The conductivity and the distribution of electric field, current, and charge density in a periodic two-component system composed of rhombs with an arbitrary vertex angle of 2α are investigated. The effective conductivity of such a medium is represented by a tensor with components σ_(eff)~(11)(α) and σ_(eff)~(22)(α) in the principal axes that satisfy the Dykhne relation σ_(eff)~(11)(α)σ_(eff)~(22)(α) = σ_1σ_2, where σ_1, σ_2 are the isotropic conductivities of media 1 and 2. In addition, the relation σ_(eff)~(22)(α) = σ_(eff)~(11)(π/2 - α) is satisfied. The principal axes are directed along the diagonals of the rhombs. It is shown that there are three lines in the rectangle 0 < α ≤ π/2, -1 < Z < 1 (Z = (σ_1 - σ_2)/(σ_1 + σ_2)) on which the charge density is expressed in terms elliptic functions. An explicit expression is obtained for all physical quantities on these lines.
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