Final answer:
No, a semiregular tessellation cannot be made from regular pentagons and squares due to the mismatch in angles and sides. Pentagons don't tessellate by themselves and don't pair with squares to cover an entire plane without gaps.
Step-by-step explanation:
No, a semiregular uniform tessellation cannot be created from regular pentagons and squares. In tessellations, shapes must fit together without any gaps or overlaps. Regular pentagons cannot tessellate by themselves, and they cannot be combined with squares to create a semiregular tessellation because the angles and sides do not match up in a way that can cover an entire plane without leaving gaps or overlapping.
In the context of close-packed arrays, the close-packed square lattice consists of squares that tessellate perfectly because their sides and angles are consistent and allow for seamless tiling. On the other hand, the close-packed hexagonal lattice, which can also tessellate uniformly, is more efficient than the square arrangement as it covers more area and has less empty space. The hexagonal packing has a coverage of 91 percent compared to square packing which covers 78 percent of the area, making it the preferred arrangement in natural systems, such as the atomic packing in crystals.