Metatrons cube doesn't contain all the platonic solids, unfortunately, but knew geometry recently discovered that Metatrons Tetraplex(the 600-cell a 4D geometry) contains all the platonic solids and much more! I seriously suggest you check his amazing video out.
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The 600-cell, which has a connection to the 64 tetrahedron grid, is a projection of E8 which I had previously shown corresponds to the 64 tetrahedron grid which I also corresponded to Metatrons cube. Metatrons Tetraplex makes this connection much more deeper and more interesting.