Ridged waveguide is a classic arrangement utilized in broadband microwave components. An analysis of triply-ridged waveguide, presented here, indicates that the dominant mode consists of a degenerate pair. Degenerate mode pairs are widely used in phase shift and control applications. It also exhibits single mode bandwidth characteristics more favorable than the conventional quadrupally-ridged cross-section. Modal hierarchy and field patterns are provided through the use of a finite element solver. Experimental results obtained from a triply-ridged cavity are also discussed and compare well with the numerical calculations.