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This is document 'Tierceron & Lierne Vaults', within the 'Styles & Traditions' section of the website. 
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Tierceron & Lierne Vaults

Tierceron vault

The TIERCERONGlossary Term VAULTGlossary Term has additional ribs (tiercerons, from tierce, third) springing from wall shaftGlossary Term or pierGlossary Term at the corner of each bayGlossary Term to the ridge ribs along the apexes of the vaultGlossary Term.

Wells Cathedral. Chapter House

The type was developed from the 13th to early 14th centuries; examples of increasing richness can be seen in the cathedrals of Lincoln, Ely, Exeter and Wells Cathedral Chapter HouseGlossary Term. Although the tiercerons are not structurally essential, they are given the same thickness as the principal diagonal ribs; as a result the visual division of the vaultGlossary Term into quadrangular bays disappears.

Gloucester Cathedral, Choir

LIERNE VAULTS have short linking ribs (liernesGlossary Term, from French lier to bind) in the crownGlossary Term of the vaultGlossary Term between the main ribs. They provide the opportunity for additional carved bosses at the junctions. At its most elaborate, such a vaultGlossary Term resembles a net stretched below the roof, creating a pattern which ignores the tradition of individual bayGlossary Term divisions.

Further Reading:

On different types of 14th-century vaults, see: Jean Bony, The DecoratedGlossary Term Style, 1979