Final answer:
Arrays of crystal structures are formed by closely packing atoms, ions, or molecules in a regular repeating pattern, such as in the face-centered cubic lattice, which appears hexagonal when inclined. Biological axes of symmetry in vertebrates are established through genetic programming and cellular interactions.
Step-by-step explanation:
Arrays of structures along an axis in a crystalline solid are formed through the regular and repeating arrangement of atoms, ions, or molecules in three-dimensional space. Close-packing in crystals, as explored in two-dimensional space, involves arranging objects such as spheres or atoms in the most efficient way to minimize the space they occupy. In the context of crystallography, this typically results in a lattice structure that can be visualized as layers stacked upon one another. The Face-Centered Cubic (FCC) structure is a common example where atoms at the corners of a cube and the centers of each face create a repeating pattern. This pattern can appear to be hexagonal when viewed along certain orientations, namely the three-fold axes that pass through opposite corners of the cube.
In the case of the FCC, the view at an inclined angle helps to understand how a cubic structure can encompass a hexagonal arrangement. The structure is rotated with respect to the cube's faces, which allows for the hexagonal arrangement along the inclined axis.
Vertebrates also establish three primary axes of symmetry in their bodies during development: lateral-medial, dorsal-ventral, and anterior-posterior. Significant biological research has identified genetic factors and cellular interactions responsible for axis formation, which is vital for establishing body plans and organism development.