We present a complete description of all the extreme points of the unit ball of Ls(l2∞3) which leads to a complete formula for ||f|| for every f∈Ls(l2∞3)*. We also show that extBLs(l2∞3)⊂extBLs(l2∞n) for every n ≥ 4. Using the formula for ||f|| for every f∈Ls(l2∞3)*, we show that every extreme point of the unit ball of Ls(l2∞3) is exposed. We also characterize all the smooth points of the unit ball of Ls(l2∞3).

Keywords: symmetric bilinear forms on ℝ,³ with the supremum norm, extreme points, exposed points, smooth points.