User:MeYCChang/ABSTRACT

ABSTRACT

A set of n points evenly distributed on a spherical surface is called an Even Distribution (E). There are five nEs corresponding to n = 4, 6, 8, 12, and 20.

My objective is to establish extensions systematically from the five basic Es and to analyze them. The extensions I established are eleven First Generations of Even Distributions (E’), three Twisted E’s (TE’) and six String Es (SE), plus an infinite number of Second Generations of Es (E”). The calculations and analyzes are using 3-dimensional geometry.

Practically, to study the structure and perform the calculations of Es and E-extensions is to assume that every point of a figure is a small ball of radius 1 unit packed in a spherical container. This induces my study of even distributions and their extensions into spherical ball packing.

The essential rule of ball packing is to pack all balls under a criterion that every ball should be in a state of having absolute 0 degree of freedom in motion. This regulates the arrangement and the structure of a pack. A pack with every ball under such a state is a well-bound (WB) pack. There are five WB criteria that an E or E-extension should satisfy.

All figures of Es and E-extensions are having all their points floating on a spherical surface. So, this kind of packing is also called the “Floating E-Packing”.

My goal is to establish and study the structure of Es and their extensions, and is not to find a smallest container for a certain number of balls. Any WB pack system is worth study.

The spherical ball packing covers more than just the floating E-packing. There is a parallel packing to the floating E-packing, called solid E-packing. Besides, there is an independent class of spherical ball packing called intruding packing, which is an asymmetric packing. All these will be my succeeding studies.

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