Unique 5 Dimensional Cube

This is a never before seen projection of the five dimensional cube into 3 dimensions. Five lines meet at each of its 32 vertexes, and every one of its 80 lines is the same length. 

We call it the Possibility Star because if the fourth dimension can in some ways be considered to be Time, the the fifth dimension can in some ways be considered to be all the alternate possible universes. Five sided symmetry, which does not fit into the matrix of three dimensions, finds its natural home in five dimensional space. This is even harder to imagine than most higher dimensional concepts because it is so unintuitive to our experience of five sided symmetry. However, when we do encounter five-sided symmetry in our three-spacial-dimensional-universe it is usually in relationship to living things. For instance, the DNA has a 5 sided twist to its double helix that can be seen when looking down the spiral. 

For an introduction to the geometric concept of the 5D cube you can read its Wikipedia page here 

VIEW IN FULL SCREEN 3D ~
Click PLAY below, and then go full screen using the bottom right icon.
Use the left and right mouse button to move the geometry.
If you have a track pad then you can zoom by using two fingers. 

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) way, 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 its 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.

The 5D Cube transcends the lower dimensional split between spirit and matter ~
In 2D space the equilateral triangle, the square, and the hexagon, can all tile space, but the pentagon does not fit into a two dimensional grid like these other forms do.  This peculiarity of the five sided forms continues in 3D where the Tetrahedron, Cube, and Octahedron all fit into each other nicely, but the 5 symmetry dodecahedron and icosahedron form a separate pair, and again they cannot be made to tile space. 

Interestingly then, the main places where we find 5 sided symmetry in the universe is in living things, such as flowers, and the DNA molecule! To my way of thinking this is because the crystalline grid of spacetime is formed of 3, 4, and 6 symmetry interlocking patterns, and life can only fit into this grid by constantly adjusting itself, using its movement through time (and possible timelines) to enable higher dimensional integration. Life is only possible because of change and choice, otherwise all would be mechanically predestined.

In 4D space the equivalent 5 symmetry forms to the dodecahedron and icosahedron, are the exceedingly complex '120 cell' and '600 cell'.

Above: The 4D 120 cell and 600 cell. 

Beyond the 4th dimension, a remarkable thing happens, and there are no higher dimensional equivalents of the dodeca and icosa.
However, once we reach the fifth dimension, the 5D cube itself unites the symmetries that were incompatible in lower dimensions. Just as 3 squares meet at right angles at the corner of a 3D cube, so 5 four dimensional cubes meet at right angles at the corner of a 5D cube! 

Symbolically then, the 5D Cube could be said to be the Possibility Star that guides the way to a higher level of integration transcending the problematic duality of spirit and matter.

GREAT BOOKS FOR UNDERSTANDING HYPERSPACE
If you really want to understand higher dimensional forms it is essential to get many different insights into what they are. I highly recommend a little book published in 1913 called 'A Primer of Higher Space' by Claude Bragdon.   You can read a pdf version here  https://archive.org/download/aprimerhighersp00braggoog/aprimerhighersp00braggoog.pdf
The video below may also help with the basics of higher dimensions being explained by Carl Sagan.

Here is Carl Sagan introducing the basic concept of higher dimensional geometry.

I take no responsibility for the fact that soon after making this model a crop circle appeared with the 2D form.

The Five Dimensional Cube ~

I love the way this 3D version '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. 

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. 

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