The current study strives to provide a haptic attribute space where texture surfaces are located based on their haptic attributes. The main aim of the haptic attribute space is to come up with a standardized model for representing and identifying haptic textures analogous to the RGB model for colors. To this end, a four dimensional haptic attribute space is established by conducting a psychophysical experiment where human participants rate 100 real-life texture surfaces according to their haptic attributes. The four dimensions of the haptic attribute space are rough-smooth, flat-bumpy, sticky-slippery, and hard-soft. The generalization and scalability of the haptic attribute space is achieved by training a 1D-CNN model for predicting attributes of haptic textures. The 1D-CNN is trained using the attribute data from psychophysical experiments and image features collected from the images of real textures. The prediction power granted by the 1D-CNN renders scalability to the haptic attribute space. The prediction accuracy of the proposed 1D-CNN model is compared against other machine learning and deep learning algorithms. The results show that the proposed method outperforms the other models on MAE and RMSE metrics.