Find here some exercises about Euler's formula, which may help you to understand the concept better:

• Draw a polyhedron with one single handle (H=1) and one single ring (R=1). Check that it fits Euler's formula
• Draw a polyhedron with one single handle (H=1) and zero rings (R=0). Check that it fits Euler's formula
• Draw a polyhedron with one single handle (H=1) and two rings (R=2). Check that it fits Euler's formula
• Draw a polyhedron with one single handle (H=1) and obtained as a result of a substraction boolean operation between a polyhedron with a "U" shape and a squared-base prism. Check that it fits Euler's formula
• Draw a polyhedron with two handles (H=2) and obtained as a result of a substraction boolean operation between a polyhedron with a "U" shape and a squared-base prism. Check that it fits Euler's formula