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The central part of the La-Ni-Si system has been investigated at 800 degrees C by means of single crystal X-ray diffraction, microscopy and analytical microprobe techniques. The result led to the identification of four new metal-rich silicides: LaNi2Si (R3m, a = 4.0263(3) angstrom, c = 15.066(2) angstrom, Z = 3), La2Ni3Si2 (P2(1)/c, a = 6.8789(7) angstrom, b = 6.2167(3) angstrom, c = 12.214(1) angstrom, beta = 90.92(1), Z = 4), La3Ni3Si2 (Pnma, a = 7.501(2) angstrom, b = 14.316(4) angstrom, c = 6.149(2) angstrom, Z = 4), La6Ni7Si4 (Pbcm, a = 6.066(1) angstrom, b = 7.488(1) angstrom, c = 29.682(5) angstrom, Z = 4). LaNi2Si belongs to the SrCu2Ga structure type, which is not represented among silicides, while La2Ni3Si2 crystallizes in its own structure type. Both compounds feature layered polyanionic motifs consisting of Ni and Si, which are separated by La. Instead, La6Ni7Si4 and La3Ni3Si2 are characterized by polyanionic networks. The former compound belongs to the Pr6Ni7Si4 structure type, with only two other representatives (Ce and Nd); the latter has been observed only with Rh and Ir. The two structures reveal close structural relationships having multiple identical slabs. Tight-binding electronic structure calculations by linear muffin-tin-orbital methods were performed for LaNi2Si, La2Ni3Si2 and La3Ni3Si2 to gain insights into their structure-bonding relationships. Their band structures suggest a metallic character for all compounds. The overall crystal orbital Hamilton populations are dominated by polar Ni-Si bonds, though homoatomic Ni-Ni and La-Ni(Si) bond contributions are not negligible. The variety of bonding patterns may serve as a logical explanation for the number of discovered compounds in this system as well as for the diversity of the observed structures.