Origami Deltahedron designed by Jo Nakashima (10/2020)
Difficulty level: simple
In geometry, a deltahedron is a polyhedron whose faces are all equilateral triangles. This definition includes some of regular polyhedra (tetrahedron, octahedron and icosahedron) and a variety of other shapes.
This is a modular origami and each unit is made from a triangular sheet of paper. Since it’s an unusual shape for origami, I show how to cut the triangles from a square sheet of paper in the beginning of the tutorials.
The units are connected in the internal side of the polyhedron, so final model is very clean with no visible creases nor unwanted layers. The downside is that it can be difficult to connect the last units. The final connection is made only with tabs and pockets, so it isn’t as secure as the other connections.
It works also as triangular pixels if you connect them flat with different colors to form some figure. If you like pixel art, see also the standard square pixel.
Video Tutorials
Icosahedron
The Icosahedron is a polyhedron with 20 triangular faces.
Octahedron
The Octahedron is a polyhedron with 8 triangular faces.
Tetrahedron
The Tetrahedron is a polyhedron with 4 triangular faces.
Stellated Octahedron
8 pointed star. Each point is a triangle-based pyramid. You can also see it as two interlaced tetrahedra.
Antiprisms tower
This is an example with variable number of units. You can use different antiprisms and any amount of levels. The model in this picture has 4 levels of square antiprisms (4×8=32 units) and a square-based pyramid on the top (+4 units). Optionally you can close the bottom with a concave pyramid (+4 units).
More Polyhedra
This model is not limited to the regular polyhedra. You can build other shapes, including non-convex forms. Here are some examples:
- Gyroelongated square bipyramid (16 units): square-based pyramids and a square antiprism between them.
- Excavated Dodecahedron (60 units): it looks like a dodecahedron with concave pentagonal pyramids in place of its faces. Although it wasn’t hard to build, the last pocket/tabs connections aren’t secure so I didn’t like it.
- Stellated Icosahedron (60 units): an icosahedron with triangular pyramids augmented to each face. The last connections are too difficult to make (maybe with larger units it could be easier).
