taylorSimplex

A library of static functions of a simplex S

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OVERVIEW TEXT
AUTHOR

Class Summary

class taylorSimplex

{

public:
static const taylorFunction unit,x1,x2,x3,x4,x5,x6, y1,y2,y3,y4,y5,y6, dih,dih2,dih3,sol, lowVorVc,highVorVc,vorSqc,vor;
static const taylorFunction eta2_126,eta2_135,eta2_234,eta2_456;
protected:
}; // taylorSimplex

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OVERVIEW TEXT

This class contains the most important taylorFunctions for sphere packings. Much more general functions can be built up by taking linear combinations of these, using the operator overloading on addition and scalar multiplication for taylorFunctions.

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AUTHOR

Thomas C. Hales

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const taylorFunction unit,x1,x2,x3,x4,x5,x6, y1,y2,y3,y4,y5,y6, dih,dih2,dih3,sol, lowVorVc,highVorVc,vorSqc,vor;

unit is the constant function taking value 1. x1,..,x6 are the squares of the edge lengths. y1,...y6 are the edge lengths. dih,dih2,dih3, are the dihedral angles along the first three edges. sol is the solid angle of a simplex lowVorVc is the voronoi function truncated at 1.255. The domain is restricted to simplices whose first three edges have heights 2.51. highVorVc is the voronoi function truncated at 1.255. The domain is restricted to simplices whose first edge is greater than 2.51 and whose second and third edges are at most 2.51. vorSqc is the voronoi function truncated at sqrt(2). vor is the analytic voronoi function.

	static const taylorFunction unit,x1,x2,x3,x4,x5,x6,
		y1,y2,y3,y4,y5,y6,
		dih,dih2,dih3,sol,
		lowVorVc,highVorVc,vorSqc,vor;

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const taylorFunction eta2_126,eta2_135,eta2_234,eta2_456;

functions on an upright,flat,or quasiregular: circumradius squared of the four faces of a simplex: The domain of eta2_126,eta2_135,eta2_234, and eta2_456 are simplices whose edges are between 2.51 and 2sqrt(2)?? The circumradius squared of the face (ijk) of a simplex is eta2_ijk;

	static const taylorFunction eta2_126,eta2_135,eta2_234,eta2_456;

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All Members

public:
static const taylorFunction unit,x1,x2,x3,x4,x5,x6, y1,y2,y3,y4,y5,y6, dih,dih2,dih3,sol, lowVorVc,highVorVc,vorSqc,vor;
static const taylorFunction eta2_126,eta2_135,eta2_234,eta2_456;
protected:

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Ancestors

Class does not inherit from any other class.

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Descendants

Class is not inherited by any others.

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