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This is from a design entrance that I am preparing for. I know it's a little different than a theoretical projection drawing that engineering books usually cover. It is more practical and visualization based question. I have tried really hard to find some resources to understand the approach to solve this kind of questions. I didn't find any. So, if someone decides to put it on hold. I would like to request them to attach some resource in the comment.

enter image description here

What would be the number of surfaces of the common part?

My initial assumption was I need to first visualize the shape of the common part then count the number of surfaces. But, as people have told that is not necessary. Still, I would also like to know

How to visualize and draw the common part?

I have tried to solve this myself but the best I can come up with this. I would also like to mention that I am not an engineering student. But for my exam asks some questions from engineering drawing. I have a book for it written by someone from my country but that does not cover any union kind of question. I would be very much obliged if you show me the proper method to do it.

enter image description here

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  • $\begingroup$ see engineering.stackexchange.com/a/28582/10902 $\endgroup$ – Solar Mike Aug 4 '19 at 11:10
  • $\begingroup$ Just look at the pictures, and see how many of the original faces are cut into two parts. $\endgroup$ – alephzero Aug 4 '19 at 11:55
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    $\begingroup$ Is "what would be the shape of the common part" part of the original question? If not, it's irrelevant to answering the question about the number of surfaces, and it is much harder than counting the number of surfaces. $\endgroup$ – alephzero Aug 4 '19 at 14:07
  • $\begingroup$ Welcome to Engineering! As mentioned by the previous comments, your question of "what would be the shape" is entirely different from the actual question asked in the embedded image. Please edit your question to clarify what it is you actually want us to answer. $\endgroup$ – Wasabi Aug 4 '19 at 21:34
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I don't want to spoil the fun of solving this for yourself so I offer the following suggestions:

  1. Redraw the assembly with all edges, including the hidden edges, shown as dotted lines.
  2. Draw solid lines on all the intersections.
  3. Join up any vertices which form edges not on the outer surfaces of the assembly.
  4. Count the faces.

Step 3 is the only tricky bit. In your example the uppermost edge of the horizontal element will form one such edge.

Post a sketch in an update to your question and we'll see if you've understood it.


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Figure 1. Intersection of two prisms. The green lines are edges that already exist on the isometric view. The orange lines will be new edges created by the intersection operation.

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  • $\begingroup$ This will answer the question (if you succeed in doing it correctly) but IMO it's not what the question is about. The key words are "visualize" and "practical". You don't need to draw anything here. If it helps, use a pencil for the hexagon and some bits of paper that you can fold up into the pentagon, and just play with them till you see what is going on. $\endgroup$ – alephzero Aug 4 '19 at 14:04
  • $\begingroup$ The OP is unable to locate any resources regarding the practice of visualizing the intersection of two solids. Transistor provided one practice which appears sound and quite simply effective. It's likely I would have used a program such as OpenSCAD to create the solids and perform the intersection, but that's not what I'd consider a suitable practice, only another method of accomplishing the goal. $\endgroup$ – fred_dot_u Aug 4 '19 at 19:42
  • $\begingroup$ @transistor sir, I am not an engineering student. But for my exam asks some questions from engineering drawing. I have a book for it written by someone from my country but that does not cover any union kind of question. I have tried what you said for two days and the best I can come up with , I am posting here. I would be very much oblidged if you show me the proper method to do it. $\endgroup$ – Ritwik Bhattacharyya Aug 6 '19 at 19:18
  • $\begingroup$ @Ritwik: I can't see your best attempt. Add it into your question. $\endgroup$ – Transistor Aug 6 '19 at 19:25
  • $\begingroup$ @RitwikBhattacharyya So, how many faces are there? as that is the point of your question. $\endgroup$ – Solar Mike Aug 6 '19 at 19:52

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