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

A cutting insert, comprising:

• a base;
• and
• a cutting part comprising a sintered body of cubic boron nitride or diamond and connecting to the base, wherein the cutting part comprises:
• a first surface,
• a second surface located on a side opposite to the first surface, and
• a third surface located between the first surface and the second surface,
• wherein the first surface comprises:
• a corner,
• a first side extended from the corner,
• a first region located along the corner and the first side and inclined upward toward an inner part of the first surface,
• a second region which is located along the first region on a more inner part than the first region, and which is inclined relative to the first region, and which is located closer to or parallel to the second surface as going toward the inner part of the first surface, and
• a third region which is located at a more inner part than the second region, and which is inclined so as to be located further away from the second surface as going toward the inner part of the first surface,
• wherein the third region comprises:
• a first inclined surface, and
• a second inclined surface located closer to the second region than the first inclined surface, and
• wherein:
• a boundary between the corner and the first side is a first point,
• a cross section that passes through the first point and is orthogonal to the first side in a plan view of the first surface is a first cross section,
• a boundary between the first region and the second region is a second point in the first cross section,
• an imaginary straight line passing through the first point and the second point is a first imaginary straight line,
• the first imaginary straight line intersects with the third region in the first cross section,
• an imaginary straight line passing through a center of the first surface and a center of the second surface is a central axis,
• a first imaginary flat surface orthogonal to the central axis is a reference plane, and
• a first angle that is an inclination angle of the first inclined surface relative to a second imaginary flat surface parallel to the reference plane is larger than a second angle that is an inclination angle of the second inclined surface relative to a third imaginary flat surface parallel to the reference plane in the first cross section.