What is the significance of the Triple Tau in Freemasonry and how it is related to the Platonic solids?

The Triple Tau, consisting of three tau crosses conjoined at their feet, serves as the badge of the Royal Arch and is designated in English ritual as the emblem of emblems 1. Functionally, the symbol signifies the sacred and threefold nature of the Deity, denoting a single God who is simultaneously three 2. Albert C. Mackey interprets the mark as a designation setting apart those who know and worship the divine name, comparing it to the protective tau mark described in the biblical prophecies of Ezekiel 1.

Its connection to the Platonic solids rests on geometric reductions detailed in early English lectures 1. The symbol forms two right angles on each exterior line and a central right angle where the three crosses meet, as the three angles of a triangle equal two right angles 1. Through its intersecting lines, the badge yields angles capable of five distinct regular combinations 1. When these angles are reduced to right angles, their total sum corresponds geometrically to the five Platonic bodies, which traditionally represent the four elements and the sphere of the universe 1.