<Tr> <Td> </Td> <Td> </Td> <Td> </Td> </Tr> <Tr> <Td_colspan="3"> The fcc arrangement can be oriented in two different planes, square or triangular . These can be seen in the cuboctahedron with 12 vertices representing the positions of 12 neighboring spheres around one central sphere . The hcp arrangement can be seen in the triangular orientation, but alternates two positions of spheres, in a triangular orthobicupola arrangement . </Td> </Tr> <P> There are two simple regular lattices that achieve this highest average density . They are called face - centered cubic (fcc) (also called cubic close packed) and hexagonal close - packed (hcp), based on their symmetry . Both are based upon sheets of spheres arranged at the vertices of a triangular tiling; they differ in how the sheets are stacked upon one another . The fcc lattice is also known to mathematicians as that generated by the A root system . </P> <P> The problem of close - packing of spheres was first mathematically analyzed by Thomas Harriot around 1587, after a question on piling cannonballs on ships was posed to him by Sir Walter Raleigh on their expedition to America . Cannonballs were usually piled in a rectangular or triangular wooden frame, forming a three - sided or four - sided pyramid . Both arrangements produce a face - centered cubic lattice--with different orientation to the ground . Hexagonal close - packing would result in a six - sided pyramid with a hexagonal base . </P>

Similarities and difference between the fcc and hcp structure
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