Origami Cube
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What is the Origami Cube?
 ... The origami cube is a cube you can fold from a square sheet of paper. Another name is water bomb.

Folding the Origami Cube top

1
 ... Fold a square sheet of paper at the diagonals and unfold it. Put the paper at both arrows together. Lay the triangles at the top and at the bottom on top of each other.

02
 ............... The result is a flier triangle, which is known from the paper swallow......

03
 ... Fold upward on the red line on the right and on the left..................

04
 ... Then it must look like this............................................................

05
 ... Fold on the red lines..................................................................

06
 ... Then it must look like this..........................................................

07
 ... Fold the two little triangles on the red lines downward..................

08
 ............................... Put the last made triangles in the two pockets on the right and on the left. This is a little bit fiddly.

09
 ... Then it must look like this.........................................................

10
 ... Turn the whole triangle and repeat the steps 3,4,5,6,7,8,9.............

11
 ... Then it must look like this............

12
 ... Fold and unfold on the red lines. ...

13
 ................................................. Take the folded cube in hand and blow into the hole at the top. Unfold the cube by this...

14
 ... finished...........................

Some Mathematics top
 If you take the cube apart, you get a nice pattern, which is made by the folds.   You find the formulas: .........

 On the left you can see the largest net of a cube, which fits a square. You find the formulas . This cube is much bigger than the folded cube.

If you like to use the whole square for a cube, you have the formula
.
This is the largest cube, theoretically.

See more in book (5), page 63f. and page 71ff.  "Der eingewickelte Würfel".

More origami cubes from one square   top
Folding cubes is apparently a widespread art. There are numerous instructions on YouTube on the Internet.
I looked around and found eleven more cubes - folded from a square.

Let a be the side length of the starting square and x the edge length of the cube.
01 Origami Cube (Shuzo Fujimoto)

Instructions can be found - if necessary - under "01 Youtube" (URL below).
 ...... It is possible to fold a cube from a square sheet of paper.  It has four smooth squares as sides. Two opposite sides show the diagonals.

 ...... To build it, you need a 15cm x 15cm square of origami paper, for example.  First create a 4x4 grid by folding it. Make sure that the fold lines are only loosely defined.

 ...... In a second step the fold lines are traced, e.g. with a fingernail,  This is done according to the pattern shown in the drawing opposite. Valley folds are marked in red, mountain folds in blue.

 ... The bottom left tip is folded over, the colour of the back becomes visible.  Two squares are labelled B and xx.

 ....... Then fold downwards at the centre line. A square is labelled A. Now it becomes three-dimensional. Push square A onto square B so that the letters remain upright and lie on top of each other. The mountain and valley folds must be observed.

 ..... This is what the folding work looks like when you slide A onto B. This is what the folding work looks like when you place A on B...................................................................

 ...... Move the square xx under the violet square underneath. You can form one side of the cube with visible diagonals.

 ...... Close the opposite side by following the fold lines.   a = 4x or x = 0.25a

02 Origami Seamless Cube
Instructions can be found under "02 Youtube" (URL below).
The Seamless Cube has six smooth squares.
 ...... If you go back from the finished cube to the square, you get the picture on the left.

 ...... One step that is not easy is to shape the pre-folded square into a cube.  The square at the top with the letter A is the base.  Once the cube has been successfully formed, three points protrude from one corner. They are placed in the pockets provided. a = 4x or x = 0.25a

03 Cube with lid
Instructions can be found under "03 Youtube" (URL below)
 ... Once you have reached this point, you have to cut the side length into thirds.  Experienced folders can do this by folding. It is easier to divide into thirds if you use a ruler to draw at least one mark.

 ... In this phase, the folding work has two potential lids.  You can push one lid into the cube and get a cube with a lid.

 ... If you want to create a smooth cube, you have to push the potential lids into each other.  You can make the points right corner disappear.

 ... If you go back from the finished cube to the square, you get the picture on the left. a =  3sqrt(2)x or approximately x = 0.24a

04 ORIGAMI SEAMLESS CUBE (Jo Nakashima)
Instructions - if necessary - can be found under "04 Youtube" (URL below).
 ... The way to make this smooth cube is easy to understand.  You fold a tube from three cubes, leaving the ends open.  The openings are closed with the open cubes.

 ... You need a 5x5 grid. Either draw it or fold it shown in the video.

 ... In a first pass, four squares are given a cross as valley folds. This is followed horizontally by two valley folds and two mountain folds.

 ... This makes it possible to push the square together so that the mountain folds abut each other.

 ... Four valley folds make it possible to form a "tube".

 ... Push the centre bead into each other.

 ... Then close the openings as shown on the left and form points as shown in the photo on the right.

 ... The four points are pushed into the pockets on the outside.  This is tedious. It works better if you sharpen the folds of the points again. a = 5x or x = 0.2a

Instructions can be found under "05 Youtube" (URL below).
 ...... This cube is similar to cube 04, which also uses a tube made of three cubes.  The difference is that the openings are closed more simply, as in the final phase of cube  the end phase of cube 01. The result is not a smooth cube, but diagonals can be seen opposite each other.

