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Toroidal Projections of Higher Dimensional Forms
My most important geometric discovery is the way that many higher dimensional forms can be enfolded into 3D so that they become toroidal (donut shaped) forms.
The 4D hypercube was the first and simplest discovery. It was many years before I realised that the 5D and 6D cubes had similar possibilities.
What is a 5 dimensional cube? Glad you asked :-)
Well there are many ways to try and understand what the geometers of the 19 century figured out about higher dimensional geometry. One of the easiest (though not necessarily the most accurate) ways is by analogy to the dimensions that we are familiar with. In the third dimension we are familiar with the Cube, and we can see that it has similarities with the two dimensional Square. By moving a square at right angles to it plane we can create a cube. Likewise (theoretically) by moving a cube at right angles to the 3d space it occupies we can create a 4D hypercube, and by moving a 4D hypercube at right angles to the 4D space it occupies we can create a 5D hypercube.
GREAT BOOKS FOR UNDERSTANDING HYPERSPACE
If you really want to understand higher dimensional forms it is essential to get many insights into what they are, from different angles so to speak. I highly recommend a little book published in 1913, 'A Primer of Higher Space' by Claude Bragdon. In fact if you purchase one of my higher dimensional geometries and then send me a message through the contact form on my site I would be happy to purchase a Kindle copy of this book for you so that you can go deeper into understanding it.
Alternatively there is another old book you may like called Flatland that uses a story set in a two dimensional world to make many higher dimensional concepts more approachable, and you can download it for free from the links at the bottom of the page here
The video below may also help with the basics of higher dimensions being explained by Carl Sagan.
Also this video bel,ow shows the basics of how to draw the 2 dimensional projection of this form. Note that although the 2D form is standard, the way we have three dimensionalized it here is a unique discovery of ours!
I take no responsibility for the fact that soon after making this model a crop circle appeared with the 2D form.
I also take no responsibility for accidentally opened wormholes into other universes, accelerated spiritual evolution, increased powers of manifestation, or any other strange effects that may be noticed in proximity to higher dimensional geometries!
More about this particular form ~ I love the way simply by its 5 dimensional symmetries it transcends the duality between the dodecahedral and cubic forms in 3D space. I also love the way it 'folds up' so that all the lines remain identical lengths. It is based on my Toroidal Hypercube model that keeps all 8 cubes equally distorted despite the projection down into 3D. Here instead of 8 cubes we have 10 hypercubes equally distorted. I take no responsibility for the fact that soon after making this model a crop circle appeared with the 2D form!
I also take no responsibility for accidentally opened wormholes into other universes, accelerated spiritual evolution, increased powers of manifestation, or any other strange effects that may be noticed in proximity to higher dimensional geometries.
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseracts
It can be called a penteract, a portmanteau of tesseract (the 4-cube) and pente for five (dimensions). It can also be called a regular deca-5-tope or decateron, being a 5-dimensional polytope constructed from 10 regular facets.
About Our Products
SacredGeometrical.com is created by web designer, author, and sacred geometry artist Narada Dan Vantari. The 3D designs and all the other artworks here represent many years of study and creative output.
We use 3 different POD (Print On Demand) companies, one for the 3D Geometries and Jewellery, one for the Clothing, and one for the Posters. The quality they provide is quite incredible and would not have been possible at almost any price a decade ago! Being POD means that these products are manufactured especially for your order.
Our 3D Printed Jewellery and Models
3D printing is a disruptive technology that is changing societies approach to manufacturing almost everything. Along with artificial intelligence and nano-engineering it will change human society as much if not more in the next decades as the computer and internet have done in the last decades!
Our 3D prints are created as 3D computer files and uploaded to the company in New York where state of the art machines (costing around half a million $) are used to print them layer by layer of tiny dots. (Just like a 2D printer going over and over building up a form out of a stack of sheets of paper). Depending on the material the print is then put through other processes, or even used to create a mold that is then filled with the molten metal.
Our Sacred Geometry Clothing Designs