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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