Re: [math-fun] 2D Einstein tile in hyperbolic plane by Penrose

Further, by combining Goucher lego idea as hexified by me using Eisenstein integers, Socular-Taylor disconnected 2D Einstein idea with Goucherian helical tentacle connection, and Penrose (Goucher has discussed this except for the Penrose part) the 2D layers each can be made aperiodic.

--that last bit was wrong. The problem is you cannot "turn the lego over" (it looks like you can in Euclidean 3-space, but we are in hyperbolic 3-space) which ruins the attempt to SocularTaylorize it.