Make a Paper Puzzle Edited by Alexander Avdeev, Eng

How to make a Tetraflexagon paper puzzle.

Steps

1

Take a sheet of paper, a ruler, and a pencil.

2

Start marking corners for three squares on the paper from the edge.

3

Put three more squares below them so that the first square in the lower row touches the last one from the row above.

4

Connect the lines to form the forward side or facet of the tetraflexagon's strip.

5

Mark it from left to right: 1, 1, 2. Below: 2, 3, 3.

6

Cut the strip along its marked edge.

7

Cut a small strip from the sheet of paper. We shall use it later.

8

Now, bend the whole strip along the marked lines.

9

10

Turn the strip over to the back side as shown in the tutorial.

11

Mark the blank squares in the lower row as 2, 1, 1. The upper row should have 3, 3, 2.

12

Turn it back over to the original side.

13

Bend the strip as shown: move two 1s behind 2.

14

15

Connect the two right 2s with the small strip of paper that we have cut off. Use paper glue to ensure that the piece stays and connects the 2s.

16

Draw a line over it if you wish.

17

The puzzle is ready. Practice folding the flexagon until you find all of the three sides, one of which is always hidden.

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Video: Make a Paper Puzzle Tetraflexagon

Method 2: Tetratetraflexagon
How to make a Tetratetraflexagon paper puzzle.

Steps

1

Mark four squares horizontally and three vertically. The length that I use is always the same (I took 30mm or 1.2-inch steps).

2

Connect all lines to form twelve similar squares.

3

You will have to cut along the line in the middle, so I mark it with a dotted line or with notches.

4

Mark the squares from left to right, row by row. The top row: 1, 1, 2, 3.

5

The middle row: 3, 2, 1, 1.

6

The last row: 1, 1, 2, 3.

7

Cut the three-by-four square out of the sheet.

8

Cut off a small strip of paper for future use.

9

Fold the paper along the lines.

10

Turn it over to the empty side.

11

You can mark the lines between squares if you wish.

12

Now, mark the squares as follows. The top row: 4, 4, 3, 2.

13

The middle row: 2, 3, 4, 4.

14

The lower row: 4, 4, 3, 2.

15

Now, turn it over to the initial side.

16

Cut out the middle part as shown.

Important! Do not cut the last line. The piece must be attached to the whole puzzle.

17

Now, move the strips as demonstrated. Move the middle 2 and 1 behind the 3 to the left of them.

18

Move the right column of 3, 1, and 3 under the 2s to the left of them.

19

Put the right column of three 2s under the 1s to the left of them.

20

Flip the leftmost 3 over the 3 next to it.

21

Connect the 1s in the middle row by gluing the small strip of paper that will hold them together.

22

You can draw the line over it if you wish.

23

The puzzle is ready. Practice folding the tetraflexagon until you find all of the four sides.

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Video: Make a Paper Puzzle Tetratetraflexagon

Method 3: Hexahexaflexagon
How to make a Hexahexaflexagon paper puzzle.

Steps

1

The layout of the puzzle will look like a line of triangles. Let us calculate the size of the triangles for the puzzle. There are ten lower sides for the triangles, so we have to pick a length for the side (which is marked as "a").

All triangles are equilateral.

2

Now, we have to calculate the height of the triangle, which is marked as "h").

3

Let us assume that the side is 20 millimeters (or 0.79 inches).

4

The height will be the side times square root of three divided by two. I use a calculator application on my iPhone to find the height. The height is 17.3mm (0.68 inches).

5

I mark the lower sides now. Each of the ten steps is 20 millimeters (0.79 inches) for this example.

6

Mark the height at 17.3mm (0.68 inches).

7

Mark the half of the side from the left side of the sheet of paper (10 millimeters or 0.4 inches).

8

Proceed with nine "a"-side steps (20 millimeters or 0.79 inches).

9

Connect the dots to form equilateral triangles.

10

Write down the numbers with a pencil as a repeated sequence of 1,2,3.

11

Leave the last triangle blank. It will be glued to another triangle later on.

12

Cut out the strip of triangles.

13

Fold the strip along the lines.

14

Put it back on the table with the numbered side facing up.

