An integrally woven three-dimensional preform (11, 15, 31, 51) with at least one sidewall (12, 13, 16, 17, 22) in at least one direction constructed from a woven base fabric, the base fabric comprising three or more layers (32, 33, 34, 52, 53, 54), wherein: (a) the three or more layers comprise at least a top layer (32, 52), a second layer (33, 53), and a third layer (34, 54); (b) the layers comprise fibers in a first direction (36, 56) and fibers in a second direction perpendicular to the first direction (37, 57); characterized in that: - the second layer is below the top layer and the third layer is below the second layer; (c) there are a plurality of first interwoven regions (38, 71,81), wherein said first interwoven regions comprise fibers of the top layer in the first direction interwoven with fibers of the third layer in the first direction; (d) there are a plurality of first integral sidewalls (12, 16) in the second direction, wherein said first integral sidewalls are formed at respective first interwoven regions, wherein said first integral sidewalls are formed by cutting and folding a first portion of the exposed top layer on a first side of a first interwoven region together with a second portion of the exposed top layer on a second side of the first interwoven region, wherein the first integral sidewalls comprise fibers from the first and the third laver; and (e) there are a plurality of second interwoven regions, wherein said second interwoven region comprises fibers of the second layer in the second direction interwoven with fibers of the third layer in the second direction; (f) there are a plurality of second integral sidewalls in the first direction, wherein said second integral sidewalls are formed at respective second interwoven regions, wherein said second integral sidewalls are perpendicular to the first integral sidewalls and are formed by folding a first portion of the exposed second layer away from the third layer on a first side of a second interwoven region together with a second portion of the exposed second layer on a second side of said second interwoven region; and (g) the first and second integral sidewalls form at least one cell. (a) the three or more layers comprise at least a top layer (32, 52), a second layer (33, 53), and a third layer (34, 54); (b) the layers comprise fibers in a first direction (36, 56) and fibers in a second direction perpendicular to the first direction (37, 57); characterized in that: - the second layer is below the top layer and the third layer is below the second layer; - the second layer is below the top layer and the third layer is below the second layer; (c) there are a plurality of first interwoven regions (38, 71,81), wherein said first interwoven regions comprise fibers of the top layer in the first direction interwoven with fibers of the third layer in the first direction; (d) there are a plurality of first integral sidewalls (12, 16) in the second direction, wherein said first integral sidewalls are formed at respective first interwoven regions, wherein said first integral sidewalls are formed by cutting and folding a first portion of the exposed top layer on a first side of a first interwoven region together with a second portion of the exposed top layer on a second side of the first interwoven region, wherein the first integral sidewalls comprise fibers from the first and the third laver; and (e) there are a plurality of second interwoven regions, wherein said second interwoven region comprises fibers of the second layer in the second direction interwoven with fibers of the third layer in the second direction; (f) there are a plurality of second integral sidewalls in the first direction, wherein said second integral sidewalls are formed at respective second interwoven regions, wherein said second integral sidewalls are perpendicular to the first integral sidewalls and are formed by folding a first portion of the exposed second layer away from the third layer on a first side of a second interwoven region together with a second portion of the exposed second layer on a second side of said second interwoven region; and (g) the first and second integral sidewalls form at least one cell.