Do it!
This is based on an octahedron. It has been subdivided 5 times as triangles and then once as edges. The simplest version would be four triangles on top and four trapezoids on the bottom. One or two subdivisions would give you 90% of the interior volume and edge length 1/4th or 1/6th the overall length.
You could cut the overall shape from a sheet, cut slits (for darts) and rivet the overlap. Brake the edges or not.
The length/width/height proportion is freely adjustable, being generally egg-like.