An acyclic edge-coloring of a graph is a proper edge-coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number m such that there is an acyclic edge-coloring using m colors and is denoted by χ′a(G). Tessellations is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps. A regular tessellation is a highly symmetric pattern made up of congruent regular polygons. There are only three regular tessellations: those made up of equilateral triangles, squares and hexagons. k-dimensional regular tessellations is obtained by taking Cartesian product of equilateral triangles, squares or hexagons with paths. We prove that χ′a(G) = Δ(G) when G is a k-dimensional regular tessellations and Δ(G) is the maximum degree in G. © Research India Publications.