Tetrahedron
The simplest of the five regular solids: four equilateral triangles on six edges, meeting three at a time. Plato gives it to fire, on the argument that fire is the sharpest and most penetrating of the bodies, and the tetrahedron is the sharpest solid, with the smallest volume for its surface.
The element attribution is Plato's, in the Timaeus, and it is a philosophical argument about sharpness and mobility rather than a traditional correspondence of the kind the corpus records elsewhere. The name Platonic solid is post-classical; Plato does not use it, and the five solids are ascribed to Theaetetus on later testimony, chiefly Proclus and the scholia on Euclid XIII. The chakra link is the corpus's element mapping, not a classical source.
Correspondences
- Element
- Fire
- Chakra
- Solar Plexus Chakra
Practice
- Magical Uses
- Fire workWillProtectionBeginnings
Nature and meaning
- Meaning
The simplest of the five regular solids: four equilateral triangles on six edges, meeting three at a time. Plato gives it to fire, on the argument that fire is the sharpest and most penetrating of the bodies, and the tetrahedron is the sharpest solid, with the smallest volume for its surface. It is the only Platonic solid that is its own dual.
Details
- Dimensions
- 3D
- Keywords
- FireFour facesSharpnessSimplicityPlatonic solid
- Sacred Ratio
- 1:3 (insphere radius to circumsphere radius)
- Construction
Take an equilateral triangle and raise a fourth point above its centre until the three new edges equal the original three. Euclid constructs it inscribed in a sphere at Elements XIII.13, and the whole family at XIII.13-17. Its faces meet three at each vertex, so the vertex figure is a triangle.
- Appears in
- The tetraktys as solidCrystal latticesDice
One of 3,120 entries in the Grimoire — the whole library, every cross-reference, is free to take. Take the whole thing Is it wrong somewhere?
Referenced by 0
Nothing in the library points at this entry yet.
More in Sacred geometry
The entries either side of this one in the same catalogue.
All of Sacred geometry →New entries, when they land
Occasional notes when a section of the grimoire is added or revised. No account, no tracking across sites, and one line to leave.