She is usually shown with a bushel of grain.
Usually a portion of the yield from their crops.
In Greek mythology, Demeter is usually depicted as an immortal goddess, so she does not age like humans do. She is often portrayed as a mature and wise deity.
The symbol of Demeter is a handful of harvested wheat
There may be a real person with the name Demeter living today. Usually however the name refers to a ancient Greek goddess.
Demeter is the Greek goddess of agriculture, fertility, and the harvest. She is usually depicted as a mature woman holding a sheaf of wheat and surrounded by abundant crops. Demeter is known for her nurturing and motherly qualities, as well as her ability to bring forth the bounty of the earth.
At one time she aided Demeter in her search for Persephone, when Hecate found her she stayed in the Underworld with her as her companion.
Demeter, being a harvest goddess, is often depicted carrying grains and/or or a cornucopia. She does not always have these, however.
The "horn" you may be mistaking for the Cornucopia, horn of plenty.Demeter is goddess of the harvest of food from the Earth.
Demeter is a goddess of fertility, grain, and agriculture. She is pictured as a mature motherly figure. Although she is the goddess who taught mankind about agriculture, she is also the goddess responsible for creating winter and a mystery religious cult. Demeter is usually accompanied by her daughter Persephone.
There was no "god of Demeter", Demeter was a Greek goddess.
Demeter
Demeter's is a cornucopia. Cornucopias are the woven cones with fruit or wheat inside of them, usually being used during thanksgiving nowadays. Grains or wheat are also some icons of Demeter but usually Cornucopias are the most accurate icon for her. She is the goddess of harvest, agriculture or the fertility of the planet. Because of that, some people think that animal life is also part of her icons, such as cows.