Spatial geometric constant is a quantization of the properties of spatial geometry. In order to further apply the geometric constant to study the geometry of the Banach space

a new generalized von Neumann constant is introduced. We give the continuity

symmetry

boundedness and the equivalent form of the generalized von Neumann constant

and judge the consistent non-square of the Banach space

and give the calculation formula or valuation of several special Banach space with two examples.