23 August 2014

Patterned Icosahedon

Above Photo : Patterned Icosahedron vertex (left) and triangular face (right)

Above Photo : Triangular face of Patterned Icosahedron and simple Icosahedron

Above Photo : Vertex of Patterned Icosahedron and simple Icosahedron

Designer :  Meenakshi Mukherji

Reference: Ornamental Origami

Video Tutorial :

No of units : 30 rectangles

Paper used : origami paper

Paper size : 3 inch : 6 inch

16 August 2014

Daisy Sonobe Cube

Reference : Marvelous Modular Origami by Meenakshi Mukherji

No of Units : 6

Paper type : Origami Paper

Paper size : 6 inch square sheets

09 August 2014

What is Sonobe?

Above Photo : Sonobe Cube, Sonobe Octahedron and Sonobe Icosahedron

I am writing this article referring to wiki definition of Sonobe (http://en.wikipedia.org/wiki/Sonobe), borrowing facts and the below table from wiki to note down some points for my quick reference.

The creator of Sonobe is Mitsunobu Sonobe. A single sonobe unit looks like a parallelogram with 135 and 45 degrees angle. Three of such Sonobe units forms a triangular pyramid (open bottomed). In geometry placing such triangular pyramids on each of the four triangular faces of a tetrahedron we get a cube. Similarly by placing triangular pyramids on octahedron and icosahedron results in augmented octahedron (Sonobe Octahedron) and augmented icosahedron (Sonobe Icosahedron).

Since the triangular pyramid we obtain by joining 3 Sonobe unit is open bottomed, the underlying polyhedra (tetrahedron/octahedron/icosahedron) is imaginary. Sonobe units is only for the pyramids.

The word Augmented in geometry means that a pyramid has been joined to a face of the solid in question. Here the solid in question is octahedron and icosahedron (or tetrahedron). We are joining triangular pyramid on it's faces. Hence we say augmented Octahedron and augmented icosahedon.

Number of Sonobe UnitsFacesEdgesVertices
s2s3ss + 2
The above table is for Sonobe : Cube (s = 6), Octahedron (s = 12) and Icosahedron (s = 30)

To explain the above table consider example of Sonobe Cube, we need 6 Sonobe units to make a Cube. 

Faces  (applying formula) 2 * 6 = 12

(Note : It's a triangular face - not to be confused with face of cube. As a matter of fact One face of Cube has 2 faces of Sonobe Cube)

Logic : A pyramid that we place on the face of tetrahedron has 3 triangular faces. We need 4 pyramids to make a cube. Hence 3 * 4 = 12

Edges (applying formula) 3 * 6 = 18

Logic : Edges of tetrahedron + 3 * (number of pyramids) = 6 + (3 * 4) = 18

Vertices (applying formula) 6 + 2 = 8

Logic : Vertices of tetrahedron + apex of pyramids (equal to number of faces of tetrahedron) = 4 + 4 = 8

Same logic can be applied for Augmented octahedron and Augmented icosahedron. It might be little confusing to visualize the above logic with the Sonobe cube since the pyramids are not protruding. The below video might help visualizing.

Basically a cube can be divided into five tetrahedra - if a cube is triangulated such that the central tetrahedron is regular. A tetrahedron is a triangular pyramid.

Reference: http://www.ics.uci.edu/~eppstein/projects/tetra/

Above Photo : Sonobe Octahedron

Sonobe Octahedron (Augmented Octahedron) might help in better understanding.

Tetrahedron, Octahedron and Icosahedron are Platonic Solids. Cube and Dodecahedron are the other Platonic Solids. A cube has square faces, Dodecahedron has pentagonal faces - hence triangular pyramids cannot be placed.

Augmented Icosahedron / Sonobe Icosahedron is widely folded in Origami to obtain attractive floral balls. A Sonobe Icosahedron has 20 pyramids because Icosahedron has 20 (triangular) faces. Similarly a Sonobe Octahedron has 8 pyramids because Octahedron has 8 (triangular) faces and Sonobe Cube has 4 pyramids because tetrahedron has 4 (triangular) faces.

Note: I have used Sonobe Icosahedron and Augmented Icosahedron names interchangeably (Similarly Sonobe Octahedron and Augmented Octahedron).

