Question

if you're polyhydron has 30 edges and 20 vertices how many faces does it have

Answer 1

No, it is not possible as you can se it by Eulers formula that is

F+V-E=x

For a convex polyhedron, or more generally any simply connected polyhedron with surface a topological sphere, x= 2.

where F is faces of the polyhedron,

V is the vertices of the polyhedron,

and E is the edges of the polyhedron

Then, by solving the equation, 3=0 which cannot be true.

Hence this kind of polyhedron can't exist.But there exist a polyhedron whose faces are 12, vertices and edges are 20 and 30 respectively and it is known as “Dodehedron”