"A hyperbolic plane is a surface in which the space
curves away from itself at every point."
Then you need to see Rebecca Peapples' Beaded Hyperbolics
There is much more in their Gallery, including an on-going crocheted coral reef.
It's too early in the day for me to take in this concept, but there is a wealth of design possibilities for beaders, crocheters and especially bead crochet,