A layout for connecting two platforms of a turbomachine which support blades. A common clearance between the blades is occupied by a seal which includes a core placed in channels under the surface of the platforms and strips which close off the clearance and which are embedded in a layer of easily eroded material. Not only do the core and the strips close off the clearances, but the seal can be designed with a sufficient stiffness to oppose any excessive movement of the platforms. The strips can also be used alone without the seal.