How to Create Our Interlocking Tetrahedra Logo

by Natural Math

A tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of 4 triangular faces, 6 straight edges, and 4 vertex corners (vertices).

Our newsletter logo is made of 5 interlocking tetrahedra. Each is shown in a different color and is made from 6 strips of paper with dimensions in the ratio of 1 to 3 (i.e., one tetrahedron requires six, 1 x 3 pieces of paper). 

This origami activity gives step-by-step instructions to recreate our interlocking tetrahedron logo. This is recommended for older students and adults as it takes patience and time to create – but the final beautiful result is well worth the effort!

To supplement this article, you may also wish to watch the following video showing Thomas Hull’s 5-interlocking tetrahedra design (produced by Lavender Home).

Here’s what you need to get started:

  • One tetrahedron requires six 1×3 pieces of paper. Start with two squares of colored paper and cut each into three 1×3 strips.
  • To make the full 5 intersecting tetrahedra modelyou’ll need a total of 10 squares of colored paper. (You may wish to practice with extra paper to become accustomed to the techniques in these instructions.)
  • Scissors and quick drying tacky glue

HINT:  I suggest creating each of the 5 tetrahedra in a different color, as shown in our logo. That way, when assembling the model, it will be easier to keep track of the placement of each interlocking tetrahedron by color, as opposed to having to figure out the arrangements if they were all the same color.

Begin by making each of the 5 tetrahedra (solid lines represent paper edges and dashed lines represent folds):

Step 1: Fold one colored square into 3 equal strips. Unfold. Cut along the folds. Do this again for the second square of the same color.  You will end up with six 1×3 strips of the same color.  Repeat Step 1 for each set of colored squares until you have 30 strips (5 x 6 = 30 strips).  Set them aside grouped by color.

Follow Steps 2 to Step 8 for each strip: 

Step 2Take one of the strips and fold it in half lengthwise by bringing both long edges towards the center.  Crease along the fold:
Then unfold:  

Step 3Fold both long edges towards the center and crease. Do not unfold.

Step 4Fold the top long edge to the center, making a small crease.  Unfold. This crease will be needed for the next step.
Step 5Fold up the bottom corner of one of the long sides to meet the creased fold line made in Step 4. Unfold.
Step 6: Reverse fold the bottom corner from Step 5 into itself. Crease to align with the center as shown:
Step 7Hide the white corner behind the layer of the other folded side.
Step 8Fold the upper corner of the strip to align with the opposite side edge as shown, forming a sharp point at the end of the strip.  Crease.
Step 9Repeat Steps 4 through 8 for the opposite end of each strip. Fold andcrease each strip lengthwise along its center. When all 30 are finished, set them aside grouped by color. We’ll refer to each of these from now on as a “segment.”  Each of the 30 segments will form the edge of one tetrahedron.  At every vertex, 3 segments will link together.

Follow Steps 10 and Step 11 to assemble a “tripod”:

Step 10Notice how the end of each segment has a flap on one side and a pocket on the other. Insert the flap of one segment end into the pocket of another segment end as shown on the left. Add glue as needed to hold together. The picture on the right shows the outcome.

Step 11Bring in a third segment. Fit it together with the result from Step 10 to form one finished vertex. Add glue as needed to hold together.  If need be, round out the edges to allow the last flap to hook around the other segment. Attach and crease the sides.  Notice how this forms a “tripod.”

Step 12Repeat Steps 10 and 11 for all remaining segments by color. Now you have 5 different colored “tripods” and 15 remaining color segments.  Set aside the tripods with their respective remaining color segments.

Step 13: At this time, make only ONE complete tetrahedron by doing the following: Choose one color tripod and its remaining 3 segments. Repeat Step 11 by adding a segment to each of the tripod’s legs to assemble the other vertices.  This results in one completed tetrahedron. Set it aside.

Follow Steps 14 to Step 16 to finish the assembly: 

 Step 14: Start with the completed tetrahedron from Step 13 and one of the tripods.  Place the tripod (in the example below it is blue) inside the finished tetrahedron (orange) so that its vertex points towards the middle of the tetrahedron base  and each of the tripod legs poke through the other 3 faces of the tetrahedron (see below).

Step 15Attach the remaining segments to the tripod (in the example, this completes the blue tetrahedron). Now you have two interlocking tetrahedra. In the illustration below, if you were to poke the blue vertex a bit through the base of the orange tetrahedron, causing the upper vertex of the orange tetrahedron to poke through the base of the blue, you would notice the two tetrahedrons are interwoven in a pattern that resembles a 3-D Star of David. 
Step 16As you continue to add each new tetrahedron to this model, move the model around to fit parts into place. Notice a symmetry in the weaving of each new tetrahedron such that any two tetrahedra are interwoven with one corner poking through the base of the other and vice versa.

Ta – Dah!

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