# 3D Form Development (Pattern Folding)

## Pattern Folding

In this subsection of the PAT, a flat pattern will be presented which can be folded into a 3D figure. You should choose which one of the four 3D shapes it would make if the flat pattern is folded. There is only one correct answer for each question.

## Techniques

Shape Matching Method: You can compare the faces that you see in the flat pattern with the faces in the shapes you see in the options given and get rid of some options through the elimination process. You can also start this process by finding the largest face or a face with specific geometry within the pattern and see how it compares with the shapes in the answer choices to see if it matches with any of them, or just to eliminate some of the choices.
Also, there is a technique called odd one out which involves identifying some unique faces and comparing it with the unfolded shape to see if you can find it. If that face is not in the unfolded pattern, then it is not possible for that option to be correct. If the identified face is present in the unfolded pattern, then that option has the potential to be the answer to the question.

In the following example, we try to find the green face in the flat shape in each option provided. When we compare the green face with the options, we can see that the green face is only matching with a face in option B, so option B is our answer.

Side Counting Method: For some problems, you may be able to use this method, but it will not work for all problems. Find the largest shape within the pattern and count the number of sides of the shape. Compare it with the answer choices to determine the correct choice, or at least to eliminate some of the incorrect choices.

Color Matching Method: This method is similar to the Shape Matching Method except that you compare a shaded part of the flat pattern to the corresponding part on the folded pattern in the options. Make sure that the shaded part is in the correct place on the folded pattern. Continue to make sure that all the shaded parts correspond to the answer choice in order to determine the correct one. Through the process of elimination and observation, you can decide which choice is correct and which is not.

In the following example, the orange parts or faces in the options cannot be found in the original flat shape

Face Exclusion Technique: In this method, you focus on the faces that you see in the options and only rotate them rather than rotating the entire pattern or trying to fold the unfolded pattern entirely, or manipulating it in your mind, in order to find out the positioning that you see in that option. You should rotate them in a way that they can be positioned relative to the option choices provided.

When we rotate the 1, 5, and 6 faces in the flat pattern in a way that corresponds to option A, we will see that it does not match with what is shown in option A. In order to have a 1-dotted face on the left, we imagine cutting the three faces and rotating the like shown below to correspond with option A. As you can see, the orientation of the dots in the face with 6 dots does not correspond to option A, in the shape we get. So option A is wrong.

We do the same thing for all options, in option B as shown in the following, the face with 1 dot has to be on the right side, so we cut the three faces present in the option and rotate them in a way that corresponds to option B. Again, the orientation of the dots in the shape we get by folding the pattern does not correspond to the orientation of the dots present in the face with 6 dots in option B.

In option C, we have to rotate the faces with 2, 4, and 3 dots so we cut them out of our flat pattern and rotate them to try to match them with option C. As we can see, it is not possible to get the faces in the flat pattern to match with option C.

Although we know through the process of elimination that D is our answer, but if we do the same process for option D as shown below, we can see that option D is correct.

The same technique applies for a shape like this. You need to find out how specific faces are oriented relative to one another.

In this example, in option A, we have black and white rectangles with horizontal orientation when the shape is folded in this way. If we fold the unfolded part of the flat shape that is highlighted with red in the flat pattern, the orientation of the black and white rectangles in the face highlighted with red would not match with the flat shape so this option is not correct.

For option B, the part that is colored by green in the flat shape doesn’t match with option B; in option B the black triangles are touching in their bases while it is not true in the flat pattern.

In option C, the positioning of the white square face that is highlighted with green is not matching with the flat pattern.

In Option D, as you can check, all the parts are placed according to the flat shape.

Remember you have to solve many problems in PAT in order to be able to become faster and accurate. You have to see and solve different types of problems with different types of shapes to become faster and manage your time more efficiently. So, if you are a bit slow in the beginning, don’t worry.

Cut and paste Technique: This method is somewhat similar to the face exclusion technique that we used for other types of shapes in that we deal with the three faces shown in each option choice rather than trying to fold the unfolded pattern entirely and then comparing it with each option.

In option A, we have two half-black faces and one entirely white face. We identify and isolate that part in the flat pattern that can match the faces shown in option A. There are three patterned or half black half white faces in the flat pattern that are candidates for the choices we have. In option A the two patterned faces are in contact with each other but the ones at the bottom of the shape can never be in contact with each other. You can realize that with a quick folding of the shape. So the isolated patterned face on top of the flat shape has to be in contact with one of the other two. It is the top and left patterned faces of the flat shape that are in contact, the black sides of the squares have to be touching which is not the case in option A. If it is the top and right patterned faces of the flat shape that are touching, the white part of the top face has to be in contact with the black part of the right face which again is not the case in option A. So option A is not correct.

By doing the same procedure for each option we can find out that option B is the correct choice. The two white faces and the one half black face in the middle and the left side of the pattern can be folded to make the option B. In option B, also the orientation of the black triangle would match with the left half black face of the flat pattern. Orientation is another factor that can help you in answering questions like this.

In option C, the two half-black faces are connected, this can’t be possible for the left and right half black faces on the left and the right side of the pattern, since they can’t connect with each other. So it must be the top half black face connecting with one of the others. If you try to fold the shape in your mind in a way that the top and the right half black shapes are connected, you will notice that there is no way they connect in a way that the half-white parts of the two faces are connecting, so this is also not possible. The same thing is true for the top and the left half black faces of the flat pattern. So option C can’t be our answer.

In option D there are three half black faces connected to each other. We can find out that the option D is not correct simply by trying to fold the faces in the shape towards the top or bottom, and then we will realize there is no way the three half black shapes connected like seen in option C.

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