A cutting insert comprising: an insert major body including two hexagonal faces comprising a front hexagonal face and a back hexagonal face , facing each other and six side faces arranged around the two hexagonal faces , wherein: the insert major body is formed to be rotationally symmetrical at 120° intervals about an insert center line (C) passing through centers of the two hexagonal faces , and the front hexagonal face and the back hexagonal face are arranged in inversely symmetrical manner; a major cutting edge and a minor cutting edge are alternately formed in a circumferential direction in each of the two hexagonal faces at twelve intersecting ridgeline portions at which the two hexagonal faces and the six side faces intersect, and each of the six side faces includes the major cutting edge formed to be located at an intersecting ridgeline portion with one hexagonal face in the two hexagonal faces and the minor cutting edge formed to be located at an intersecting ridgeline portion with the other hexagonal face in the two hexagonal faces ; a major flank face connected to the major cutting edge and a minor flank face connected to the minor cutting edge are formed at the side face ; each of the six side faces is concavely folded between the major flank face and the minor flank face at a cross-section view along the insert center line (C), a sum of a major flank face angle (α) formed by the major flank face with respect to a plane which is perpendicular to the insert center line (C) and a minor flank face angle (β) formed by the minor flank face with respect to a plane which is perpendicular to the insert center line (C) is smaller than 180°, the major flank face angle (α) is an obtuse angle, when viewed from a direction facing one hexagonal face in the two hexagonal faces along the insert center line (C), in each of the six side faces , the minor cutting edge protrudes to an outside of the insert major body more than the major cutting edge , and a width of the major flank face is larger than a width of the minor flank face in a direction of the insert center line (C). the insert major body is formed to be rotationally symmetrical at 120° intervals about an insert center line (C) passing through centers of the two hexagonal faces , and the front hexagonal face and the back hexagonal face are arranged in inversely symmetrical manner; a major cutting edge and a minor cutting edge are alternately formed in a circumferential direction in each of the two hexagonal faces at twelve intersecting ridgeline portions at which the two hexagonal faces and the six side faces intersect, and each of the six side faces includes the major cutting edge formed to be located at an intersecting ridgeline portion with one hexagonal face in the two hexagonal faces and the minor cutting edge formed to be located at an intersecting ridgeline portion with the other hexagonal face in the two hexagonal faces ; a major flank face connected to the major cutting edge and a minor flank face connected to the minor cutting edge are formed at the side face ; each of the six side faces is concavely folded between the major flank face and the minor flank face at a cross-section view along the insert center line (C), a sum of a major flank face angle (α) formed by the major flank face with respect to a plane which is perpendicular to the insert center line (C) and a minor flank face angle (β) formed by the minor flank face with respect to a plane which is perpendicular to the insert center line (C) is smaller than 180°, the major flank face angle (α) is an obtuse angle, when viewed from a direction facing one hexagonal face in the two hexagonal faces along the insert center line (C), in each of the six side faces , the minor cutting edge protrudes to an outside of the insert major body more than the major cutting edge , and a width of the major flank face is larger than a width of the minor flank face in a direction of the insert center line (C). <EOS>