The process
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The simplest of the platonic solids, the tetrahedron, is also a simple starting point. Take as a given that the initial measurement of each edge is just one meter. Starting at the human scale, that object is both divided and multiplied by 2. If one starts at the Planck length, it would always be multiplied by 2. If one were to start at the edges of the observable universe, the result would always be divided by 2.
The limits of base2 scientific notation
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There are limits. Going within, the limit of the smallest division is the Planck length. It is reached in 115 notations by dividing by 2. Going out through multiplication, the limit is to the edges of the observable universe. It is reached in 91 notations multiplying by 2. The result is similar to the orders of magnitude using base10 scientific notation.
Diversity
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With each successive division and multiplication, base2 scientific notation within geometry readily expands to include the other four basic platonic solids, then the Archimedean and Catalan solids, and other regular polyhedron. Cambridge University maintains a database of some of the clusters and cluster structures.
Base2 scientific notation in geometry involves every form and application of geometry and geometric structures. Arthur Loeb (Space Structures, Their Harmony and Counterpoint ^{[1]}) analyzes Dirichelt Domains (Voronoi diagram) in such a way that spacefilling polyhedra can be distorted (nonsymmetrical) without changing the essential nature of the relations within structure (Chapters 16 & 17).
There is no necessary and conceptual limitation of the diversity of embedded or nested objects ^{[2]}.
Geometers
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Geometers throughout time  people such as Pythagoras, Euclid, Euler, Gauss, Buckminster Fuller, Robert Williams, Károly Bezdek, John Horton Conway, and thousands of others have contributed to this knowledge of geometric diversity. These manifestations of structure are welldocumented within many notations (see Buckyballs and Carbon Nanotubes, using electron microscopy). The FrankKasper phases^{[3]} including the WeairePhelan polyhedral structure have even contributed to architectural design within the human scale, i.e. Beijing National Aquatics Centre.
Constants & Universals
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There are constants, inheritance (in the legal sense as well as that used within objectoriented programming) and extensibility between notations. Each notation has its own rule sets^{[4]}. Taken as a whole, from the smallest to the largest, this polyhedral cluster has been described as dodecahedral by astrophysicist JeanPierre Luminet at the Observatoire de Paris in France.
Polyhedral combinatorics is a subgroup of base2 scientific notation in geometry.
206 notations
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In 91 steps of multiplying, one reaches the edges of the observable universe, the largest possible representational geometric number. In 115 steps of dividing, one enters the area of Planck's constant, the smallest possible representational geometric number. In 206 notations every scientific discipline is necessarily related between notations. Every act of dividing and multiplying involves the formulations and relations of nested objects, embedded objects and space filling. All structures are necessarily related. Every aspect of the academic inquiry from the smallest scale, to the human scale, to the large scale is defined within one of these 206 notations. Both calotte model of space filling and the pleisohedron of space filling are used and continuity, symmetry, and harmony are taken as given to define order, relations, and dynamics respectively.
Geometries within base2 scientific notations have been applied to virtually every academic discipline from game theory, computer programming, metallurgy, psychology, econometric theory, linguistics ^{[5]} and, of course, cosmological modeling.
See also
Bibliography
 An Amazing, Space Filling, Nonregular Tetrahedron Joyce Frost and Peg Cagle, Park City Mathematics Institute, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
 Aspects of Form, editor, Lancelot Law Whyte, Bloomington, Indiana, 4th Printing, 1971
 Foundations and Fundamental Concepts of Mathematics, Howard Eves, Boston: PWSKent. Reprint: 1997. Dover, 1990
 Jonathan Doye's Research Group at http://physchem.ox.ac.uk/~doye/
 Magic Numbers in Polygonal and Polyhedral Clusters, Boon K. Teo and N. J. A. Sloane, Inorg. Chem. 1985, 24, 45454558
 Pythagorean triples, rational angles, and spacefilling simplices [PDF], WD Smith  2003
 Quasicrystals, Steffen Weber, JCrystalSoft, 2012
 Space Filling Polyhedron http://mathworld.wolfram.com/SpaceFillingPolyhedron.html
 Space Structures, Arthur Loeb, AddisonWesley, Reading 1976
 Structure in Nature is a Strategy for Design, Peter Pearce, MIT press (1978)
 Synergetics I & II, Buckminster Fuller,
 Tilings & Patterns, Branko Grunbaum, 1980 http://www.washington.edu/research/pathbreakers/1980d.html
References and External Links
 ^ Loeb, Arthur (1976). Space Structures  Their harmony and counterpoint. Reading, Massachusetts: AddisonWesley. pp. 169. ISBN 0201046512.
 ^ Thomson, D'Arcy (1971). On Growth and Form. London: Cambridge University Press. pp. 119ff. ISBN 0 521 09390.
 ^ Frank, F. C.; Kasper, J. S. (1958). "Complex alloy structures regarded as sphere packings. I. Definitions and basic principles". Acta Crystall. 11. Frank, F. C.; Kasper, J. S. (1959). "Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures". Acta Crystall. 12
 ^ Smith, Warren D. (2003). "Pythagorean triples, rational angles, and spacefilling simplices". http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.124.6579&rep=rep1&type=pdf .
 ^ Gärdenfors, Peter (2000). Conceptual Spaces: The Geometry of Thought. MIT Press/Bradford Books. ISBN 9780585228372.
 Kees Bopeke (Holland), Cosmic View, The Universe in 40 Jumps. In 1957 Nobel laureate in physics, Arthur Compton, wrote the introduction for this work. In 1968 Charles Eames and his wife, Ray, produced a documentary, Powers of Ten based on that book. MIT physics professor, Phil Morrison, narrated the movie. See also, Phil and Phyllis Morrison, Powers of Ten: A Book About the Relative Size of Things in the Universe and the Effect of Adding another Zero (1982)
 Bergman clusters, http://met.iisc.ernet.in/~lord/webfiles/Coordinates.pdf, Indian Institute of Science, Bangalore, India, Department of Materials Engineering
 Jonathan P. K. Doyle, Cluster structures, http://physchem.ox.ac.uk/~doye/research/cluster_structure.html See J. Chem. Phys., 119, 11361147 (2003)
 Econometric modelling http://www.spacefillingdesigns.nl
 Howard Eves, page 131, 1990. Foundations and Fundamental Concepts of Mathematics. 3rd. ed. Boston: PWSKent. [Reprint: 1997. Dover Publications.]
 FrankKasper coordination polyhedra http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.188.2092&rep=rep1&type=pdf
 Polyhedral Clusters, Indian Institute of Science, Bangalore, India, Department of Materials Engineering, http://met.iisc.ernet.in/~lord/webfiles/clusters/polyclusters.pdf
 Qisheng Lin and John D. Corbett, "New Building Blocks..." "According to higher dimensional projection methods, a series of cubic ACs (approximant crystals) exist with orders (q/p) denoted by any two consecutive Fibonacci numbers, i.e., q/p = 1/1, 2/1, 3/2, 5/3 … F n+1/F n (1)." http://www.pnas.org/content/103/37/13589.full
 JeanPierre Luminet et al. 2003 Nature 425 593 http://physicsworld.com/cws/article/news/18368
 Weisstein, Eric W., "Spacefilling polyhedron" from MathWorld" http://mathworld.wolfram.com/SpaceFillingPolyhedron.html
