Is it possible to take two equilateral triangles in the configuration depicted and create a moebius strip by connecting up the points of the traingles in a certain order. I'm working in a 3d app(Houdini) and am asking for a client to find out if this shape is even possible, and if so what kind of maths i'd need to learn to program it.
Would really appreciate any help as i'm way out of my depth here.
The margin of the desired mobius strip is shown in yellow here
The surface of the strip should also align with the green lines connecting the points of the opposing triangles as show here
The locations of each triangles vertices in this screenshot
Currently I am trying to solve this by connecting the points together in the order show, then resampling the resulting curve and copying lines to it and then converting them to a surface:
latest attempt following suggestions: 