Hexaflexagons look like standard hexagons from the front, but they hide many more surfaces within. Folding a hexaflexagon is a fun, quick craft that can trigger a higher appreciation of geometry. There are a few different hexaflexagons you can fold, among which the trihexaflexagon and hexaflexagon are the easiest to master. Keep reading to learn more.

Steps

Trihexaflexagon[1]

Make a strip of 10 equilateral, adjacent triangles. The first triangle of the strip must be upside-down, with the tip pointed toward the bottom, while the last triangle should have its tip pointed up.The triangles in between alternate from right-side-up to upside-down.

The end triangles only have one shared edge, but all the triangles in between have two shared edges, with only the base edge remaining separate from the other triangles.

Make sure that each edge of each triangle matches the length of all the other edges and triangles. Accuracy is key.

Do not detach the triangles.

Label the front and back of the strip. Starting from the left side, the front triangles should be labeled with the number 1 through 10. Flip the triangle over to its backside and label the triangles 11 through 20.Label the triangles lightly so that you can erase the marks later, if desired.

Note that each back triangle will be exactly 10 greater than the number marked on the front side of the same triangle.

Crease each triangle along the adjacent edges. Fold each shared edge back and forth a few times to crease these edges thoroughly. This will make it easier to fold the hexaflexagon.

Fold the first three triangles down and behind. The triangles labeled 1, 2, and 3 should be folded backward along the edge shared by triangles 3 and 4.Once the fold is completed, triangles 12 and 11 should be visible below the strip. Triangle 12 will be directly below triangle 4.

Fold the last four front triangles down and in front. The triangles labeled 7, 8, 9, and 10 should be folded in front, along the edge shared by triangles 7 and 6.Triangle 6 will be covered by this new fold.

The only original front triangles remaining will be 4 and 5. The other triangles currently visible from the front are triangles that were originally along the back.

Note that the main shape will now be a hexagon with a small triangle sticking out from the bottom.

Slide triangle 11 over triangle 19. At present, triangle 11 is covered by triangle 19 at the lower bottom edge of the hexagon. Swap the two triangles so that 11 overlaps 19.The rest of the shape should remain unchanged.

Fold triangle 20 in front of triangle 11. Triangle 20 should be folded up along its shared base edge. As a result, it will cover triangle 11.Triangles 11 and 20 are no longer visible, but in their place, triangle 10 should become visible again.

Note that you now have a full hexagon shape.

Place tape along the edge of triangles 10 and 11. Fold a small piece of tape around the right hand edges of triangles 10 and 11. The tape should fold around the front and back of these triangles.This step will help hold the hexaflexagon together.

Flex the hexaflexagon. Now that the basic trihexaflexagon has been completed, you can “flex” it as the name suggests.Hold the hexaflexagon in front of you with two hands.

Pinch two adjacent triangles together. Note that you should choose two triangles that are next to each other but do not share a creased edge.

Use your non-dominant hand to pinch the triangles together.

Use your dominant hand to push down on the extension of the pinched edge. This extension should be a shared edge, and pushing it down should cause you to push into the center of the hexaflexagon.

As the hexaflexagon opens at the center, use your dominant hand to open it at the edge and bend the triangles outward.

Hexahexaflexagon[2]

Make a strip of 19 equilateral, adjacent triangles. Both end triangles should be right-side-up, with the point facing upward and the base edge at the bottom.The triangles in between alternate from right-side-up to upside-down.

The end triangles only have one shared edge, but the triangles in between have two connected edges, with only the base edge remaining separate.

Each edge of each triangle must match the length of all the other edges and triangles. Do not detach the triangles.

Label the front and back of the strip. Label the front triangles using a pattern of 1, 2, 3, repeating the pattern six times until the first 18 triangles are labeled with either a 1, 2, or 3. On the back, skip over the first triangle, and label each triangle in a double pattern of 4, 5, 6 (4, 4, 5, 5, 6, 6, etc.). This pattern should repeat three times before you reach the end of the strip.Note that the last triangle from the front and the first triangle from the back will have no number label.

Label the triangles lightly so that you can erase the marks later, if desired.

Crease each triangle along the adjacent edges. Fold each shared edge back and forth a few times to crease these edges thoroughly. This will make it easier to fold the hexaflexagon.

Fold the strip so that the triangles labeled 4, 5, and 6 face each other. Bend the first triangle labeled 4 along the edge it share with the second triangle labeled 4. Do likewise with the first and second triangles labeled 5 and the first and second labeled 6. Repeat until all three sets of 4, 5, and 6 triangles have been folded over.Essentially you are folding the strip into one long spiral. This spiral should create a strip similar in appearance to the starting strip used for a trihexaflexagon. As such, the folding instructions from here on out are almost identical to those for folding trihexaflexagons.

Fold the “first” three triangles down and behind. The first three triangles from the left should be folded backward along the edge shared by the third and fourth visible front triangles.The backsides of the “first” two triangles you just folded down should now be visible from the front.

Fold the last four front triangles down and in front. The last four triangles from the right edge should be folded over the front of the strip, along the edge shared by the fourth-last and fifth-last visible front triangles.The fifth-last triangle will be covered.

At this point, note that the overall shape will be a hexagon with a single triangle sticking out from the bottom. If this triangle is sticking out from another portion of the shape, turn the entire shape until it faces the bottom.

Swap the overlapping bottom triangles. The triangles at the bottom edge of the hexagon will overlap. Swap the overlapping triangles so that the bottom section now rests on top.

Fold the extra triangle in front of the bottom front triangle. The triangle extending below the edge of the hexagon should be folded up along its shared base edge.After you make this fold, you should have a full hexagon shape.

Glue the two blank faces under the bottom triangle together. This step holds the hexaflexagon together.

Flex the hexaflexagon. Now that the basic trihexaflexagon has been completed, you can “flex” it as the name suggests.Hold the hexaflexagon in front of you with two hands.

Pinch two adjacent triangles together. Note that you should choose two triangles that are next to each other but do not share a creased edge.

Use your non-dominant hand to pinch the triangles together.

Use your dominant hand to push down on the extension of the pinched edge. This extension should be a shared edge, and pushing it down should cause you to push into the center of the hexaflexagon.

As the hexaflexagon opens at the center, use your dominant hand to open it at the edge and bend the triangles outward.

Things You’ll Need

Heavy paper

Pencil

Tape or glue

Related wikiHows

How to Make a Flexagon

How to Draw a Hexagon

How to Make 3D Photos

Sources and Citations

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