The peculiar and principal symbol of this Degree is the Tetractys of Pythagoras.

Tetractys of Pythagoras

Pike now discusses the principle symbol of the 31st degree and its significance, “The peculiar and principal symbol of this Degree is the Tetractys of Pythagoras, suspended in the East, where ordinarily the sacred word or letter glitters, like it, representing the Deity.” He also makes reference to the 31st degree Mason being a Judge, like that of the 30th degree, “To us, as Masonic Judges…” Enjoy my friends:

The peculiar and principal symbol of this Degree is the Tetractys of Pythagoras, suspended in the East, where ordinarily the sacred word or letter glitters, like it, representing the Deity. Its nine external points form the triangle, the chief symbol in Masonry, with many of the meanings of which you are familiar.

To us, its three sides represent the three principal attributes of the Deity, which created, and now, as ever, support, uphold, and guide the Universe in its eternal movement; the three supports of the Masonic Temple, itself an emblem of the Universe:–Wisdom, or the Infinite Divine Intelligence; Strength, or Power, the Infinite Divine Will; and Beauty, or the Infinite Divine Harmony, the Eternal Law, by virtue of which the infinite myriads of suns and worlds flash ever onward in their ceaseless revolutions, without clash or conflict, in the Infinite of space, and change and movement are the law of all created existences.

To us, as Masonic Judges, the triangle figures forth the Pyramids, which, planted firmly as the everlasting hills, and accurately adjusted to the four cardinal points, defiant of all assaults of men and time, teach us to stand firm and unshaken as they, when our feet are planted upon the solid truth.

It includes a multitude of geometrical figures, all having a deep significance to Masons. The triple triangle is peculiarly sacred, having ever been among all nations a symbol of the Deity. Prolonging all the external lines of the Hexagon, which also it includes, we have six smaller triangles, whose bases cut each other in the central point of the Tetractys, itself always the symbol of the generative power of the Universe, the Sun, Brahma, Osiris, Apollo, Bel, and the Deity Himself. Thus, too, we form twelve still smaller triangles, three times three of which compose the Tetractys itself.

I refrain from enumerating all the figures that you may trace within it: but one may not be passed unnoticed. The Hexagon itself faintly images to us a cube, not visible at the first glance, and therefore the fit emblem of that faith in things invisible, most essential to salvation. The first perfect solid, and reminding you of the cubical stone that sweated blood, and of that deposited by Enoch, it teaches justice, accuracy, and consistency.

The infinite divisibility of the triangle teaches the infinity of the Universe, of time, of space, and of the Deity, as do the lines that, diverging from the common centre, ever increase their distance from each other as they are infinitely prolonged. As they may be infinite in number, so are the attributes of Deity infinite; and as they emanate from one centre and are projected into space, so the whole Universe has emanated from God (Albert Pike, Morals and Dogma, 1871, p. 826-827).