 Hi and welcome to the session. Today we will discuss the following question. The question says can a polyhedron have 10 faces, 20 edges and 15 vertices? Before proceeding for the solution let's recall that for any polyhedron, Euler's formula f plus v minus e equal to 2 is true. Here f stands for number of faces, v stands for number of vertices, e stands for number of edges. This is the key idea for this question. Now let's see its solution. Here in the question the given polyhedron have 10 faces that means f is equal to 10, 20 edges that means e is equal to 20 and 15 vertices that is v is equal to 15. Now we need to check that whether a polyhedron can have 10 faces, 20 edges and 15 vertices and we know that a polyhedron with these values is only possible if it satisfies the Euler's formula. So by Euler's formula we have f plus v minus e equal to 2. Now let's substitute the values, we will substitute the values in left hand side that is f plus e minus e. So LHS will be equal to f that is 10 plus v that is 15 minus e that is 20 and this is equal to test is equal to therefore LHS is not equal to RHS right is not equal to 2. So we can say that Euler's formula is not satisfied the polyhedron cannot have 10 faces, 20 edges and vertices. The answer for this question is no. Yes we finished this session hope you must have understood the question goodbye take care and have a nice day.