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SrCu2(PO4)2 was prepared by the solid-state method at 1153 K. Its structure was solved by direct methods in the space group Pccn (No. 56) with Z = 8 from synchrotron X-ray powder diffraction data measured at room temperature. Structure parameters were then refined by the Rietveld method to obtain the lattice parameters, a = 7.94217(8) A, b = 15.36918(14) A, and c = 10.37036(10) A. SrCu2(PO4)2 presents a new structure type and is built up from Sr2O16 and Cu1Cu2O8 units with Cu1...Cu2 = 3.256 A. The magnetic properties of SrCu2(PO4)2 were investigated by magnetic susceptibility, magnetization up to 65 T, Cu nuclear quadrupole resonance (NQR), electron-spin resonance, and specific heat measurements. With spin-dimer analysis, it was shown that the two strongest spin-exchange interactions between Cu sites result from the Cu1-O...O-Cu2 and Cu2-O...O-Cu2 super-superexchange paths with Cu1...Cu2 = 5.861 A and Cu2...Cu2 = 5.251 A, and the superexchange associated with the structural dimer Cu1Cu2O8 is negligible. The magnetic susceptibility data were analyzed in terms of a linear four-spin cluster model, Cu1-Cu2-Cu2-Cu1 with -2J(1)/kB = 82.4 K for Cu1-Cu2 and -2J(2)/k(B) = 59 K for Cu2-Cu2. A spin gap deduced from this model (Delta/kB = 63 K) is in agreement with that obtained from the Cu NQR data (Delta/kB = 65 K). A one-half magnetization plateau was observed between approximately 50 and 63 T at 1.3 K. Specific heat data show that SrCu2(PO4)2 does not undergo a long-range magnetic ordering down to 0.45 K. SrCu2(PO4)2 melts incongruently at 1189 K. We also report its vibrational properties studied with Raman spectroscopy.