Recently, the Chinese puzzle lover Fenz (a mathematician, researcher of some classes of puzzles, a programmer who created his simulator and a designer who made several puzzles) created a simulator - https://mc.fenzland.com
I really like several of his ideas, and with his permission I created a new puzzle !!!
Fenz Bermuda Pyraminx (I made three versions - Mercury, Venus and Earth). I did all the drawings and calculations on my own.
I used hyperbolic cuts to get straight lines in the pattern on the edges. In the simulator there are several versions, but they do not turning.