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There is Saint Joan of Arc and Saint John of the Cross but no Saint Joan of the Cross.
Joan Cross was born on September 7, 1900, in London, England, UK.
Joan Cross died on December 12, 1993, in Aldeburgh, Suffolk, England, UK.
Joan of Ark asked a child to hold up a cross so that she could see it through the flames.
No, neither organization existed until hundreds of years after Joan's death.