A polyhedron has 20 vertices and 30 edges. It has () faces. This geometry is ()

A polyhedron has 20 vertices and 30 edges. It has () faces. This geometry is ()

In topology, the Euler formula V + F-E = x (P), V is the number of vertices of polyhedron P, f is the number of faces of polyhedron P, e is the number of edges of polyhedron P, and X (P) is the Euler characteristic number of polyhedron P. if P can be homeomorphic to a sphere (which can be understood as being able to inflate and stretch on a sphere), then x (P) = 2, if P is homeomorphic to a sphere connected with H ring handles, Then x (P) = 2-2 h. x (P) is called the Euler characteristic number of P, which is a topological invariant, that is, a quantity that will not change no matter how it is topologically deformed, Application in polyhedron: there is a relationship between the number of vertices V, the number of faces F and the number of edges e of a simple polyhedron. V + F-E = 2. This formula is called Euler's formula. The formula describes the unique rules of the number of vertices, the number of faces and the number of edges of a simple polyhedron. 20 + X-30 = 2x = 12, so it is a 12hedron