Next, the group of 1-cycles is the kernel of the homomorphism ∂ above, which is isomorphic to Z, with a basis given (for example) by ("v"0,"v"1) − ("v"0,"v"2) + ("v"1,"v"2). (A picture reveals that this 1-cycle goes around the triangle in one of the two possible directions.) Since "C"2 = 0, the group of 1-boundaries is zero, and so the 1st homology group "H"1("S") is isomorphic to Z/0 ≅ Z. This makes precise the idea that the triangle has one 1-dimensional hole.