This paper reviews studies on the tactile dimensionality of physical properties of materials in order to determine a common structure for these dimensions. Based on the commonality found in a number of studies and known mechanisms for the perception of physical properties of textures, we conclude that tactile textures are composed of three prominent psychophysical dimensions that are perceived as roughness/smoothness, hardness/softness, and coldness/warmness. The roughness dimension may be divided into two dimensions: macro and fine roughness. Furthermore, it is reasonable to consider that a friction dimension that is related to the perception of moistness/dryness and stickiness/slipperiness exists. Thus, the five potential dimensions of tactile perception are macro and fine roughness, warmness/coldness, hardness/softness, and friction (moistness/dryness, stickiness/slipperiness). We also summarize methods such as psychological experiments and mathematical approaches for structuring tactile dimensions and their limitations.