The perdalpha, or Triangle of Pythagoras, is usually called also the Triple Triangle, because three triangles are formed by the intersection of its sides. But there is another variety of the Triple Triangle which is more properly entitled to the appellation, and which is seen in the illustration. It will be familiar to the Knight Templar as the form of the jewel worn by the Prelate of his Order. Like every modification of the triangle, it is a symbol of the Deity; but as the Degree of Knights Templar appertains exclusively to Christian Freemasonry, the Triple Triangle there alludes to the Mystery of the Trinity. In the Ancient and Accepted Scottish Rite Degree of Knight of the East the symbol is also said to refer to the triple essence of Deity; but the symbolism is made still more mystical by supposing that it represents the sacred number 81, each side of the three triangles being equivalent to 9, which again is the square of 3, the most sacred number in Freemasonry.
In the Twentieth Degree of the Ancient and Accepted Scottish Rite, or that of “Grand Master of all Symbolic Lodges,” it is said that the number 81 refers to the triple covenant of God, symbolized by a Triple Triangle said to have been seen by Solomon when he consecrated the Temple. Indeed, throughout the Ineffable and the Philosophic Degrees, the allusions to the triple triangle are much more frequent than they are in Ancient Craft Masonry. The Indian Trimourti, or Triple Triangle of the Hindus is of a different form, consisting of three concentric triangles. In the center is the sacred triliteral name, Aum. The interior triangle symbolizes Brahma, Vishnu, and Siva; the middle one Creation, Preservation, and Destruction; and the exterior one, Earth, Water, and Air.