10 April 2013

Five Intersecting Tetrahedra

Designed by Tom Hull

Paper should be in 1:3 ratio.
I took 2 inch : 6 inch paper size.
Color printer paper used.
Not an easy one.Can get confusing.

Step 1: Cut the papers in 1:3 ratio. 5 colors. 6 pieces in each color. 5 * 6 = 30 pieces totally

Step 2: Fold the papers 

Step 3: Assemble

2 intersecting tetrahedra:

3 intersecting tetrahedra:

4 intersecting tetrahedra:

Finally 5 intersecting tetrahedra:

  1. First time I tried by taking all white sheets. I could assemble 3 tetrahedra easily. 4th one was slightly confusing. I messed up with 5th one. Do not take all white sheets if you are doing for the first time.
  2. First time I took bigger piece, 3 inch: 9 inch. It was easy to connect due to the bigger size. Better start with bigger ratio and keep reducing once it is clear.
  3. Second time I took 5 different colored sheets and paper size 2 inch : 6 inch. I was able to figure out easily. It came out neat and perfect. I was very happy to hold it in the end.
  4. To assemble first time it took me 3-4 days. Gave me lot of trouble mainly because of all white color sheets. 
  5. Second time I took 2 days to do. First day to cut papers and make units - 2-3 hours. Second day to assemble, time taken = around 2 hours.

Some interesting facts about tetrahedra/Mathematics behind it:

In a regular dodecahedra, if we join 4 mutually equidistant corners, a tetrahedra is formed. Similarly we can form 4 more tetrahedra. Totally 5 intersecting tetrahedra as shown. Explained beautifully in the above link.

Some more links that inspired me to make this model (other than above two links by adkit2 and jonakashima):


  1. Looks like this one is pretty difficult to assemble. Nice to know more about tetrahedra. Thanks for the links :)

  2. Sure Ashwini. Yes this was not an easy one. Had to try hard. Failed first time but got it the next time :)