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

A cutting insert, comprising:

• a first surface having a polygonal shape and comprising a first corner, and a first side and a second side each being extended from the first corner;
• a second surface having a polygonal shape located on a side opposite to the first surface;
• a lateral surface which is located between the first surface and the second surface, and which comprises a first lateral surface located along the first side and a second lateral surface located along the second side;
• a first cutting edge located on a first ridgeline where the first surface intersects with the first lateral surface;
• and
• a second cutting edge located on a second ridgeline where the first lateral surface intersects with the second lateral surface,
• wherein
• the first lateral surface comprises
• a first inclined surface located along the first ridgeline,
• a second inclined surface located along the first inclined surface,
• a third inclined surface located along the second ridgeline,
• a fourth inclined surface located along the third inclined surface, and
• a flat surface located along the second inclined surface and the fourth inclined surface,
• an imaginary flat surface, which is parallel to the flat surface and located more inside than the first lateral surface, is a reference plane,
• each of the first inclined surface and the second inclined surface is closer to the reference plane as going away from the first ridgeline,
• each of the third inclined surface and the fourth inclined surface is closer to the reference plane as going away from the second ridgeline,
• in a cross section orthogonal to the first ridgeline in a front view of the first lateral surface,
• an inclination angle of the first inclined surface relative to the reference plane is a first inclination angle, and
• an inclination angle of the second inclined surface relative to the reference plane is a second inclination angle,
• in a cross section orthogonal to the second ridgeline in a front view of the first lateral surface,
• an inclination angle of the third inclined surface relative to the reference plane is a third inclination angle, and
• an inclination angle of the fourth inclined surface relative to the reference plane is a fourth inclination angle,
• the second inclination angle is smaller than the first inclination angle, and
• the fourth inclination angle is larger than the third inclination angle.