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This is how to create your own tangram puzzle which can be used to create both 2D and 3D objects.

Step 1: What You Need to Get Started

Materials needed:

1 x A3 Masonite Board 3.2 mm thickness.

Tools needed:

1 x Laser Cutter on 80% power.

Image of Laser Cutter:
http://www.engravingmachinesite.com
Accessed on 29/08/2012

Step 2: Cutting the Tangram

Send the file as a PDF/CDR format to the Laser Cutting machine and cut it on the masonite board.

Step 4: Assembling the Container

Step 1: Remove the container pieces from the cut-out.
Step 2: Fit the side panels on to the bottom panel ensuring that the there is one.
Step 3: Locate the lid on top of the sides of the container.

Step 5: Making a 2D Object

Place tangram puzzle pieces on a flat surface to create shapes from the geometric puzzle pieces, make sure that the pieces do not overlap, but rather that the edges are side by side.

Step 6: Creating 3D Objects

Use the slots in the 2D pieces to press-fit into one another, ensure that you do not force the pieces together, the pieces will support each other on a 3D scale. 

Step 7: Packing Away the Tangram

The Tangram pieces:

2 x Large Triangles.
1 x Medium Traiangle.
2 x Small Triangles.
1 x Parallelogram.
1 x Square.

There are 5 sets of each of the pieces mentioned above.
The sets stack on top of each other in the manner shown in the image below.
I can't seem to upload the file to the instructions section but here is the A3 PFD file. For the puzzle to match up well use a 5mm or slightly thinner material. If you would like to customize a design on the lid then you would need to set the laser cutter to a slightly less intense setting, this will produce an engraved effect in stead of cutting right through the material. Hope this helps.
Thank you very much Cuan, I think this will work. now I can see the drawing in your pdf. <br>I will try this and will let you know the result..again thank you for your quick reaction. and thanks for the nice tangram, great idea!
No problem, please let me know if there's anything you're not quite sure of. Thank you.
Hello, can you please tell me how to cut out the puzzle, because i can't find the drawing in the pdf file..do I have to send the complete pdf file to the laser cutter or what? I hope you will react soon because i will give the puzzle for someone's birthday. Is there also a possibility to draw a name in it? Thanks for reacting.
Hello, I will try find the PDF with the correct measurements and upload it as soon as possible.
I have posted the PDF on the comments section for you and everyone to use.
<a href="https://www.instructables.com/id/Rewards-for-New-Authors/" rel="nofollow">https://www.instructables.com/id/Rewards-for-New-Authors/</a>Nice first instructable! Publish it on the link!
Can you share the digital file you used so others can make their own version?

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