Norms of Minimal Projections

It is proved that the projection constants of two- and three-dimensional spaces are bounded by 43 and (1 + √ 5)/2, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and dodecahedron. In fact, a general inequality for the projection constant of a real or complex n-dimensional space is obtained and the question of equality therein is discussed.