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

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2

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

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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

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

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5

Mark it from left to right

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1, 1, 2. Below: 2, 3, 3.

6

Cut the strip along its marked edge

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7

Cut a small strip from the sheet of paper

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We shall use it later.

8

Now, bend the whole strip along the marked lines

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10

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

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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

Turn it back over to the original side

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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

Draw a line over it if you wish

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17

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

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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

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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

Mark the squares from left to right, row by row

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

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6

7

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

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8

Cut off a small strip of paper for future use

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9

Fold the paper along the lines

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10

Turn it over to the empty side

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11

You can mark the lines between squares if you wish

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12

Now, mark the squares as follows

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

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15

Now, turn it over to the initial side

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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

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

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

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19

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

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20

Flip the leftmost 3 over the 3 next to it

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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

You can draw the line over it if you wish

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23

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

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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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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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Start with laying the first 4 over the next 4.

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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

The puzzle layout looks like a long strip of triangles

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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

Let us calculate the size of the triangles for the puzzle

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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)

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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

We can use a calculator to find the height

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The height is 21.7 millimeters (0.85 inches).

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

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

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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

Proceed with marking the length of the side ten times

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11

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

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12

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

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13

Now, connect the dots to form equilateral triangles as demonstrated

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14

Mark the lower strip as follows

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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

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16

Cut out both strips of triangles

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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

Fold the strip along the lines

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19

Put the strip with the numbered side facing up

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20

Turn the strip over vertically

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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

Lay the first 7 upon the next 7

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23

Lay the leftmost 8 upon the next 8

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24

Lay the first 9 upon the next 9

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25

Lay the first 10 upon its neighbouring 10

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26

Lay the first 11 upon the next 11

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27

Put the first 12 upon the next 12

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28

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

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29

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

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30

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

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31

Lay the 5 over its adjacent 5

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32

Lay the first 4 over the next 4

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33

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

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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

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

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36

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

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37

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

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38

Turn the dodecahexaflexagon over

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39

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

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40

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

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41

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

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Video: Make a Paper Puzzle Dodecahexaflexagon

If you have problems with any of the steps in this article, please post in the comments section below.

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