Our motivation in this talk is the 13th-century Anxi iron-plate doubly-classic 6x 6 bordered magic square discussed by Kai-Tai Fang at the 22nd International Workshop on Matrices and Statistics in Toronto (IWMS-2013), and which we define by the matrix A. We also study the magic square in the "16th-century magical square in a manuscript" given on the "Bedouin Silver: magical squares" website, and which we define by the matrix B. In his "Bordered magic squares" website, Harry White observed that for such magic squares, in all there are 140 "border groups". Of these 140 we found 93 displayed in the literature. We identify all 140 and find that they occur in 70 pairs, with the matrices A and B forming one such pair. Moreover, we find that the rank depends only on the rank of the inner 4x4 heart submatrix H, which is Plato-like in that H = P + hE, where P is the well-known Plato magic matrix and E has every entry equal to 1; here h = 10. We end our talk by displaying some seals and talismans with Plato-like magic squares.