A linkage brick assembly, comprising: a plurality of second linkage bricks, each comprising a top face, a bottom face and four side faces (323, 324, 325, 326) between said top face and said bottom face, each of two opposite side faces (323, 325) of said side faces forming a traverse engaging protrusion (3231, 3251) extending laterally, and each of the other two opposite side faces (324, 326) of said side faces forming a vertical engaging protrusion (3241, 3261) extending vertically; a plurality of third linkage bricks, each comprising a top face, a bottom face and four side faces (333, 334, 335, 336) between said top face and said bottom face, each of said side faces forming a vertical engaging groove (3331, 3341, 3351, 3361) extending vertically; wherein a top face (32411, 32611) and an outer side face (32412, 32612) of each of said vertical engaging protrusions (3241, 3261) of said second linkage bricks defines a wedged corner, and each of said vertical engaging grooves (3331, 3341, 3351, 3361) of said third linkage bricks correspondingly forms a wedged grooved portion; a plurality of unit linkage bricks, each comprising a top face, a bottom face and four side faces (353, 354, 355, 356) between said top face and said bottom face, each of said side faces forming a traverse engaging groove (3531, 3541, 3551, 3561), a vertical engaging protrusion (3532, 3542, 3552, 3562) and a traverse engaging groove (3533, 3543, 3553, 3563) sequentially; wherein said traverse engaging protrusions (3231, 3251) of said plurality of second linkage bricks are used to engage with said traverse engaging grooves (3531, 3541, 3551, 3561, 3533, 3543, 3553, 3563) of said plurality of unit linkage bricks through lateral sliding respectively; and wherein said vertical engaging grooves (3331, 3341, 3351, 3361) of said plurality of third linkage bricks are used to engage with said vertical engaging protrusions (3532, 3542, 3552, 3562) of said plurality of unit linkage bricks through downward sliding in order to connect said plurality of unit linkage bricks. a plurality of second linkage bricks, each comprising a top face, a bottom face and four side faces (323, 324, 325, 326) between said top face and said bottom face, each of two opposite side faces (323, 325) of said side faces forming a traverse engaging protrusion (3231, 3251) extending laterally, and each of the other two opposite side faces (324, 326) of said side faces forming a vertical engaging protrusion (3241, 3261) extending vertically; a plurality of third linkage bricks, each comprising a top face, a bottom face and four side faces (333, 334, 335, 336) between said top face and said bottom face, each of said side faces forming a vertical engaging groove (3331, 3341, 3351, 3361) extending vertically; wherein a top face (32411, 32611) and an outer side face (32412, 32612) of each of said vertical engaging protrusions (3241, 3261) of said second linkage bricks defines a wedged corner, and each of said vertical engaging grooves (3331, 3341, 3351, 3361) of said third linkage bricks correspondingly forms a wedged grooved portion; a plurality of unit linkage bricks, each comprising a top face, a bottom face and four side faces (353, 354, 355, 356) between said top face and said bottom face, each of said side faces forming a traverse engaging groove (3531, 3541, 3551, 3561), a vertical engaging protrusion (3532, 3542, 3552, 3562) and a traverse engaging groove (3533, 3543, 3553, 3563) sequentially; wherein said traverse engaging protrusions (3231, 3251) of said plurality of second linkage bricks are used to engage with said traverse engaging grooves (3531, 3541, 3551, 3561, 3533, 3543, 3553, 3563) of said plurality of unit linkage bricks through lateral sliding respectively; and wherein said vertical engaging grooves (3331, 3341, 3351, 3361) of said plurality of third linkage bricks are used to engage with said vertical engaging protrusions (3532, 3542, 3552, 3562) of said plurality of unit linkage bricks through downward sliding in order to connect said plurality of unit linkage bricks.