A paperfolding paradise
The website of writer and paperfolding designer David Mitchell
page gives brief details about the folding of Corporals.
According to the online Catholic Encyclopaedia, a Corporal is 'A square white linen cloth, now usually somewhat smaller than the breadth of an altar, upon which the Sacred Host and chalice are placed during the celebration of Mass. ... It is quite probable that in the early centuries only one linen cloth was used which served both for altar-cloth and corporal, this being of large size and doubled back to cover the chalice ... it is in the eleventh and twelfth centuries that the practice, of doubling the corporal over the chalice gave place to a new plan of using a second (folded) corporal to cover the mouth of the chalice when required. The question is debated in some detail in one of the letters of St. Anselm, who quite approves of the arrangement (P. L., CLVIII, 550); and a hundred years later we find Pope Innocent III stating, "there are two kinds of palls or corporals, as they are called [duplex est palla qu dicitur corporale] one which the deacon spreads out upon the altar, the other which he places folded upon the mouth of the chalice" (De Sacrif. Miss , II, 56).'
A Corporal folded into half in one direction and into four in the other is shown in Israel van Meckenem's 'Mass of St Gregory' which dates from c1485.
A Corporal folded into thirds in both directions is shown in Albrecht Durer's engraving of the 'Mass of St Gregory' which dates from 1511 (the date is in the chest at bottom left).