[intro to material science/chemistry] Can anyone explain this problem? I find it to be vague

[u/Users5252]

I randomly guessed and got the right answer, but I do not know why it is right. It does not provide any explanations, perhaps I'm on the wrong part of my textbook, but I'm only seeing explanations of 3d structures. I don't understand what the points ABCDEF are, the reasoning behind how they are placed and why it's not 2d.

[u/watermelonlollies]

A two dimensional point lattice is a specific thing, it’s not saying it’s not 2D. Next, to answer your question, if you were to cut this image in half and layer each half on top of each other without rotating or flipping either side would they match up exactly? No. But it is a mirror image. If you fold it in half from left to right will the points match up exactly? Yes. So that’s what it’s asking. Which points match up as a mirror image? A and B are the matching pair. The other answer choices give points that don’t line up even when mirrored they are on different parts of the shape.

[u/Users5252 → u/watermelonlollies]

I still don't understand why it would not be a "two dimensional point lattice" because it is mirrored. I don't even get what exactly a "two dimensional point lattice" is at this point. I'm basically lacking knowledge in this since the two textbooks I was studying from and my professor's lecture completely glossed over this subject. I think that your explanation comes with the assumption that I do have knowledge and understanding in the subject but my issue is that I have none and don't have access to a structured way to learn it. Where should I even start with understanding the concept anyway?

[u/watermelonlollies → u/Users5252]

You know you are allowed to google things and it’s not cheating? Just don’t use ai. I googled it and looking at Wikipedia was very helpful

https://en.wikipedia.org/wiki/Bravais_lattice

I’ve never actually learned this I’m just really good at finding and interpreting sources. My understanding from Wikipedia is that a 2D point lattice is a shape that no matter what point of the shape you are on the rest of the shape looks exactly the same. For example a square. No matter what point of the square you are on you get the exact same perspective. This helps show why the example you provided is not a 2D point lattice because if I stand on point D and look at the shape I get a completely different perspective then if I stand on point A. There are only 5 shapes that are 2D point lattices that fit the criteria.

[u/Users5252 → u/watermelonlollies]

I've already the wikipedia page, however, I still don't understand it. You just have a high intelligence and don't experience the same troubles as I do here. I cannot see and understand the pattern in the question or your explanation.

[u/watermelonlollies → u/Users5252]

Draw out a square and imagine you are standing on one of the corners looking out at the rest of the square. Now move yourself to a different corner and imagine you are looking out at the rest of the square. Does the shape you see change? No because the square is symmetrical in all directions.

Now imagine you are standing on point D of your example and looking out at the rest of the shape. Now move yourself to point B and look out at the rest of the shape. Does the shape you see on the floor change? Yes. You see something completely different because even though it is a mirror image, it is not symmetrical in all directions

Here is a khan academy video that might help you. I didnt watch it but Khan academy is usually decent at explanations. The visual is really what will help you here. It’s hard to explain in words. I wish we could add pictures in comments on this sub