15

16

Start marking the other side as a sequence of double 4s, 5s, and 6s, leaving the first triangle empty.

17

Prepare to lay 4s over 4s, 5s over 5s, and 6s over 6s as shown in the video. Start with laying the first 4 over the next 4.

18

Lay the left 5 over the next 5 to the right of it.

19

Lay the 6 over the 6 next to it.

20

Continue doing that the previous three steps until all of the strip is folded.

21

Position the strip with the 1 and 2 to the left.

22

Now, bend the whole left part behind the 2s to the right.

23

Put the remaining tail after the 2s under the last 2.

24

Take the 2 from under the 3.

25

Fold the 1 to the back, gluing it.

26

Practice solving the puzzle until you find all of the six facets.

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Video: Make a Paper Puzzle Hexahexaflexagon

Method 4: Dodecahexaflexagon
How to make a Dodecahexaflexagon paper puzzle.

Steps

1

The puzzle layout looks like a long strip of triangles.

2

We will have to split the strip into two halves and merge them into one strip later on owing to the overall length of the layout.

All triangles are equilateral.

3

Let us calculate the size of the triangles for the puzzle. We have to pick a length for the side (which is marked as "a").

4

Let us assume that it is 25 millimeters (0.98 inches).

5

To calculate the height of the triangle, which is marked as "h", we have to multiply the side by the square root of three divided by two.

6

We can use a calculator to find the height. The height is 21.7 millimeters (0.85 inches).

7

Start marking the lower sides now. Each of the nine steps is 25 millimeters (0.98 inches) for this example.

8

Mark the first height at 21.7mm (0.85 inches) up from the lower edge of the sheet.

9

Take a half of the side and measure it from the left on the upper line. In this case, it is 12.5 millimeters (0.49 inches).

10

Proceed with marking the length of the side ten times.

11

Mark the second height at 21.7mm (0.85 inches) up from the upper line.

12

Proceed with marking the length of the side on the uppermost line ten times.

13

Now, connect the dots to form equilateral triangles as demonstrated.

14

Mark the lower strip as follows: 4, 6, 1, 3, 6, 5, 2, 1, 5, 4, 3, 2, 4, 6, 1, 3, 6, and 5.

15

The upper strip is blank, 2, 1, 5, 4, 3, 2, 4, 6, 1, 3, 6, 5, 2, 1, 5, 4, 3, 2, and blank.

16

Cut out both strips of triangles.

17

Glue the back side of the 5 from the lower strip to the blank triangle of the upper strip to merge both parts. We can use simple paper glue.

18

Fold the strip along the lines.

19

Put the strip with the numbered side facing up.

20

Turn the strip over vertically.

21

Start marking the other side as a sequence of double 7s, double 8s, double 9s (make sure to distinguish 9s from 6s), double 10s, double 11s, and double 12s, leaving the first triangle empty.

22

Lay the first 7 upon the next 7.

23

Lay the leftmost 8 upon the next 8.

24

Lay the first 9 upon the next 9.

25

Lay the first 10 upon its neighbouring 10.

26

Lay the first 11 upon the next 11.

27

Put the first 12 upon the next 12.

28

Continue with the same pattern for the rest of the unfolded triangles.

29

You should get a row of 4s, 5s, and 6s as shown here.

30

Now, start a new pattern by laying the 6 over the next 6.

31

Lay the 5 over its adjacent 5.

32

Lay the first 4 over the next 4.

33

Repeat the three steps above twice to continue with the row of 4s, 5s, and 6s.

34

Position the strip as shown. The strip must be positioned with 2, 2, 1, 1, 3 on the right.

35

Pull the triangles with the 2s on the right behind the nearest triangle with the 1.

36

Pull the next couple of triangles with 2s behind the nearest triangle with the 1.

37

Pull out the 1 from under the 3 to form a whole hexagon of 1s.

38

Turn the dodecahexaflexagon over.

39

Put the blank triangle under the 2 so that you see two 4s.

40

Put the two 4s together and glue the blank triangles together.

41

The puzzle is ready. Practice solving the puzzle until you find all its twelve facets.

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Video: Make a Paper Puzzle Dodecahexaflexagon
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