Reactions of the elements in proportions near 37.3 at. % Na at approximately 500, 410, and then 250-degrees-C readily produce the well-crystallized title phase. The tetragonal structure at the indium-rich limit was solved by standard single-crystal X-ray means at room temperature (P4(2)/nmc, Z = 12; a = 16.093 (4) angstrom, c = 23.384 (8) angstrom; R(F)/R(W) = 3.4/3.6%). The network structure consists of interbonded clusters-the first example of closo-In16 icosioctahedra (4m2BAR symmetry) that are 8-exo-bonded, 10-bonded nido icosahedra (fractional occupancy of the eleventh cluster site generates approximately 36% 1,3-arachno units) and four-bonded indium atoms in pairs of triangles (In16:In11(10):In1 = 1:4:12). Extended Huckel calculations that include significant interactions between directional nonbonding pairs on atoms in neighboring In16 and In11 units indicate 2n + 4 skeletal electrons are necessary for each, with no nonbonding pairs on the latter, and a closed shell for 504 electrons per cell vs 507 for the refined stoichiometry. Observed properties are in good agreement; at the indium-rich limit, the phase is a poor metal (rho-295 approximately 540-mu-OMEGA.cm) with a Pauli-like paramagnetism chi(M) = (1.7 - 1.8) X 10(-4) emu/mol after correction for core and orbital diamagnetism. The intercluster interactions appear to be closely correlated with a small region of nonstoichiometry and changes in the c lattice parameter. Some general factors in a diverse indium cluster chemistry are noted.