A wear member assembly (100, 10), comprising: a nose (203, 1100, 1400) attachable to a bucket lip, the nose comprising: a rear portion (207, 1122) having a first set of eight surfaces (204a-h) converging toward a longitudinal axis (211, 1105) of the nose towards a distal end of the rear portion, the first set of eight surfaces comprising: a first subset of surfaces having a top surface and a bottom surface (204e, 204g); a second subset of side surfaces (204f, 204h); and a third subset of surfaces, the third subset of surfaces (204a-d) being angled and positioned between the first subset of surfaces and the second subset of surfaces; and a forward portion (205, 1124) positioned forwardly of the rear portion, the forward portion having a second set of eight surfaces (202a-h) converging toward the longitudinal axis of the nose towards the distal end of the forward portion, the second set of surfaces comprising: a fourth subset having a top surface and a bottom surface (202e, 202g); a fifth subset of vertical side surfaces (202f, 202h); and a sixth subset of surfaces, the sixth subset of surfaces (202a-d) being angled and positioned between the fourth subset of surfaces and the fifth subset of surfaces; and an intermediate portion disposed between the rear portion and the forward portion, the intermediate portion comprising a number of surfaces (216a-f, 204a-d) in cross-section that is greater than a number of surfaces of the forward portion in cross-section and the rear portion in cross-section; and a wear member (104, 1200) having a cavity opening toward a rearward end, the cavity comprising a forward and a rear portion, the forward and rear portions comprising bearing surfaces corresponding to at least some of the surfaces (202, 204) of the forward and rear portions of the nose. a nose (203, 1100, 1400) attachable to a bucket lip, the nose comprising: a rear portion (207, 1122) having a first set of eight surfaces (204a-h) converging toward a longitudinal axis (211, 1105) of the nose towards a distal end of the rear portion, the first set of eight surfaces comprising: a first subset of surfaces having a top surface and a bottom surface (204e, 204g); a second subset of side surfaces (204f, 204h); and a third subset of surfaces, the third subset of surfaces (204a-d) being angled and positioned between the first subset of surfaces and the second subset of surfaces; and a forward portion (205, 1124) positioned forwardly of the rear portion, the forward portion having a second set of eight surfaces (202a-h) converging toward the longitudinal axis of the nose towards the distal end of the forward portion, the second set of surfaces comprising: a fourth subset having a top surface and a bottom surface (202e, 202g); a fifth subset of vertical side surfaces (202f, 202h); and a sixth subset of surfaces, the sixth subset of surfaces (202a-d) being angled and positioned between the fourth subset of surfaces and the fifth subset of surfaces; and an intermediate portion disposed between the rear portion and the forward portion, the intermediate portion comprising a number of surfaces (216a-f, 204a-d) in cross-section that is greater than a number of surfaces of the forward portion in cross-section and the rear portion in cross-section; and a rear portion (207, 1122) having a first set of eight surfaces (204a-h) converging toward a longitudinal axis (211, 1105) of the nose towards a distal end of the rear portion, the first set of eight surfaces comprising: a first subset of surfaces having a top surface and a bottom surface (204e, 204g); a second subset of side surfaces (204f, 204h); and a third subset of surfaces, the third subset of surfaces (204a-d) being angled and positioned between the first subset of surfaces and the second subset of surfaces; and a first subset of surfaces having a top surface and a bottom surface (204e, 204g); a second subset of side surfaces (204f, 204h); and a third subset of surfaces, the third subset of surfaces (204a-d) being angled and positioned between the first subset of surfaces and the second subset of surfaces; and a forward portion (205, 1124) positioned forwardly of the rear portion, the forward portion having a second set of eight surfaces (202a-h) converging toward the longitudinal axis of the nose towards the distal end of the forward portion, the second set of surfaces comprising: a fourth subset having a top surface and a bottom surface (202e, 202g); a fifth subset of vertical side surfaces (202f, 202h); and a sixth subset of surfaces, the sixth subset of surfaces (202a-d) being angled and positioned between the fourth subset of surfaces and the fifth subset of surfaces; and a fourth subset having a top surface and a bottom surface (202e, 202g); a fifth subset of vertical side surfaces (202f, 202h); and a sixth subset of surfaces, the sixth subset of surfaces (202a-d) being angled and positioned between the fourth subset of surfaces and the fifth subset of surfaces; and an intermediate portion disposed between the rear portion and the forward portion, the intermediate portion comprising a number of surfaces (216a-f, 204a-d) in cross-section that is greater than a number of surfaces of the forward portion in cross-section and the rear portion in cross-section; and a wear member (104, 1200) having a cavity opening toward a rearward end, the cavity comprising a forward and a rear portion, the forward and rear portions comprising bearing surfaces corresponding to at least some of the surfaces (202, 204) of the forward and rear portions of the nose.