Number of triple points on complete intersection Calabi–Yau threefolds

We discuss bounds for the number of ordinary triple points on complete intersection Calabi–Yau threefolds in projective spaces and for Calabi–Yau threefolds in weighted projective spaces. In particular, we show that in $\mathbb {P}^5$ the intersection of a quadric and a quartic cannot have more than ten ordinary triple points. We provide examples of complete intersection Calabi–Yau threefolds with multiple triple points. We obtain the exact bound for a sextic hypersurface in $\mathbb {P}[1:1:1:1:2]$, which is $10$. We also discuss Calabi–Yau threefolds that cannot admit triple points.