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We present SinGAN-3D, a variation of the deep neural network architecture presented originally by SinGAN, for the generation of 3D contents, starting from a single three-dimensional voxelized model. Our network uses a pyramid of 3D convolutional networks to model the third dimension and exploits periodic activation functions to capture the latent structure of the input model. The approach can synthesize contents at different resolutions and aspect ratios, and can be extended to implement super resolution. To evaluate the performances of the proposed model we use the Single Image Frechèt distance, and the multiscale structural similarity index. The metrics highlight the similarities between the synthesised-three dimensional assets and their corresponding original template. An additional user study has also been conducted to assess the quality of the generated shapes. The code can be found at: (GitHub link upon acceptance).