What is the historical derivation of the jewel of the royal arch, and how do the older commentators interpret its geometric layout?

The jewel or badge of the Royal Arch centers upon the triple tau, formed by three tau crosses conjoined at their feet 1. Historically, the single tau cross derives from ancient religious and symbolic marks, including the protective sign mentioned in Ezekiel to distinguish the faithful, the Egyptian monogram of Thoth representing hidden wisdom, the Druidical Gallicum tau, and the crux ansata symbolizing life 1. Adopted into the Masonic system as an emblem of salvation and eternal life, the tau in its triple combination serves to distinguish those devoted to the worship of the true deity 1.

Regarding its geometric layout, older commentators and early English Royal Arch lectures analyze the mathematical properties created by its intersecting lines 1. The lecture notes that the triple tau forms two right angles on each exterior line and another at the central point where the three feet meet 1. Through these intersections, the emblem forms a set number of angles that can be grouped into five regular combinations 1. When reduced, the total sum of these right angles corresponds geometrically to the five Platonic solids, which traditionally represent the four physical elements and the sphere of the universe 1. In capitular regalia, this triple tau is frequently situated inside a triangle, which is itself enclosed within a circle 1.

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