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sage: C = Cone([[1,1,0,0],[1,0,1,0],[1,0,0,1],[0,1,1,0],[0,1,0,1],[0,0,1,1]])

sage: C.polyhedron(backend='normaliz').hilbert_series(grading=[1]*4)
(t^3 + 3*t^2 - t + 1)/(t^7 - t^6 - 3*t^5 + 3*t^4 + 3*t^3 - 3*t^2 - t + 1)