Classification of the extreme points of ${\mathcal L}_s(^2l_{\infty}^3)$ by computation

Let $l_{\infty}^3=\mathbb{R}^3$ be endowed with the supremum norm. In [Comment. Math. 2017,  57 (1), 1-7], S.G. Kim classified the extreme points of the unit ball of ${\mathcal L}_s(^2l_{\infty}^3)$ only using Mathematica 8, where ${\mathcal L}_s(^2l_{\infty}^3)$ is the space of symmetric bilinear forms on $l_{\infty}^3$. It seems to be interesting and meaningful to classify the extreme points of the unit ball of ${\mathcal L}_s(^2l_{\infty}^3)$ without using Mathematica 8. The aim of this paper is to make such classification by mathematical calculations.