Is there a Calabi-Yau threefold with $h^{1,1}=1$ and $h^{1,2}=0$?

Is there a Calabi-Yau threefold with $$h^{1,1}=1$$ and $$h^{1,2}=0$$?

• As of three years ago no such CY threefold was known to the authors of arxiv.org/pdf/1602.06303.pdf. Dec 26, 2019 at 13:15