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n-Dimensional Space

Occult diagrams such as the Tree of Life are studied to help us understand the universe. Unless we have, ourselves, a very profound understanding of such matters then some doubt remains over their authenticity and value. Has the diagram structure itself been distorted over time, does it truly reflect universal principles or is it whole or partly an arbitary invention? These questions concern most true seekers whilst the majority of students are happy to rehash portions of the often conflicting literature on the subject.

VirtueScience looks to universal provable facts to help find the golden thread of truth running through the world's spiritual and occult beliefs often obscured delibrately or accidentally for various reasons.

A thought experiment to help us identify the universality and usefulness of a concept is to imagine a hyperthetical alien race. Would any such race, given sufficient insight, discover it? The platonic solids are worthy of study precisely because they are "there" to be discovered in any hyperthetical 3 dimensional realm. Those readers who are interested in the Cube of Space but ignore the other 4 platonic solids are, in my opinion making an error. If universal secrets are contained in the structure of the cube, if the cube is a universal/eternal three dimensional diagram, then the other platonic solids must be similarily endowed because they share so many of the cube's known qualities. But what of the other dimensions of space?

If the beauty and simplicity of the regular 3 dimensional solids conceal, or indeed reveal, deep truths then surely this applies to the regular shapes in other spacial dimensions as well. You see, just as we seek to strip away personal and cultural bias, we would also like to strip away any three dimensional bias as well.

Regular Polytopes in n-Dimensions

Number of Regular Polytopes
The Point.
The Line.
There are an infinite number of regular polygons, the simplest of which is the triangle.
The are 5 platonic solids.
There are six 4 dimensional regular polytopes.
For n dimensions with n>4 there are only 3 regular convex polytopes. The hypercube, the cross polytope and regular simplex which are based on the cube, octahedron and tetrahedron.

Note that in evey dimension of space, there is at least one regular form. These are the infinite series of simplexes which are connected to the base 2 (ie binary) number system, pascal's triangle and partition theory. I believe they are also conected to a set of simple concepts, the basis of a Universal Language.

Note also that apart from the first 2 dimensions, all the other dimensions have at least 3 regular forms. In fact every dimension from 5 to infinity has exactly 3 regular forms. These 3 infinite series are the infinite series of simplexes (the 3-dimensional simplex being the tetrahedron) and 2 other infinite series which are the dual of each other: at the 3 dimensional level these duals are the cube and the octahedron which reflect each other.

Where as the simplexes are connected with base 2, the hypercube series and it's dual the cross polytope series are connected with the trinary base-base 3.

Imagine the simplex series as a central balanced series, with the hyper-cube series on one side and its dual the cross-polytope series on the other side. Perhaps these 3 series correspond in some way to the 3 energy channels said to run along the spine.

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Hi, I am James Barton the founder of VirtueScience and Author of "Inner Medicine" which details my discoveries regarding the virtues along with practical exercises to awaken natural virtue. I have a wide range of interests but the main focus of this site now is the virtues and character. Please feel free to explore the site and comment on any pages that you are interested in/agree with or disagree with.
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