Wednesday, March 6, 2013


Alright, I've put this off long enough. You want to know what the best polyhedron is?

The Octahedron, that's what.

Octahedra are Platonic solids consisting of eight triangular faces meeting at each other's vertices, like two pyramids joined at the base. Regular octahedra are composed of equilateral triangles. Interestingly, the octahedron is the only Platonic solid with an even number of faces meeting at each vertex, meaning it's the only such solid that possesses mirror planes that do not pass through any of it's faces. In case you don't know, a mirror plane is an imaginary line that passes through a solid at it's vertices. Thanks to the octahedron's superior reflective symmetry, it can pass through a mirror plane without it touching any of it's faces. The same can't be said for it's dual polyhedron: the cube, who also has eight faces.

Plus, the octahedron is a cross-polytope; a regular, convex polytope that exist in any number of dimensions. The two-dimensional polytope is the square, our three-dimensional representative being the octahedron and our neighbor in four dimensions being the 16-cell.

The most well known example of octahedra in real life would probably be in fluorite crystals. Fluorite is an isometric mineral with a tendency towards cubic crystals, but more complex shapes like octahedra are common.

Fluorite has seen use as flux in the iron industry, but it's extreme range of color means it gets more than enough use in decoration. In fact, many have gone so far as to call fluorite the most colorful mineral in the world, appearing purple, blue, green, yellow, colorless or in rare cases red, pink, brown, white and even black depending on impurities and exposure to radiation.

But it doesn't stop there, this particular solid has seen plenty of use in fiction and art, appearing on a disproportionate number of album covers.

The most popular octahedron in fiction would probably be Ramiel, the mysterious Fifth Angel who attacked Tokyo-3 in Neon Genesis Evangelion in an attempt to merge with Lilith and initiate "Third Impact", an event that would destroy all life on Earth, forcing it to revert to a substance that looks eerily similar to Tang.

Ramiel's most notable contribution to the series would probably have to be the time it liquified a skyscraper with it's particle beams. I'm just saying.


linda said...

As much as I liked all the different way this was described, I must admit I like the jewels so much better. Of course, any gem attracts my eyes so much more then abstract art or menacing vehicles bent on destroying the world. Thanks Tyler for the tutorial.

Shadgrimgrvy said...

Well yeah, I think most people would prefer jewels to death rays.

Zy Gazint said...
Another part of the method engages a platonic solid called the octahedron. An octahedron is an eight-sided solid that is essentially two square-based pyramids that are joined at their bases. Octahedrons naturally occur in many crystalline and molecular structures. We have referred to octahedrons in previous messages especially when we discussed the Holon of Balance. At a subtle energy level octahedrons impart balance.
In this method you imagine an octahedron in the center of your head. It is about one inch (or two centimeters) in height. This imagined octahedron is in the center of your head, and interestingly this is also the location of your pineal gland. The octahedron and your pineal gland also sit within your pranic tube.
Read the whole thing - quite fascinating ! Enjoy the ride :)

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