#deltahedra

[benji-cheung]

Masquerade, Ekaterina Lukasheva || 2-8, 10, 30 units (7.50 x 7.50, square) Instructions in Ekaterina Lukasheva’s Modular Origami Kaleidoscope

I’ve made the complete set of deltahedra before from an analogous unit which is assembled in the same configuration, but obviously this one has the added patterns.

Assembling in this manner has two key differences from the usual spiked-face configurations we see in many kusudamas:

Each unit represents a pair of faces, instead of an edge

You can, and often have to, mix the handedness of the units.

The combinations of handedness for the deltahedra here are as follows:

2 units = 1+1 = Tetrahedron 3 units = 3+0 = Triangular Bipyramid 4 units = 4+0 = Octahedron 5 units = 5+0 = Pentagonal Bipyramid 6 units = 4+2 = Snub Disphenoid 7 units = 4+3 = Triaugmented Triangular Prism 8 units = 4+4 = Gyroelongated Square Bipyramid 9 units cannot form a convex polyhedron; see the wiki page on deltahedra. 10 units = 5+5 = Icosahedron

Some tips if you want to try on your own, whether with this unit or @neutrinoprism’s unit:

2 units has only one option

3 units can also be 1+2, which might be easier to assemble. However, especially because of the patterns on this unit, 1+2 is definitely less pleasing.

4, 5, 8, and 10 units likely have other configurations, but they’re already both aesthetically pleasing and easy to assemble.

6 units can also be 3+3 or 5+1. 4+2 is the most symmetrical, but 5+1 definitely has aesthetic value.

7 units must have 2+2, and then the remaining 3 can be any handedness; the 2 that are the same form one square pyramid, the 2+2 are a belt of 8 triangles, and the last, opposite the first pyramid, can be the same or different as the first 2.

[benji-cheung]

Deltahedra

Designed (as far as I can tell) by @neutrinoprism (they’re cool)

8.9 by 8.9

Pink: Icosahedron, 5+5 Pcs Red: Snub Disphenoid, 5+1 Orange: Gyroelongated Square Bipyramid, 4+4 Yellow: Octahedron, 4 Green: Tetrahedron, 1+1 Teal: Triaugmented Triangular Prism, 5+2 Dark Blue: Pentagonal Bipyramid, 5 Light Blue: Triangular Bipyramid, 1+2

Note that there are multiple ways to achieve these figures using different combinations of the units.

Instructions