The New 1k Achievement in The Talos Principle II

Story-related; cannot be missed.

After activating all three lighthouses (see above achievements), you'll be able to access and complete the Hexahedron puzzle. First you'll need to actually climb up the disorienting paths to get to the start of the puzzle (a normal purple barrier), and then you can start to solve it. This is a long puzzle with multiple checkpoints along the way in case you need to reload checkpoint. Thankfully, once you get to the puzzle area you can't accidentally fall off of any edges, so don't worry about that. The game will prompt you to press  if you actually want to jump off the edge, similar to jumping onto a cube.

Even with a guide, this puzzle will take you over half an hour to solve, but most of the puzzle is figuring out how to traverse this crazy area and then where to place Connectors. If you need help or want to follow a video, refer to the following.