In heraldry, an ordinary is described as quadrate (or more fully nowy quadrate) when it has a square central boss.
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Shield of Durham University: Argent, a cross paty quadrate gules; on a canton azure a chevron or between three lions rampant argent.
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Banner of the Burgh of Markinch, Scotland: Gules, on a cross nowy quadrate argent a cock gules.
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Gules, a cross paty quadrate or, charged with five mullets of six points gules: a chief arched ermine charged with two Cornish choughs proper - Vickers, England
Only certain ordinaries are usually shown quadrate: the cross, the pale, and the fess – but not, for example, a bordure or chevron.
A saltire quadrate has the square oblique:
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Arms of North West Province, South Africa: Per saltire gules and azure, a saltire quadrate vert, fimbriated argent ...