Abstract: A fast algorithm for finding the common facets of adjacent tetrahedrons is presented， which can be employed in the moment-method-based solver for the volume integral equation.The algorithm is derived by means of the concepts and principles of adjacency and incidence matrices for graphs， and it can be implemented with the transpose and multiplication operations for sparse matrices， with the computational and storage complexities of O(N).The numerical results verify the effectiveness of the algorithm which needs less arithmetic operations.It is suitable for the pre-processing of solving electromagnetic fields from electrically large dielectric bodies， for a general purpose software tool or an algorithm test platform．