SageMath math says the genus is $1$.
sage: G = Graph([[0,1],[0,2],[1,2],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[1,3],[1,5],[1,6],[1,7],[1,8],[1,9],[2,3],[2,4],[2,6],[2,7],[2,8],[2,9]])
sage: G.genus()
1
sage: G.get_embedding()
{0: [1, 2, 4, 5, 6, 7, 8, 9],
1: [0, 9, 2, 3, 6, 5, 8, 7],
2: [0, 7, 6, 3, 1, 9, 8, 4],
3: [1, 2],
4: [0, 2],
5: [0, 1],
6: [0, 1, 2],
7: [0, 2, 1],
8: [0, 1, 2],
9: [0, 2, 1]}