Cutting insert, cutting tool, and method for manufacturing machined product

A cutting insert, comprising:

• an upper surface having a polygonal shape and comprising a first side;
• a lower surface on a side opposite to the upper surface;
• a lateral surface between the upper surface and the lower surface;
• an upper cutting edge on an intersection of the upper surface and the lateral surface;
• and
• a lower cutting edge at an intersection of the lower surface and the lateral surface,
• wherein
• an imaginary straight line passing through a center of the upper surface and a center of the lower surface is a central axis,
• the lateral surface comprises a first lateral surface located between the first side and the lower surface,
• the first lateral surface has a convex shape in a cross section orthogonal to the central axis, and comprises
• a first region that is flat, and
• a second region that is flat and inclined relative to the first region, the first region comprises:
• a first upper region, wherein a width of the first upper region in a direction orthogonal to the central axis increases in a direction toward the upper surface, and
• a first lower region is closer to the lower surface than the first upper region, wherein a width of the first lower region in a direction orthogonal to the central axis increases in a direction toward the lower surface.

A cutting tool, comprising:

• a holder having a columnar shape extended along a rotation axis from a first end to a second end, the holder comprising a pocket on a side of the first end;
• and
• a cutting insert at the pocket, wherein
• the cutting insert comprises:
• an upper surface having a polygonal shape and comprising a first side;
• a lower surface on a side opposite to the upper surface;
• a lateral surface between the upper surface and the lower surface;
• an upper cutting edge at an intersection of the upper surface and the lateral surface;
• and
• a lower cutting edge at an intersection of the lower surface and the lateral surface, wherein
• an imaginary straight line passing through a center of the upper surface and a center of the lower surface is a central axis,
• the lateral surface comprises a first lateral surface located between the first side and the lower surface,
• the first lateral surface has a convex shape in a cross section orthogonal to the central axis, and comprises:
• a first region that is flat and in direct contact with the pocket, and
• a second region that is flat and inclined relative to the first region, the second region being in direct contact with the pocket,
• the first region comprises:
• a first central region,
• a first upper region which is closer to the upper surface than the first central region, and the first upper region has a larger width in a direction orthogonal to the central axis than the first central region, and
• a first lower region which is closer to the lower surface than the first central region, and the first lower region has a larger width in a direction orthogonal to the central axis than the first central region.