Here's a link to assemble the above Sonobe models: Make Sonobe-Cube-Octahedron-Icosahedron

03 August 2014

With Meenakshi Mukerji

Above Photo : Origami models display by Meenakshi Mukerji in Sunnyvale Public library
(All models on display are designed and folded by herself)

Above Photo : Myself with Meenakshi Mukerji

I was very happy to meet origami artist and author Meenakshi Mukerji on Friday (1 Aug 2014). She has been designing and displaying several modular origami models for over two decades. Her models are for public display in Sunnyvale public library. Last year her Origami exhibit in Sunnyvale Public Library (in the same curio cabinet) inspired me to try Origami in it's modular form. I folded some of her designs Sun Burst, Star Burst, Ixora, Impatient Trillium Bouquet, Tuberose and went on to try Intersecting planes from her book Ornamental Origami. Lately I have folded some more of her designs. I was glad to meet her just as I started to post them in this blog. I will continue to post the remaining models I folded from her book.

26 July 2014

Whipped Cream Star

Above Photo : Whipped Cream Star designed by Meenakshi Mukerji

Above Photo : Another view of Whipped Cream Star Kusudama

Above Photo : Reflection of the model in my dining table

Above Photo : Close up view of the model

Reference : Origami Inspirations by Meenakshi Mukerji

Paper type : Origami paper

No of units : 30

Paper size : Rectangles of size 3 inch x 6 inch

Difficulty : Intermediate.

Note : In step 6, I missed a folding. Instead of mountain folding the point A to the tip and valley folding the sides, I valley folded the sides without mountain folding point A to tip. This way, I got stuck at step 12.

Making single unit is simple. Assembly in dodecahedron style. The model gets squishy during assembly, sturdy in the end. Loved this kusudama, folding was fun.

Time : 3 - 4 hours

19 July 2014

Flower Dodecahedron

Above photo : Flower Dodecahedron

Reference : Origami Inspirations by Meenakshi Mukerji

Paper type : Printer paper

No of units : 12 for the flowers (yellow) and 30 pink units to connect the flowers (Dodecahedron F=12 E=30)

Paper size : 8.5 inch square sheets for flowers and to make pink units

Difficulty : Low intermediate.

There's lot of work involved. It was a 4 day project for me.. The flowers are made from pentagonal sheet (instructions to make pentagon from square sheet is given in the book). I started with 8.5 inch square paper and made pentagons using printer paper that has same color on both the sides because of which the final model actually looks like below. If duo paper is used you get different color in the center. Finally I inserted blue paper to get a different color in the center. Assembly is very simple, assemble in dodecahedron style. The final model is about 8 inches in height.

No glue or paper clip used during assembly.

 Started on June 1st 2014 and completed on 5th June 2014

12 July 2014


Above pic : Daffodils Floral Ball designed by Meenakshi Mukerji

Above pic : Another view of floral ball for the center pyramids view

Above pic : close up view of a flower

Above Photo : Dimpled model with curls and Daffodils Floral Balls

I added a tab in the header menu. It's a direct link to my Flickr photo gallery dedicated to Origami. It's nice and colorful to see all the photos together.

No of units : 30 square sheets

Paper used : color printer paper

Paper size : 4 inch square sheets

Difficulty : Easy to make units. Assembly in Dodecahedon fashion. Lot of delicacy required while assembling. Quite sturdy in the end.

Time : 3-4 hrs

02 July 2014

Dimpled Model with Curls

Above Photo : Dimpled Model with Curls designed by Meenakshi Mukerji 

Above Photo : The dimpled curly model reflection in my glassy black dining table

An interesting observation in the above photo is it causes optical illusion. The central dimple in the front appears to be a pyramid.  It looks like there is a pentagonal pyramid inside a pentagonal bowl where in reality it is actually an elevated pentagonal bowl. This is a good example of optical illusion!

Above Photo : Close up view of the dimple

Above photo : The model and it's reflection 

No of units : 30 square sheets

Paper used : color printer paper

Paper size : 4 inch square sheets

Difficulty : Easy to make units. Assembly in Dodecahedon fashion. Assembly is very simple but doesn't tightly lock the units and hence requires lot of delicacy during assembly. Quite sturdy in the end. First half dodecahedron assembly has to be done very carefully as the model is highly unstable. The other half was pretty fine as it starts getting to converge to a ball. This is one of my favorite floral balls.

Time : 3 to 4 hours easily

No glue or paper clips used during assembly.

21 June 2014

21 June 2014

Hexagon Box - Tomoko Fuse

Above Photo : Hexagon boxes with lids - Right: six-petal pinwheel, left : flower and star

Above photo : Hexagon box bases and front view of the two lids

Above photo : Back view of hexagon box base and two lids

Reference: Origami Boxes by Tomoko Fuse

Paper : Origami paper

Paper size: 6 inch square papers

No of units : 6 for each lid/base