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A pilgrim's hat, cockel hat or traveller's hat is a wide brim hat used to keep off the sun. It is highly associated with pilgrims on the Way of St. James. The upturned brim of the hat is adorned with a scallop shell to denote the traveller's pilgrim status.
Heraldry
Pilgrim's hats are used in heraldry.
References
Pilgrim's hat Wikipedia(Text) CC BY-SA