The Icosahedral Kit is yet another of the Polyhedron kits from Miyuki Kawamura's book 'Polyhedron Origami'. In this modular origami, 2 kinds of modules are used - the Edge module and the Vertex module. The icosahedron kit is made from a total of 12 vertex modules and 30 edge modules - a grand total of 42 modules.

Double-sided paper works best, since the back of the vertices are visible through all those gaps. The modules are fairly easy to fold and assemble. I used glue as a precaution, but it is not absolutely needed. The size of the paper that I had used was 3 inches and it resulted in a fairly big icosahedron - about 6 inches in diameter.

Model Details:

Model: Icosahedron Kit

Creator: Miyuki Kawamura

Book: Polyhedron Origami

Author: Miyuki Kawamura

Difficulty Level: High Intermediate

Paper Ratio: Square

Paper Size: 3 inches

Model Size: 6 inches diameter

Number of Modules: 42

Tutorial: Youtube

Let me start off by saying that the more I read about origami snapology, the more information I find! Plenty of tutorials are available to make the basic snapology unit. As for assembling the units into various polyhedra, there are tutorials for assembling the Icosahedron but all other polyhedra are strictly DIYs :) But once we understand the polyhedral shapes, using snapology units to form those shapes is fascinating, though challenging.

To start off with the basics, snapology is a term coined by Heinz Strobl and involves folding units from paper strips. The beauty of snapology is that, these units can be used to form any polyhedra, starting from the Tetrahedron (4 vertices and 4 triangular faces) to the complex Truncated Icosidodecahedron (120 vertices and 63 polygonal faces!).

The basic snapology units are assembled along the wire frame of a polyhedra (for a polyhedral solid, when the faces of the solid are removed, the edges along remain. These edges, that retain the shape of the solid, is the wire frame) to form the various shapes. Each unit has 2 parts - a strip that forms the basic shape (a triangle for the icosahedra in this post) and a second strip that acts as a connector and links 2 shapes.

The icosahedra has a total of 12 vertices and 20 triangular faces. So we need 20 strips to form the 20 triangles. To determine the number of connector units, we need to determine the number of edges that the polyhedron has. Here's where a little Maths helps - the Euler's formula, which goes thus:

Euler's Formula:

V + F - E = 2

where V = number of vertices, F = number of faces and E = number of edges

We need E, so the formula works out as

E = V + F - 2

For the icosahedron, E = 12 + 20 - 2 = 30.

So, we need a total of 50 strips (20 for the triangles and 30 for the connectors). I used A4 sized paper, cut into 8 strips each, which I then cut into halves. So a single A4 gave me 16 strips. So 3 A4 sheets + 1 additional strip gave me the 50 strips I required.

Model Details:

Model: Icosahedron using Snapology 

Creator: Heinz Strobl

Difficulty Level: Low Intermediate

Paper Ratio: A4 paper cut into 8 strips

Model Size: ~4 inches tall

Instructions: Haligami

Tutorial: Youtube

The dodecahedron kit is a part of a series of similar kits from the book 'Polyhedron Origami', by Miyuki Kawamura. The other kits in the series include the Edge Module, Tetrahedron, Octahedron and Icosahedron kits.

Each of these kits are made up of 2 kinds of modules - the vertex modules (which forms the corners of the polyhedron) and the edge modules (which connects 2 vertex modules). The vertex module is different for different polyhedra, with changes in the angle and in the number of arms radiating from it.

The dodecahedron kit is made from 50 modules - 20 dodecahedron vertex modules and 30 edge modules. The vertex modules have 3 radiating arms, so are connected to 3 edge modules. 5 such vertex modules link together to form 1 face of the dodecahedron. 12 such faces are joined together to form the dodecahedron.

I found it an interesting piece to fold and might also fold the other kits if possible. The only disappointment for me was that I had used single-sided paper. And when folding the vertex modules, a little of the white can be seen at the back. I didn't think much of it till I started assembling the piece and realised that, since it is a structure with a lot of big windows, the back of the modules are also visible - as can be seen in the pic! So, if you are folding this, remember to use paper coloured on both sides, at least for the vertex modules.

The model is pretty stable but if you are going to move it around a lot, then I suggest a dab of glue at the joints. Else the vertex modules tend to put out of the edge modules. And another thing, remember to use fairly small paper. I used squares of 2.5 inches and ended up with a model that measured about 7 inches across.

Model Details:

Model: Dodecahedron Kit

Creator: Miyuki Kawamura

Book: Polyhedron Origami

Author: Miyuki Kawamura

Difficulty Level: High Intermediate

Paper Ratio: Square

Paper Size: 2.5 inches

Model Size: 7 inches diameter

Number of Modules: 50

I recently bought Tomoko Fuse's 'Unit Polyhedron Origami' and I was immediately tempted to try out one of the first models described in the book - the regular polyhedron.

It is an interesting model to make and I must say I love the end result :) Assembly is slightly difficult in the initial stage, where you have each module trying to come apart. But after around 7 modules have been added, adding the rest is quite easy.

I will probably be trying out more from this book; there are quite a few lovely models explained in the book.

Model Details:

Model: Regular Dodecahedron 

Creator: Tomoko Fuse

Book: Unit Polyhedron Origami
 
Author: Tomoko Fuse
 
Difficulty Level: Low Intermediate

Paper Ratio: Square

Paper Size: 5 inches

Modules: 12

The Scaled Octahedron is yet another modular origami that I have had the pleasure to work on, in recent days. It is not the easiest piece that I have made, mainly because of all the different size square that are needed.

The one that I have made required a total of 24 squares and 12 rectangles. The 24 squares were converted into 6 pyramids of 4 levels each. The number of levels in the pyramids can be changed as desired - in multiples of 4. So instead of 4 levels, one can also do the same with 5 per pyramid or even with just 3 levels per pyramid. The number of rectangles remain the same - these are the units needed to connect the various pyramids together.

The size of square paper for making the pyramidal modules change for each level. If we assume 'x' is the side of the smallest level, then the side of the next level is 1.5x. Followed by 2x, 2.5x and so on. So in my case, I started with 2 inches squares, 3 inches, 4 inches and 5 inches. The rectangular connectors have one side that is the same as the largest square (5 inches in my case), the other size is a quarter of this side. For me, this was 1.25 inches. A total of 12 rectangles are needed.

Folding the individual modules is fairly easy. Assembly is a little more challenging. It is better to use printer or copy paper for this model. For one - it is firmer which makes assembly a lot easier. And for another, the back of the paper is also visible, which means the white part of single-sided paper will be seen and that is not a very pretty sight for this model.

Model Details:

Model: Scaled Octahedron 

Creator: Laura Azcoaga

Difficulty Level: Low Intermediate

Paper Ratio: Squares and Rectangles

Paper Size: 2 inches, 3 inches, 4 inches and 5 inches squares + 5 inches * 1.25 inches rectangles

Model Size: ~8 inches across

Modules: 36

Instructions: Origami Modular en Argentina

Tutorial: Youtube