Use 'regimental' when referring to matters specific to an army regiment, like traditions or attire. His regimental crest signifies his unit's storied past.
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Organizational Use
'Regimental' often implies formal organization within the military beyond personal qualities. The regimental headquarters is located in the old fort.
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Cultural Pride
It may suggest pride or honor associated with one's regiment, not only the structure. The soldiers shared a deep regimental spirit.