Two different samples of Ce3Rh4Ge4 were synthesized from different starting compositions by melting of the elements in an arc-melting furnace followed by annealing sequences in a sealed tantalum ampoule in a muffle furnace. The structures of two different stacking variants were refined on the basis of temperature dependent single-crystal X-ray diffractometer data. At high temperature Ce3Rh4Ge4 adopts the U3Ni4Si4 type structure with strongly enhanced anisotropic displacement parameters for the Rh1 atoms. For the two different crystals, additional reflections start to appear at different temperatures. The first crystal showed additional reflections already at room temperature (stacking variant I) and the second one showed additional reflections emerging below 270 K (stacking variant II). Stacking variant I could be described with the (3+1)D superspace group I2/m(α0γ)00; α=1/2a*, γ=1/2c*; (Z=2), 1252 F2 values, 48 variables, wR=0.0306 for the main and wR=0.0527 for 440 1st order satellite reflections, similar to Pr3Rh4Ge4. For stacking variant II the (3+1)D superspace group is Immm(α00)00s; α=1/2a*; (Z=2). The structure could be refined with 1261 F2 values, 53 variables and residuals of wR=0.0331 for the main reflections and wR=0.1755 (R1obs=0.0788) for the 1st order satellite reflections, [a=406.2(1), b=423.7(1) and c=2497.1(1) pm]. The commensurate description could be transformed to a three-dimensional (3D) supercell with space group Pnma and Z=4: a=812.5(1), b=423.7(1), c=2497.1(2) pm, 1261 F2 values, 69 variables and wR=0.0525. The relation of the U3Ni4Si4 type structure, the (3+1)D modulated and the 3D supercells are discussed on the basis of group-subgroup schemes. Ab initio electronic structure calculations are in line with the diffraction experiments, revealing the lowest total energy for the Pnma phase.< Réduire