Origami Star Dodecahedron

Origami Star Dodecahedron designed by Francesco Mancini.


Reference:

Paper used : Color printer sheet

No.of units : 30

Paper size : 2 inch x 4 inch rectangle

(22 May 2014 - 23 May 2014)

Star Flower

Star Flower by Meenakshi Mukherji

Reference : Exquisite Modular Origami by Meenakshi Mukherji

No of units : 30

Paper size : 3 inch x 6 inch rectangles

Paper type : Origami paper

Vortex Dodecahedron

Vortex Dodecahedron

Reference : Exquisite Modular Origami by Meenakshi Mukherji

No of units : 30

Paper size : 3 inch squares

Paper type : Origami paper

Pinwheel Dodecahedron Variation

Reference : Exquisite Modular Origami by Meenakshi Mukherji

No of units : 30

Paper size : 3 inch squares

Paper type : Origami paper

Striped Sonobe Icosahedron

Dear readers,

Today is Mahalaya, beginning from tomorrow is Navaratri - celebration of good triumph. Wishing everybody a very happy Navaratri.

Thanks and Regards,

Deepika

Reference : Marvelous Modular Origami by Meenakshi Mukherji

Paper used : Origami paper

No of units : 30

Paper Size : 6 inch square

Top: Left to Right : Striped Sonobe Icosahedron, Pinwheel Dodecahedron, Daisy Sonobe, Patterned Icosahedron. Bottom: Left to Right : Normal Sonobe , Dodecahedron, Sonobe cube, Icosahedron

Pinwheel Dodecahedron

Reference : Exquisite Modular Origami by Meenakshi Mukherji

No of units : 30

Paper Size : 6 inch square

Paper type : Origami Paper

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 Mukerji

Reference: Ornamental Origami

Video Tutorial :

No of units : 30 rectangles

Paper used : origami paper

Paper size : 3 inch : 6 inch

Daisy Sonobe Cube

Reference : Marvelous Modular Origami by Meenakshi Mukherji

No of Units : 6

Paper type : Origami Paper

Paper size : 6 inch square sheets

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.

(Reference: http://en.wikipedia.org/wiki/Augmentation_(geometry)#Names)

Number of Sonobe Units	Faces	Edges	Vertices
s	2s	3s	s + 2
6	12	18	8
12	24	36	14
30	60	90	32

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

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)

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.

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

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.

Loved this kusudama, folding was fun.

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

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

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

Daffodils

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.

Reference : Exquisite Modular Origami by Meenakshi Mukerji

No of units : 30 square sheets

Paper used : color printer paper

Paper size : 4 inch square sheets

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 

Reference : Exquisite Modular Origami by Meenakshi Mukerji

No of units : 30 square sheets

Paper used : color printer paper

Paper size : 4 inch square sheets

21 June 2014

Tomoko Fuse Boxes - The entire collection

Origami Boxes - Tomoko Fuse - Entire Collection

1. Lid of tsuzura and Base of tsuzura
2. Square Boxes : First and Second Series and Lozenge Lid Variation
3. Lid of a square box : fancy pinwheel
4. Octagon Box : Lid of an octagon Box (little flower and double stars) : Base of an octagon box
5. Triangle Box : Small, Medium and Large sizes
6. Hexagon Box : Lid of a hexagon box (six petal pinwheel and flower and star) and base of hexagon box

Folded in the month of March 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

Triangle boxes - Tomoko Fuse

Above Photo : Triangle box

Above Photo : Left to right, triangle box large, medium and small size

Above Photo : Triangle boxes stacked

Reference: Origami Boxes by Tomoko Fuse

Paper : Color Printer Paper

Paper size: 4 inch square papers

No of units : 3 for each lid/base

Octagon box - Tomoko Fuse

Above photo: Right - lid of an octagon box: little flower, Left - lid of an octagon box: double stars

Above photo: Base of an octagon box

Above photo: Back view of the bases and lids

Reference: Origami Boxes by Tomoko Fuse

Paper : Origami paper

Paper size: 6 inch square papers

No of units : 4 for each lid/base

Lid of a square box : Fancy pinwheel - Tomoko Fuse

Above Photos: Fancy pinwheel Lid of a square box

Reference: Origami Boxes by Tomoko Fuse

Paper : Origami paper

Paper size: 6 inch square papers

No of units : 4 for each lid/base

Square Boxes - Tomoko Fuse

Above photo : Front view of different designs of square boxes base and lids

Above Photo : Back view of different designs of square boxes base and lids

Reference: Origami Boxes by Tomoko Fuse

Paper : Color Printer paper

Paper size: 4 inch square papers

No of units : 4 for each lid/base