 Hi and welcome to the session. I am Nihar and today I am going to help you with the following question. The question says using Euler's formula find the unknown. Here we are given the faces, vertices and edges of the polyhedral and we need to find the unknowns. Before proceeding for the solution let's recall Euler's formula for a polyhedral plus V minus E is equal to 2, where F represents the number of faces, V represents the number of vertices and E represents the number of edges. This is the key idea for this question. Now let's see its solution. In first part we need to find faces so F is unknown. V vertices are 6 that means V is equal to 6 and edges are 12. So edges is represented by E so E is equal to 12. Therefore by Euler's formula F plus V minus E is equal to 2. Now substituting the values of F, V and E, F is unknown so we will write F as it is plus V is 6 minus E is 12 equal to 2. This implies F minus 6 is equal to 2. Now adding 6 on both sides we will get F minus 6 plus 6 equal to 2 plus 6. So here minus 6 and plus 6 will get cancelled and we will get F equal to 8. Therefore here the number of faces is. Now let's do the second part. Let's see that faces are 5 that means F is equal to 5 vertices that is V is unknown and edges are 9 that means E is equal to 9. So let's do this one we are given faces that is F equal to 5 vertices V is unknown and edges E is equal to 9 by Euler's formula F plus V minus E is equal to 2. Now let's substitute the values F equal to 5 plus V is unknown so let's write V as it is minus E that is 9 equal to 2. Now this implies V minus 4 is equal to 2. Now adding 4 on both sides we get V minus 4 plus 4 equal to 2 plus 4 which implies here minus 4 and plus 4 will get cancelled and we are left with V equal to 6. So here the number of vertices is 6. Now in third part faces F is equal to 20 vertices V is equal to 12 and edges E is unknown. So here we are F equal to 20, V equal to 12 and E is unknown. So by Euler's formula F plus V minus E is equal to 2. Substituting the values F 20 plus V 12 minus E is equal to 2. This implies 32 minus E is equal to 2. Now adding E on both sides we will get 32 minus E plus E equal to 2 plus E. This implies here minus E and plus E will get cancelled and we will get 32 equal to 2 plus E. Subtracting 2 from both sides we get 32 minus 2 equal to 2 plus E minus 2. So here plus 2 and minus 2 will get cancelled and we get 30 equal to E. So here number of edges is equal to 30. Therefore for this question our answer is first part number of faces is 8. So faces are 8. In next part there are 6 vertices. So vertices is equal to 6 and in third part edges are 30. So edges equal to 30. And hence this is our required answer. With this we finish this session. Hope you must have understood the question. Goodbye take care and have a nice day.