It seems to me that there is an assumption that atoms are somehow "solid" entities. As the two discussions above indicate the distance between atoms is not a direct or simple statement. Since the atomic structure is mostly space (whatever that may mean) the amount of space, aor the location in space will depend on a variety of factors and therefore one needs to specifiy the conditions in wnich the desired information is sought. The complexities in discussing the properties of "solid" state materials leads to many a difference of opinion about the location and arrangement of atoms. Enjoy our flexible universe.
But..but..but.. Fe has 4 modifications.For density 7,9g/sm3 really. it is the minimal distance. But its phenomenon is continuing to the temperature 770degrees centigrade , distance between atoms consist of 2,85A^0.At the increase of temperature there is a further transition of properties from ferromagnetic in paramagnetic and changed of network from cubic volume centered to the side centered.The process characterized by increase of distance between the atoms.This state constantly changes to the temperature of melting of Fe (1536 d/C). In such state of Fe what you described Fe has ferromagnetic properties.Maybe, you want to know more about ferromagnetic properties?