The ellipticity of an anisotropic energy functional is a property that ensures a flat k-cube is the unique minimizer of the functional among all competitors with the same (k-1)-dimensional boundary as the cube. There is a strong relation between the ellipticity of a functional and the (poly)convexity of its integrand, which has been investigated by Burago-Ivanov, and recently by De Rosa, Lei, and Young. In this talk, we extend a recent result by De Rosa, Lei, and Young and show that the uniform ellipticity of an anisotropic energy functional with respect to polyhedral chains implies the uniform polyconvexity of the integrand.