Table:
text: Euler characteristic
Polyhedra
Polyhedra
Name_ Vertices_V Edges_E Faces_F Euler_characteristic_V_E_F
Tetrahedron 4 6 4 2
Hexahedron or cube 8 12 6 2
Octahedron 6 12 8 2
Dodecahedron 20 30 12 2
Icosahedron 12 30 20 2

Question: What is the total number of E-edges of the polyhedra with vertices V greater than 20 under the Euler characteristic?

Question: What is the smallest Euler characteristic V-E+F of a hexahedron or cube that has less than 20 faces F, less than 30 edges E and less than 8 vertices V?