Origami Snapper, Model, Extension, Triangular Bipyramid

####Model and Extension for the Origami Snapper: Flexible Filament Recommended.

In an origami project, we made a snapper hexahedron out of a rectangular piece of construction paper (see ref. 1). The solid is, more accurately, a triangular bipyramid, where each face is an isosceles right triangle. It is playful, opening and closing like a snapper! Two copies of the snapper can hug each other in a cube. Then, a question was posed about the volume of the solid. If we treat the snapper as a filled solid, what is its volume? Is it one half of the corresponding cube? The answer is NO. It is one third of the corresponding cube. We can certainly open the snapper and figure out the length of each edge of a tetrahedron, and then calculate its volume: baseArea * height /3, and there are at least two ways to do it. Doubling that, we get the volume of the whole snapper.


I need a physical model to convince my audience that there is something missing ( a regular tetrahedr