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Origami Snapper, Model, Extension, Triangular Bipyramid

p0.jpg Origami Snapper, Model, Extension, Triangular Bipyramid
p1.jpg Origami Snapper, Model, Extension, Triangular Bipyramid
p3.jpg Origami Snapper, Model, Extension, Triangular Bipyramid
HexahedronHalf_Ver_A.png Origami Snapper, Model, Extension, Triangular Bipyramid
tetraH.png Origami Snapper, Model, Extension, Triangular Bipyramid
cube_45mm.png Origami Snapper, Model, Extension, Triangular Bipyramid
HexahedronHalf_Ver_B.png Origami Snapper, Model, Extension, Triangular Bipyramid
HexahedronHalf_Ver_A.stl Origami Snapper, Model, Extension, Triangular Bipyramid
HexahedronHalf_Ver_B.stl Origami Snapper, Model, Extension, Triangular Bipyramid
tetraH.stl Origami Snapper, Model, Extension, Triangular Bipyramid
cube_45mm.stl Origami Snapper, Model, Extension, Triangular Bipyramid
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  • HexahedronHalf_Ver_A.stl
  • HexahedronHalf_Ver_B.stl
  • cube_45mm.stl
  • tetraH.stl

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Publication date 2021-09-08 at 23:03
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Published to Thingiverse on: 2021-09-08 at 17:54
Design number 514637
LGBU

LGBU

3D printer file info

3D model description

####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

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