Wait... what is it, an extended 1x2x4-siamese 4x4x4? That's a cool idea, although I'd prefer a fully working 4x6x7
I'd prefer a fully working 7x7x7
Would you settle for two 3½ x 3½ x 3½?
(Yeah yeah, mathematically it should really be eight of them to satisfy the "cube" aspect, but if they're not attached properly the fourth axis could rotate through the dimension of time. Or fifth dimension if you ask Rod Serling.)