A sealed and thermally insulating tank for storing a fluid, the sealed and thermally insulating tank including an insulating barrier and a sealing barrier arranged on an inner surface of the insulating barrier, the insulating barrier being arranged on a support surface holding anchoring members and retained on the support surface by said anchoring members, the support surface having at least two flat regions that form an angle between them and meet at an arris zone, in which the insulating barrier includes a row of corner structures (30, 130, 230, 330) arranged along said arris zone of the support surface and flat insulating panels (29, 129, 329) arranged on the flat regions of the support surface on either side of the row of corner structures, in which at least one said corner structure includes: - a dihedral insulating block (31, 231, 331) having two faces respectively parallel to the flat regions and forming an angle between them, said face including a flat outer surface pressing against the corresponding flat region of the support surface and a flat inner surface parallel to said corresponding flat region and spaced apart from said flat outer surface in a thickness direction, and - a metal angle section (32, 65, 132, 232, 332) fastened to the flat inner surfaces of the dihedral insulating block in order to form said sealing barrier in line with the arris zone of the support surface, the metal angle section having a protruding portion (53, 153, 253, 353) that protrudes relative to the dihedral insulating block along the direction of the arris zone, in which two successive corner structures in said row are arranged so that there is a space (38, 138, 338) along the direction of the arris zone between the dihedral insulating blocks, said space being at least partially covered by the protruding portion (53, 153, 253, 353) of the metal angle section of at least one of the two consecutive corner structures, characterized in that the support surface holds one said anchoring member (45, 145, 345) arranged between the dihedral insulating blocks of the two corner structures, said at least one of the two consecutive corner structures having a cut-out (54, 254, 354) made in the protruding portion of the metal angle section in line with said anchoring member arranged between the dihedral insulating blocks, to form an access to said anchoring member (45, 145, 345). in which the insulating barrier includes a row of corner structures (30, 130, 230, 330) arranged along said arris zone of the support surface and flat insulating panels (29, 129, 329) arranged on the flat regions of the support surface on either side of the row of corner structures, in which at least one said corner structure includes: - a dihedral insulating block (31, 231, 331) having two faces respectively parallel to the flat regions and forming an angle between them, said face including a flat outer surface pressing against the corresponding flat region of the support surface and a flat inner surface parallel to said corresponding flat region and spaced apart from said flat outer surface in a thickness direction, and - a metal angle section (32, 65, 132, 232, 332) fastened to the flat inner surfaces of the dihedral insulating block in order to form said sealing barrier in line with the arris zone of the support surface, the metal angle section having a protruding portion (53, 153, 253, 353) that protrudes relative to the dihedral insulating block along the direction of the arris zone, - a dihedral insulating block (31, 231, 331) having two faces respectively parallel to the flat regions and forming an angle between them, said face including a flat outer surface pressing against the corresponding flat region of the support surface and a flat inner surface parallel to said corresponding flat region and spaced apart from said flat outer surface in a thickness direction, and - a metal angle section (32, 65, 132, 232, 332) fastened to the flat inner surfaces of the dihedral insulating block in order to form said sealing barrier in line with the arris zone of the support surface, the metal angle section having a protruding portion (53, 153, 253, 353) that protrudes relative to the dihedral insulating block along the direction of the arris zone, in which two successive corner structures in said row are arranged so that there is a space (38, 138, 338) along the direction of the arris zone between the dihedral insulating blocks, said space being at least partially covered by the protruding portion (53, 153, 253, 353) of the metal angle section of at least one of the two consecutive corner structures, characterized in that the support surface holds one said anchoring member (45, 145, 345) arranged between the dihedral insulating blocks of the two corner structures, said at least one of the two consecutive corner structures having a cut-out (54, 254, 354) made in the protruding portion of the metal angle section in line with said anchoring member arranged between the dihedral insulating blocks, to form an access to said anchoring member (45, 145, 345).