 Next we have to write down elements of symmetry. Elements of symmetry also they have asked question on to this. Elements of symmetry. The first one we write down center of symmetry. Center of symmetry. How many center of symmetry possible? Cubic crystal we are assuming. Cubic universal. How many center of symmetry? Just one. What is center? Center of symmetry is a point from where the distance of all the faces is equal. Like this part is empty if you see. This distance and that distance is same. This distance and this distance is same. Right? So write down center of symmetry COS. Write down it is a point inside a crystal. It is a point inside a crystal such that when a line is drawn through it such that when a line is drawn through it it intersects the faces. It intersects the faces of the crystal at equal distance from either side. Next we write down. So number of COS. Number of COS is equals to what? One. Only one such point is possible. That is at the border center. Ok? Number of COS is one. The second one we write down plane of symmetry. COS. Plane of symmetry. It is an imaginary plane. It is an imaginary plane which passes through. Imaginary plane which passes through the center of crystal, passes through the center of the crystal and divide the crystal into and divide the crystal into, divide the crystal into two equal halves, divide the crystal into two equal halves such that each half is the mirror image of each other. Now you look at this. We have a cube. Now can you imagine a plane here? Can you imagine this plane like when you cut the cube like this? So you have a plane like this and the two halves is the mirror image of each other. This is the plane of symmetry. Now how many such plane of symmetry possible? Tell me. How many? Sir, you cut it like this also. See the thing is what we are taking? We are taking in two two faces like this, this cube go and cutting like this. So, this face and the feature of S we are taking right like this. Now, if this two faces if you take two opposite faces you can cut like this also. And this two faces if you take you can cut like this also. Sir, but it is the same thing like. No, this, this and this opposite, opposite sides. Sir, but when you rotate the cube. No, fine, but we can cut this way, this way, this way, this way. So, we are looking at one point and then cutting. Yes, rotating we are not considering, you cannot rotate yourself or the cube. So, and basically you see this is the plane of symmetry with the help of two faces right, one and two, one two faces. So, we have six faces total, two faces gives you one, so six gives you three. So, three such kind of plane of symmetry is possible, diagonal also we can take, let us see how many diagonal. So, this is one, this is one plane of one type of plane of symmetry where you take the two opposite faces, three plane of symmetry possible. What about this if you consider. Sir, so then you have a total of two different diagonal. Sir, can you imagine this. Sir, basically you get into it is this one and this one or you take this corner, this edge and that edge right or you can imagine it is very difficult to understand. And when you understand this one, you cannot say. So, let us start taking the help of this like this. So, basically two edges gives you, two edges gives you one such plane of symmetry and how many edges are there? 12. So, how many will you get? Six. Six p u s. So, six p u s will be given. So, how will it happen? One, two, one, this is done, this is done, this is done, this edge is done and that one is down. And this is done. So, six p u s. So, six p u s, three p u s. So, total plane of symmetry is what? Nine plane of symmetry possible. Total p u s if they ask you, it will be three plus six, nine. So, separately they have a task yet. How many plane of symmetry possible? Total elements of symmetry they have asked once. Total elements of symmetry proved to be correct. Now, third one we write on axis of symmetry. Right down it is an imaginary line a u s. It is an imaginary line about which, about which the crystal, the crystal when rotates, about which the crystal when rotates, it gives the same impression, same impression more than one, more than one in one complete rotation. One complete rotation means what? 60 degree rotation. So, there are three different types of mainly three for cubic. We have one more for that, but that comes for hexagonal not cubic unit cell. Three different unit cell possible, sorry, axis of symmetry possible for cubic unit cell. The first one in this, you write down two fold axis of symmetry. Two fold axis of symmetry. Two fold axis of symmetry means what? When you rotate in one complete rotation, the same impression appears twice. So, for example, you see we also call this direct, if you do not want to add, direct forward. So, you see this, see you imagine this line we have to e to n center opposite n center. So, this line you imagine and when you rotate the cube for this line, as simple as that. You see 180 pay a same impression, again this is the same impression. Imagine this line around, if you rotate like this, this corner will come here, but it still is the same cube. So, that is why this along this line will have two axis of symmetry possible and that is why it is two fold axis of symmetry. So, if I ask you how many diodes possible for this kind? How many diodes possible here? Though edge in there are six. Though edge in there are, we have total how many edges? 12. So, 12 edge six there. So, there are six diodes possible in this. Next write down three fold and one more thing, the same appearance appears here at what angle? 180. So, it is not important, but you can understand. 180 pay same appearance and then 360 pay same appearance. The third one write down three fold axis of symmetry. Three fold we also call it as what? Trial. Trial. Trial. Trial what we do here in this only I am excluding you see, corners. We are taking the corners. This yellow one gives you trial and this blue one gives diodes. So, here the same appearance appears at what angle? 120. So, number of tried, how many tried possible here? This is not important, how do we get tried? Corner line of a central line. Once they have asked this question in need exam that how many elements of symmetry are there? So, total number you should know, but you never know if they ask you how many tried possible then you should know how the tried will get by the corners. So, there are eight corners right. So, four tried possible. Next one write down four fold axis of symmetry and we also call it as what? Trial. Four fold. The same appearance appears four times in what complete rotation? Tried with three times over four times over. So, each appearance the same appearance appears at what angle in this? This is the tried opposite face centered along if you draw a line, you will get a tried. So, this corner will come here, this corner will go here, you will get the same appearance. This gives you tried. How many tried possible? Two. Two face centered. So, we have total six face centered. If they ask you how many exosymmetry possible total what is the answer? The sum of tried plus tried. That will be? Tried is six plus four plus three. So, total AOS is equals to 13. Total POS is nine and total COS is one. So, total elements of symmetry is what? Total elements of symmetry is equals to what we have to do? We have to add all these three that is COS plus POS plus AOS. One plus nine plus 13 that will be 23. This question they have asked many times. 23 elements of symmetry. Okay. Individually they have not asked you have not know they can ask this also you should know this. So, in cubic crystal this is only for cubic crystal like I said for exosymmetry there is one more exosymmetry possible that is in hexagonal unit cell. So, in hexagonal unit cell we have six fold exosymmetry possible where the same appearance appears at 16. So, only one such exosymmetry possible. So, write down one note in this. So, mostly they will ask you for unit cell only. Okay. Cubic unit cell not hexagonal. Okay. Write down in hexagonal unit cell in hexagonal unit cell six fold exosymmetry possible six fold exosymmetry possible and there is only one there is only one such line possible.