Icosahedron - frame

An icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids.

Reference:  Ployhedron Origami for Beginners - Miyuki Kawamura
No of units: 12 units (Blue for vertices) + 30 units (Yellow for edges)
Paper size used : 3" x 3"  
Paper used: normal color printer paper
Time: around 2 hours to make the units and assembling

Note: I found it little unstable while assembling. The joints came apart while assembling new ones. I realized this is where Origami tests our patience.  Finally very reluctantly I used glue, just to complete the model.  

There was dodecahedron too in the book, I didn't try it. 

This is the end of platonic solids frame type. 

I will be posting more of intersecting planes, very interesting and very beautiful models. I have finished up to 8 intersecting planes starting from 3 (XYZ co-ordinates). As we go up units are more, need to spend more time cutting and folding individual units. Look forward for intersecting planes family on my blog.

Octahedron - frame

Reference:  Ployhedron Origami for Beginners - Miyuki Kawamura
No of units: 6 units (Green for vertices) + 12 units (Pink for edges)
Paper size used : 3" x 3"  
Difficulty: A very simple and easy to make module. No hassle while assembling.
Paper used: normal color printer paper
Time: around 1.5 to 2 hours to make the units and assembling

No glue or paper clip used for assembling. 

Cube - Frame

Reference:  Ployhedron Origami for Beginners - Miyuki Kawamura
No of units: 8 units (Pink for corners) + 12 units (Blue for edges)
Paper size used : 3" x 3"  
Difficulty: very easy , easy to assemble and very sturdy model.
Paper used: normal color printer paper
Time: around 2 hours

No glue or paper clip used.

Tetrahedra - Frame

Reference:  Ployhedron Origami for Beginners - Miyuki Kawamura
No of units: 4 units (Yellow for vertices) + 6 units (Green for edges)
Paper size used : 5" x 5"  
Difficulty: very easy , easy to assemble and very sturdy model.
Paper used: normal color printer paper
Time: 1.5 to 2 hours

No glue or paper clip used.

Platonic Solids

Platonic Solids are five and only five:

1. Tetrahedron
2. Cube
3. Octahedron
4. Dodecahedron
5. Icosahedron

A tetrahedron has 4 triangles, 3 triangles meet at a vertex, angle at a vertex = 3 * 60 = 180 degrees
A cube has 6 squares, 3 squares meet at a vertex, angle at a vertex = 3 * 90 = 270 degrees
An octahedron has 8 triangles, 4 triangles meet at a vertex, angle at a vertex = 4 * 60 = 240 degrees
A Dodecahedron has 12 pentagon, 3 pentagons meet at a vertex, angle at a vertex = 3 * 108 = 324 degrees
A Icosahedron has 20 triangle, 5 triangles meet at a vertex, angle at a vertex = 5 * 60 = 300 degrees

In all the above cases:

angle at a vertex < 360 degrees.

So it is possible to form a polyheda. It is not possible with any other case. For proof read on the link which is very interesting. The proof is simple using Euler's formula.

http://www.mathsisfun.com/geometry/platonic-solids-why-five.html


Some more interesting facts on wiki:

From wikipedia - The ancient Greeks studied the Platonic solids extensively. Some sources (such as Proclus) credit Pythagoras with their discovery. Other evidence suggests he may have only been familiar with the tetrahedron, cube, and dodecahedron, and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. In any case, Theaetetus gave a mathematical description of all five and may have been responsible for the first known proof that there are no other convex regular polyhedra.
The Platonic solids feature prominently in the philosophy of Plato for whom they are named. Plato wrote about them in the dialogue Timaeus c.360 B.C. in which he associated each of the four classical elements (earth, air, water, and fire) with a regular solid. Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron.
Read more on:

http://en.wikipedia.org/wiki/Platonic_solid

Coming up more of Origami Platonic solids on my blog...

Five Intersecting Tetrahedra

Designed by Tom Hull

Paper should be in 1:3 ratio.
I took 2 inch : 6 inch paper size.
Color printer paper used.
Not an easy one.Can get confusing.

Step 1: Cut the papers in 1:3 ratio. 5 colors. 6 pieces in each color. 5 * 6 = 30 pieces totally

Step 2: Fold the papers 

Reference: http://www.youtube.com/watch?v=4pAsrMd78Us by Adkit2

Step 3: Assemble

Reference: https://www.youtube.com/watch?feature=player_embedded&v=aT2UHxA4uRY by Jo Nakashima

2 intersecting tetrahedra:

3 intersecting tetrahedra:

4 intersecting tetrahedra:

Finally 5 intersecting tetrahedra:

Note: 

1. First time I tried by taking all white sheets. I could assemble 3 tetrahedra easily. 4th one was slightly confusing. I messed up with 5th one. Do not take all white sheets if you are doing for the first time.
2. First time I took bigger piece, 3 inch: 9 inch. It was easy to connect due to the bigger size. Better start with bigger ratio and keep reducing once it is clear.
3. Second time I took 5 different colored sheets and paper size 2 inch : 6 inch. I was able to figure out easily. It came out neat and perfect. I was very happy to hold it in the end.
4. To assemble first time it took me 3-4 days. Gave me lot of trouble mainly because of all white color sheets. 
5. Second time I took 2 days to do. First day to cut papers and make units - 2-3 hours. Second day to assemble, time taken = around 2 hours.

Some interesting facts about tetrahedra/Mathematics behind it:

Read: http://info250.info/cgao2/FiveIntersectingTetrahedra.pdf

In a regular dodecahedra, if we join 4 mutually equidistant corners, a tetrahedra is formed. Similarly we can form 4 more tetrahedra. Totally 5 intersecting tetrahedra as shown. Explained beautifully in the above link.

Some more links that inspired me to make this model (other than above two links by adkit2 and jonakashima):

http://gurmeet.net/origami/five-intersecting-tetrahedra-by-tom-hull/

http://www.origaminut.com/10/origami-star-five-intersecting-tetrahedra

Origami Dragon Boat

Reference: YouTube video
No of units: - In the video
Paper size used : - 
Difficulty: easy 
Paper used: normal color printer paper
Time: I took two weeks. Depends on individual's speed
Glue used.

Impatient Trillium Bouquet

Above Photo: Impatient Trillium Bouquet designed by Meenakshi Mukerji

Reference: Meenakshi Mukerji's Ornamental Origami
No of units: 12
Paper size used : 3" x 3" (can also use 3" - 5" square papers)
Difficulty: moderate, used paper clips to hold the units while assembling..
Paper used: normal color printer paper
Time: 2 - 3 hours

No glue used.

Flower Basket

Reference: YouTube video
No of units: -
Paper size used : - 
Difficulty: easy 
Paper used: normal color printer paper
Time: -
Glue used.

3D Origami Swan

Reference: YouTube video
No of units: White - 342 Red - 220
Paper size used : - 
Difficulty: easy 
Paper used: normal color printer paper
Time: -
Glue not used.