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Min is always depicted ithyphallic and because of that some sources say that Min in a fertility god which tends to lead people to think human fertility but that's not the case here. Sources point in the direction of agricultural fertility. It is also suggested that he is god of the Eastern desert and patron of traveling caravans.

Epithets
Bull of His Mother
Protector of the Moon
Bull of the Great Phallus
Lord of Foreign Lands
Lord of the Eastern Desert

Common Offerings
Food/Drink
Lettuce - Historically
--Wild Lettuce
--Prickly Lettuce
Rich meats
Intoxicating liquids
Beef

Items
White bull
Barbed arrow

Sources:
Henadology
KO
Tour Egypt
Ancient Egypt Online
Wepwawet.org