It's a stand for a standard 55 mm 3x3x3 twisty cube puzzle ("Rubik's Cube"). Pictured is the QiYi WuWei M 3x3 , for which this stand was originally designed.

Note that the tolerance is pretty exact: a 56 mm cube will not fit. If your cube is any other size than 55 mm, you'll need to scale it by the factor n/55, where n is the length of a side of the cube. For best results, measure your cube using an accurate calliper that can measure to the nearest 0.1mm.

For example, for a 56 mm cube you will need to scale it up to 101.82%. For a 54 mm cube, scale it down to 98.18%. Note: scale the base by the same amount, or else you'll have problems fitting the two parts together.