geometry:3d [Cauldron Wiki]

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====== Sacred Geometry in 3D ======

So far we’ve been working in 2 dimensions, as if on a piece of paper, for the most part. But sacred geometry can be carried to the solid world of 3 dimensions. We’ve already seen that the major 2-dimensional shapes all have 3D analogs: [b]sphere [/b]for the circle, [b]tetrahedron [/b](4 sides) for the triangle, hexahedron a.k.a. the [b]cube [/b](6 sides) for the square, and [b]dodecahedron [/b](12 sides) for the pentagon.
 
Using identical regular polygons, there are only 5 regular solids (or, to use the mathematical term, convex polyhedra) one can construct: 

[img]https://i.imgur.com/biSZW5l.jpg[/img]
the tetrahedron…

[img]https://i.imgur.com/uCvbOjC.jpg[/img]
…the cube…

[img]https://i.imgur.com/7VGV0MH.jpg[/img]
…the [b]octahedron [/b](8 triangular sides; like 2 pyramids joined at the base)…

[img]https://i.imgur.com/hkiU2p7.jpg[/img]
…the dodecahedron…

[img]https://i.imgur.com/6lnZgPI.jpg[/img]
…and the [b]icosahedron [/b](from triangles again, but with 20 sides). 

These are called the [b]Platonic solids[/b], because Plato assigned each one to an element: the tetrahedron to [b]fire[/b], the cube to [b]earth[/b], the octahedron to [b]air[/b], the icosahedron to [b]water[/b], and the dodecahedron to the [b]astral[/b].

Next--[[geometry:personalpractice|Sacred Geometry in Personal Practice]]\\ 
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