I am applying the Subdivision Surface modifier on the model of a queen chess piece. Does anyone know why some of the crown's horns are modified like in the second picture? The topology seems to be exactly the same for each individual horn. My desired outcome is for all the horns to remain pointy.
Actually your topology should not allow to have sharp tips, it's just because some of your faces are flipped that you get them sharp, if you recalculate the normals you'll have the same result:
To fix this, bring some edge loops with the knife (K to activate, Z to cut through):