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 tetrahedron) inside the hugging snappers. So I made a 3D model. Among the files are two versions of the snapper, the inside tetrahedron, and the cube. One can use water or rice to demonstrate the volume relationships.

References

1. https://www.origami-fun.com/origami-snapper.html
2. https://en.wikipedia.org/wiki/Triangular_bipyramid

FlashForge

Finder

No

No

0.2mm

10-20%

Flexible filament is recommended for the snapper parts. Otherwise, the snapper will break apart into two pieces upon bending. PETG might work to some extent. The center tetrahedron could be printed with PLA or any other filament.