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Picture of 10 Cell Tetrahedral Kite
This is a 10 cell tetrahedral kite, based on the bendy straw design by emilyfis.  http://www.instructables.com/member/emilyfis/

Materials: (Most can usually be purchased at a dollar store)

Bendy Straws
Straight Straws
Packing Tape
Scotch Tape
4" mini zip ties
Mylar wrapping paper. 
Yogourt container lid

 
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Step 1: Straws

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Connect 3 bendy straws to make a triangle. Tape is not needed. Build 20 triangles.

Step 2: Make basic cell

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Tape 2 triangles together with scotch tape at about 80 degrees to make a cell. Make 10 cells.

Step 3: Skin Cell

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Tape the cell to Mylar wrapping paper with packing tape. Do not cover the corners of the  triangles with tape or joining them together will be difficult. Cut off excess paper.  Do this with each of the 10 cells.

For the sake of clarity, the kite is constructed from 3 cell layers, each a different color. 

Step 4: Bottom Row

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Join 3 cells together with zip ties.

Step 5: Middle Row

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Zip tie 4 cells to the bottom 3.

Step 6: Top Row

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Zip tie the top 3 cells to the middle 4.

Step 7: Braces

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To keep the kite as light as possible, straight straws are used as bracing, instead of wooden dowels. Tape the straight straws together to build 3 braces. Zip tie the braces to the back of the kite.

Step 8: Bridle

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Tie a bridle loop from the top to the bottom of the first cell. Optionally  for greater control, the bridle can go from the top of the first cell to the bottom of the last.

Use a paper punch to make a hole in the lid of  a yogourt container and cut a circle around it to make a soft plastic washer. This washer will let you quickly adjust how the kite flies. Thread the bridle through the washer and attach with a simple loop. Tie your kite string to the washer.

General Rules:

To make the kite more stable, slide the washer up. To make the kite catch more wind, slide the washer down.