\mathbb P(1,1,r),\quad r\geq1$}
Two neighboring smooth cones can be normalized so that the three rays are $(1,0),(0,1),(-1,-r)$, with $r\geq1$. Completeness forces the negative sign and their primitive relation has weights $(1,r,1)$. Thus these surfaces are precisely the <weighted projective planes> $\mathbb P(1,1,r)$. For $r=1$ the surface is the <projective plane>; for $r>1$ its unique singularity is the <cyclic quotient surface singularity> $\frac1r(1,1)$.
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