The spectra of normalized volumes for ideal right-angled hyperbolic polyhedra lie in [1/6 v_oct, 1/2 v_oct] with sharp bounds, discrete below 1/4 v_oct and dense above; compact ones lie in [5/192 v_oct, 5/8 v_tet] with upper bound sharp, discrete below 1/32 v_oct and dense in a higher subinterval.
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Normalized volume spectra of right-angled hyperbolic polyhedra
The spectra of normalized volumes for ideal right-angled hyperbolic polyhedra lie in [1/6 v_oct, 1/2 v_oct] with sharp bounds, discrete below 1/4 v_oct and dense above; compact ones lie in [5/192 v_oct, 5/8 v_tet] with upper bound sharp, discrete below 1/32 v_oct and dense in a higher subinterval.