1. A tire and rim assembly wherein the tire comprises a tread portion, a tread reinforcement in the tread portion, a pair of sidewalls respectively on opposite sides of the tread portion, a pair of beads respectively at the inner edges of the sidewalls, a pair of bead rings respectively in the beads, and a carcass reinforcement that is radial at least from the midheight of the respective sidewalls to the respective beads and extends from one bead to the other, the tire having a height H and a breadth B, the ratio H/B being less than one, and the carcass reinforcement having a neutral fiber that follows, at least between the midheight of the respective sidewalls and the locations where it meets the respective bead rings, the natural equilibrium curve of a single-ply radial carcass that is without a tread reinforcement and that is subjected to internal pressure, said curve being tangent to the bead rings and passing through the edges of the tread reinforcement and through equator points where the sidewalls have a maximum distance B from each other and wherein the rim comprises a base, a bead seat on either side of the base, and an edge on the outer side of each seat, each edge comprising a portion substantially parallel to the adjacent segment of said neutral fiber, said portion being connected to the adjoining bead seat by an S-shaped curve and being terminated on the outside by a curvature towards the axis of rotation of the tire.

12. A tire and rim assembly wherein the tire comprises a tread portion, a tread reinforcement in the tread portion, a pair of sidewalls respectively on opposite sides of the tread portion, a pair of beads respectively at the inner edges of the sidewalls, a pair of bead rings respectively in the beads, and a carcass reinforcement that is radial at least from the midheight of the respective sidewalls to the respective beads and extends from one bead to the other, the tire having a height H and a breadth B, the ratio H/B being less than one, and the carcass reinforcement having a neutral fiber that follows, at least between the midheight of the respective sidewalls and the respective bead rings, the natural equilibrium curve of a single-ply radial carcass that is without a tread reinforcement and that is subjected to internal pressure, said curve being tangent to the bead rings and passing through the edges of the tread reinforcement and through equator points where the sidewalls have a maximum distance B from each other and wherein the rim comprises a base, a bead seat on either side of the base, and an edge on the outer side of each seat, each edge comprising a portion substantially parallel to the adjacent segment of the neutral fiber of the carcass reinforcement, said portion being connected to the adjoining bead seat by an S-shaped curve and being terminated on the outside by a curvature towards the axis of rotation of the tire, said portion furthermore being conical and having an inclination towards the outside less than 90*with respect to the axis of rotation, and the S-shaped curve connecting the conical portion of the edge of the rim to the bead seat having one branch tangent to the bead seat and one branch tangent to said conical portion, the point of inflection common to the two branches being located radially at the level of the core of the bead ring and the tangent to the S-shaped curve at said point of inflection being parallel to the median plane of the neutral fiber of the carcass of the tire.