# Make a Paper Puzzle

Edited by Alexander Avdeev, Eng

### Method 1: Tetraflexagon

How to make a Tetraflexagon paper puzzle.

## Steps

1. 1
Take a sheet of paper, a ruler, and a pencil
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2. 2
Start marking corners for three squares on the paper from the edge
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3. 3
Put three more squares below them so that the first square in the lower row touches the last one from the row above
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4. 4
Connect the lines to form the forward side or facet of the tetraflexagon's strip
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5. 5
Mark it from left to right
:
1, 1, 2. Below: 2, 3, 3.
6. 6
Cut the strip along its marked edge
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7. 7
Cut a small strip from the sheet of paper
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We shall use it later.
8. 8
Now, bend the whole strip along the marked lines
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9. 9
Unfold the paper strip
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10. 10
Turn the strip over to the back side as shown in the tutorial
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11. 11
Mark the blank squares in the lower row as 2, 1, 1
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The upper row should have 3, 3, 2.
12. 12
Turn it back over to the original side
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13. 13
Bend the strip as shown
:
move two 1s behind 2.
14. 14
Flip 3 onto 3
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15. 15
Connect the two right 2s with the small strip of paper that we have cut off
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Use paper glue to ensure that the piece stays and connects the 2s.
16. 16
Draw a line over it if you wish
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17. 17
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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. 1
Mark four squares horizontally and three vertically
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The length that I use is always the same (I took 30mm or 1.2-inch steps).
2. 2
Connect all lines to form twelve similar squares
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3. 3
You will have to cut along the line in the middle, so I mark it with a dotted line or with notches
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4. 4
Mark the squares from left to right, row by row
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The top row: 1, 1, 2, 3.
5. 5
The middle row
:
3, 2, 1, 1.
6. 6
The last row
:
1, 1, 2, 3.
7. 7
Cut the three-by-four square out of the sheet
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8. 8
Cut off a small strip of paper for future use
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9. 9
Fold the paper along the lines
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10. 10
Turn it over to the empty side
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11. 11
You can mark the lines between squares if you wish
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12. 12
Now, mark the squares as follows
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The top row: 4, 4, 3, 2.
13. 13
The middle row
:
2, 3, 4, 4.
14. 14
The lower row
:
4, 4, 3, 2.
15. 15
Now, turn it over to the initial side
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16. 16
Cut out the middle part as shown
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Important! Do not cut the last line. The piece must be attached to the whole puzzle.
17. 17
Now, move the strips as demonstrated
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Move the middle 2 and 1 behind the 3 to the left of them.
18. 18
Move the right column of 3, 1, and 3 under the 2s to the left of them
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19. 19
Put the right column of three 2s under the 1s to the left of them
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20. 20
Flip the leftmost 3 over the 3 next to it
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21. 21
Connect the 1s in the middle row by gluing the small strip of paper that will hold them together
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22. 22
You can draw the line over it if you wish
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23. 23
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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. 1
The layout of the puzzle will look like a line of triangles
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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")
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• 3
Let us assume that the side is 20 millimeters (or 0.79 inches)
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• 4
The height will be the side times square root of three divided by two
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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
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Each of the ten steps is 20 millimeters (0.79 inches) for this example.
• 6
Mark the height at 17.3mm (0.68 inches)
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• 7
Mark the half of the side from the left side of the sheet of paper (10 millimeters or 0.4 inches)
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• 8
Proceed with nine "a"-side steps (20 millimeters or 0.79 inches)
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• 9
Connect the dots to form equilateral triangles
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• 10
Write down the numbers with a pencil as a repeated sequence of 1,2,3
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• 11
Leave the last triangle blank
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It will be glued to another triangle later on.
• 12
Cut out the strip of triangles
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• 13
Fold the strip along the lines
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• 14
Put it back on the table with the numbered side facing up
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• 15
Turn it over vertically
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• 16
Start marking the other side as a sequence of double 4s, 5s, and 6s, leaving the first triangle empty
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• 17
Prepare to lay 4s over 4s, 5s over 5s, and 6s over 6s as shown in the video
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• 18
Lay the left 5 over the next 5 to the right of it
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• 19
Lay the 6 over the 6 next to it
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• 20
Continue doing that the previous three steps until all of the strip is folded
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• 21
Position the strip with the 1 and 2 to the left
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• 22
Now, bend the whole left part behind the 2s to the right
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• 23
Put the remaining tail after the 2s under the last 2
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• 24
Take the 2 from under the 3
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• 25
Fold the 1 to the back, gluing it
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• 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. 1
The puzzle layout looks like a long strip of triangles
.
2. 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
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All triangles are equilateral.
3. 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. 4
Let us assume that it is 25 millimeters (0.98 inches)
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5. 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
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6. 6
We can use a calculator to find the height
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The height is 21.7 millimeters (0.85 inches).
7. 7
Start marking the lower sides now
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Each of the nine steps is 25 millimeters (0.98 inches) for this example.
8. 8
Mark the first height at 21.7mm (0.85 inches) up from the lower edge of the sheet
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9. 9
Take a half of the side and measure it from the left on the upper line
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In this case, it is 12.5 millimeters (0.49 inches).
10. 10
Proceed with marking the length of the side ten times
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11. 11
Mark the second height at 21.7mm (0.85 inches) up from the upper line
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12. 12
Proceed with marking the length of the side on the uppermost line ten times
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13. 13
Now, connect the dots to form equilateral triangles as demonstrated
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14. 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. 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
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16. 16
Cut out both strips of triangles
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17. 17
Glue the back side of the 5 from the lower strip to the blank triangle of the upper strip to merge both parts
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We can use simple paper glue.
18. 18
Fold the strip along the lines
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19. 19
Put the strip with the numbered side facing up
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20. 20
Turn the strip over vertically
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21. 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
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22. 22
Lay the first 7 upon the next 7
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23. 23
Lay the leftmost 8 upon the next 8
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24. 24
Lay the first 9 upon the next 9
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25. 25
Lay the first 10 upon its neighbouring 10
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26. 26
Lay the first 11 upon the next 11
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27. 27
Put the first 12 upon the next 12
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28. 28
Continue with the same pattern for the rest of the unfolded triangles
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29. 29
You should get a row of 4s, 5s, and 6s as shown here
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30. 30
Now, start a new pattern by laying the 6 over the next 6
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31. 31
Lay the 5 over its adjacent 5
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32. 32
Lay the first 4 over the next 4
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33. 33
Repeat the three steps above twice to continue with the row of 4s, 5s, and 6s
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34. 34
Position the strip as shown
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The strip must be positioned with 2, 2, 1, 1, 3 on the right.
35. 35
Pull the triangles with the 2s on the right behind the nearest triangle with the 1
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36. 36
Pull the next couple of triangles with 2s behind the nearest triangle with the 1
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37. 37
Pull out the 1 from under the 3 to form a whole hexagon of 1s
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38. 38
Turn the dodecahexaflexagon over
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39. 39
Put the blank triangle under the 2 so that you see two 4s
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40. 40
Put the two 4s together and glue the blank triangles together
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41. 41
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Practice solving the puzzle until you find all its twelve facets.
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## Article Info

Categories : Papercrafts

Recent edits by: Alexander Avdeev