The Mile High Magic Pyramid

Using a unified formulation of $\mathcal{N}=1,2,4,8$, super Yang-Mills theories in $D=3$ spacetime dimensions with fields valued respectively in $\mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O}$, it was shown that tensoring left and right multiplets yields a Freudenthal magic square of $D=3$ supergravities. When tied in with the more familiar $\mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O}$ description of super Yang-Mills in $D = 3, 4, 6, 10$thisresultsinamagicpyramidofsupergravities:theknown$4 \times 4$magicsquareatthebasein$D=3$,a$3\times 3$squarein$D=4$,a$2 \times 2$squarein$D=6$andTypeIIsupergravityattheapexin$D=10$.