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A mechanism is proposed for the nucleus formation at the mutual transformation of austenite and cementite crystals. The mechanism is founded on the interpretation of the considered structures as crystallographic tiling onto non-intersecting rods of triangulated polyhedra. A 15-vertex fragment of this linear substructure of austenite (cementite) can be transformed by diagonal flipping in a rhombus consisting of two adjacent triangular faces into a 15-vertex fragment of cementite (austenite). In the case of the mutual austenite-cementite transformation, the mutual orientation of the initial and final fragments coincides with the Thomson-Howell orientation relationships which are experimentally observed [Thompson & Howell (1988). Scr. Metall. 22, 229-233] in steels. The observed orientation relationship between f.c.c. austenite and cementite is determined by a crystallographic group-subgroup relationship between transformation participants and noncrystallographic symmetry which determines the transformation of triangulated clusters of transformation participants. Sequential fulfillment of diagonal flipping in the 15-vertex fragments of linear substructure (these fragments are equivalent by translation) ensures the austenite-cementite transformation in the whole infinite crystal. The energy barrier for diagonal flipping in the rhombus with iron atoms in its vertices has been calculated using the Morse interatomic potential and is found to be equal to 162 kJ mol -1 at the face-centered cubic-body-centered cubic transformation temperature in iron.