the (inside-out) cubic sections. a symbol?

in my continued efforts to unravel the mystery of the CHAOTIC FRACTAL i have been working with, i made a 3D model of the mathematical figures i am working with in the functions....specifically sqrt(1) sqrt(2) and sqrt(3).

they turned out really nice, so i thought i would share.











i started with a cube with all of its vertices connected, and then flipped all of the vertices outward. other than that, i have not made much of an analysis of the polygon. info would be helpful.


i read a thread yesterday where someone mentioned "metatron's cube".


hmmmm.... i wonder.....

Have you looked at the joints, counted them, to see if there are any correlations to the Fibonacci Sequence?

Ribbit

third from the bottom looks a lot like the tree of life

great work, youve inspired me to do some home craft

The top image is a rhombic dodecahedron, aka tesseract. It contains both the cube and octahedron. It's dual is the cubeoctahedron. It's one of my favorite 3D shapes. It's a perfect space-filling polyhedron so you can clump a bunch together with no space left in between. A very fundamental shape and yes it has connections with metatron's cube as that contains both the cube and octahedron as well.

Here's a render I made: It's a bunch of tesseracts put together and sliced so you can see the honeycomb-like structure.

reply to post by circlemaker


perfect! I was leaning toward hypercube, but wasn't sure. the pictures are great, but really, this shape on 3D is a real trip.

thanks for posting the image!

reply to post by tgidkp


Looks like a variation of a tesseract cube to me... If your not familiar with tesseract, the theory explores the possibility of a forth spacial dimention that remains unseen. Marko rodin was trying to conceptualize a four dimensional sphere when he developed the Rodin Coil. I believe he was also working with fractals.
You may find an exploration of Tesseract and Rodin maths educational...

Two things came to mind! Not really that close but it still was enough to make me think of them.

1. A Bacteriophage.


and

2. The Jewish-Kabbalistic Sephirot.



By the way, I love the saturated effect on these pictures.

reply to post by ErroneousDylan


i should admit that i was pretending to be more aloof to the significance of these forms than i really am.

actually, this polygon is built from (and produces) extremely significant length ratios. probably the MOST significant ratios in all of sacred geometry. the comparison to the kabbalah tree of life is not a coincidence.

i learned to use these segment lengths by using a technique of "squaring the circle" which i learned from a thread posted by a freemason here on ATS. below are some pages from my notebook. in the third image you can see that i was able to draw a (near) perfect circle by freehand using this technique. the ratios in the third image are, in my opinion, the foundation of the universe.






thanks everyone!