Searching for a origami parabole/paraboloid (not hyperbole)

[El Papiroturgo]

Hello, I am searching for a diagram to make a origami/kirigami parabole (not hyperbole or hyperboloid), ie, a thing like parabolic antenna, with the next shape:

or

[Baltorigamist]

I'm not sure one exists (if it's even possible), but you might be able to ask some of the more math-oriented origamists about the requirements of possibly creating one. The first two who come to mind are Andrew Hudson and Robert Lang.

I imagine it would need several curved creases in a specific pattern though.

[Andre-4]

Most concave modules have 5 or 6 sometimes 8 units that sink like that...the dip is usually reflected on each face of the polygon....Search for Sonobe or Kusudama on boards like pinterest....