 ........ 01 .... 05 Here you can see the difference between Cube 01 and Cube05. a = 4x or x = 0.25a

 ...... You need to know this:  Where two squares lie on top of each other, you only have to press the inner square down into the cube when closing.

06 Origami Gift Box / Ring Box Puzzle
Instructions can be found under "06 Youtube" (URL below).
 ...... The almost identical cube as 06 is presented, but the finished cube has a groove in the centre because the tube is folded the other way round.  a = 4x or x = 0.25a

07 Cube from the net
Instructions can be found under "07 Youtube" (URL below).
 ...... This is an obvious method of folding a cube from a square.  You can see the net of the cube, where four squares are used for the lid. The white squares disappear inside.  a = 3sqrt(2)x or approximately x = 0.24a

 ... It is difficult to form the four points, but it can be done. The points are placed on top of each other and the last one is tucked away.

08 Origami Gift Box with one piece of paper
Instructions can be found under "08 Youtube" (URL below).
 ... This is the moment when folding is no longer necessary. It then becomes three-dimensional

 ...... ... The cube has two halves.  When not in use, it is open a little bit.

 If you go back from the finished cube to the square, you get the picture on the left. a =  3sqrt(2)x or approximately x = 0.24a

09 Origami Box with Lid
Instructions can be found under "09 Youtube" (URL below).

It is not possible to close the cube without help. The open cube is stable.
......

 ... If you go back from the finished cube to the square, you get the picture on the left. a =  3sqrt(2)x or approximately x = 0.24a

10 Fancy Origami Cube
 ... Instructions can be found under "10 Youtube" (URL below).

The special thing is that you can form an open-top cube with just a few folds.
 ... .....a = 4x or x = 0.25a

11 Origami Cubic Dice
Instructions can be found under "11 Youtube" (URL below).
 ...

 ... Compared with the cubes presented so far, this is the smallest.  a = 4*sqrt(2) x or approximately x=0.17a.

Origami Cube from several Squares     top
12 Cube made from two squares
Instructions can be found under "12 Youtube" (URL below).
 ...... It is obvious to create a cube with two cubes open at the top.  One cube is inserted upside down into the other.  To do this, you have to make sure that the inner cube is slightly smaller.

 ...... In this video, the problem is solved more elegantly. You fold two identical cubes that are open at the top.  The cubes are then pushed into each other over the wedges between the squares into each other.  The video shows how this is done. It can be done with patience.

13 DIY : Origami 3D Cube
 ...... ... The cube is made up of six U-shaped modules. How the modules are put together is shown in the video "13 Youtube" (URL below).

14 Cube of six Sonobe modules
 ...... ... How six modules are folded and put together is shown   on my web page Sonobe Star.

15 Variant of the Sonobe cube
 ... ......
How six modules are folded and put together is shown on my German web page Körper flechten.

Cubes from Strips top
16 Cube made of three strips
...
More details on my German website Körper flechten

17 Open cube made of six strips

...
More details on my website Körper flechten

18 Cube made of four strips
 ... More details on my German website Körper flechten

19 Cube made of one strip
 ... More on my website A Strip of Paper Only

Origami-Cube on the Internet     top

Englisch

Dr Stephen O'Hanlon (Ring of Origami Art)
Water Bomb  (  .pdf file)

Gerwin Sturm (Origami for everyone)
Waterbomb

01 Youtube "Origami with Thao Bui"
Origami Cube - "Magic" Cube (Shuzo Fujimoto)

Origami Seamless Cube

Wie man eine Papierschachtel mit Deckel macht

04 Youtube "ORIGAMI SEAMLESS CUBE (Jo Nakashima)"
ORIGAMI SEAMLESS CUBE

06 Origami Gift Box / Ring Box Puzzle - (@Easy Origami)
Origami Gift Box / Ring Box Puzzle

07 Youtube "Closed Origami Cube Box Instructions - DIY - Paper Kawaii"
Closed Origami Cube Box

08 Youtube "Origami Gift Box with one piece of paper - Mica's Paper Craft C"

09 Youtube "Origami Box with Lid How to make Origami box" - ArtsfronmHeart
Origami Box with Lid

10 Youtube "Fancy Origami Cube Tutorial (Hyo Ahn)"
Fancy Origami Cube

11 Origami Cubic Dice
Origami Cubic Dice

13 Youtube  "Ventuno Art How to Fold an DIY : Origami 3D Cube"
3D Cube

German

Michael Schmitz  (Mathegami)
Der Kolumbus-Würfel

Wikipedia
Wasserbombe (Spielzeug)

zzzebra
Wasserbombe

References   top
(1) Joachim Schönherr, Wir falten und falzen, Leipzig 1990
(2) Therese Mielhaht: Origami Spaß mit Papierfalten, Köln 1990
(3) Kunihiko Kasahara: Origami - figürlich und geometrisch, München 2000
(4) Kunihiko Kasahara: Origami - ohne Grenzen, München 2001
(5) Martin Gardner: Mathematische Hexereien, Berlin/Frankfurt am Main/Wien 1988 [ISBN 3550065787]

Feedback: Email address on my main page