By Tony Lance Dip.Math(Open) 27th June 2014 Update XI from http://www.bigberthathing.com/structur.html 2011 Review of Particle Physics. K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010) and 2011 partial update for the 2012 edition. Reviews Included 1980, 1992, 1994, 1996, 1998, 2000, 2002, 2004, 2006, 2008, 2010, 2011. Review from http://pdg.lbl.gov/2011/listings/contents_listings.html M Mesons: B Baryons: L Leptons: S Summary Particle List: N Nominal entry X Full Experimental Particle List: C Ratio Match Checked Review used in 1st, 3rd, last & part of 2nd columns. Col.1 Actual Particle Mass MeV (Electron .510998902) Col.2 Nominal Particle Mass Error MeV (Electron Mass MeV 0.510998902 Nominal Electron Error MeV 1.0D-09) Col.3 Particle Charge Exists (0:1:2) None, single, double. Col.4 Particle Detail Line No. Col.5 Polygon Edge Length in Photons Col.6 Particle Structure Type (1-10,77,88,99) Col.7 Particle Mass in Photons (Electron 15989995035) Col.8 Particle Pair Mass Ratio Col.9 Index From Above (MBL, NXS, C one from each group) Mass MeV Error charge Line N Type Sumation N (Type 1) Ratio Leptons/Baryons/Mesons 0.510998902 1.0D-09 1 1 178829 1 15989995035 1.0000000000000000000000000000 XLC 938.272013000 3.5D-07 1 2 1638649 6 29360071622303 1836.1526415760391135105815247053 XBC6 939.565346000 .00003 0 3 2060001 4 29400541376052 1838.6835838096306200635415019064 XBC4 Let X = charge * 15989995035 Type 1 Polygon 1 III Electron Sumation N = (N * N + N)/2 = 15989995035 Type 2 Polyhedron 4III Tetrahedron 4(N * N + N)/2 + X Type 3 Polyhedron 8III Octahedron 8(N * N + N)/2 + X Type 4 Polyhedron 6IV Cube N * int(2 * N/sqrt(3)) - int(N/sqrt(3)) + X Type 5 Polyhedron 20III Icosahedron 20(N * N + N)/2 + X Type 6 Polyhedron 8III6IV Cuboctahedron (8(N * N + N)/2)+6(N * int(2 * N/sqrt(3)) - int(N/sqrt(3))) + X Type 7 Polyhedron 4III4VI Truncated Tetrahedron (4(N * N + N)/2)+4(1 + 6 * (N * N + N)/2) + X Type 8 Polyhedron 32III6IV Snub Cube (32(N * N + N)/2)+6(N * int(2 * N/sqrt(3)) - int(N/sqrt(3))) + X Type 9 Polyhedron 18IV8III Small Rhombicuboctahedron (8(N * N + N)/2)+18(N * int(2 * N/sqrt(3)) - int(N/sqrt(3))) + X Type 10 Polyhedron 6IV8VI Truncated Octahedron 8(1 + 6 * (N * N + N)/2)+6(N * int(2 * N/sqrt(3)) - int(N/sqrt(3))) + X Three Equations III An equilateral triangle has a mass of sumation N, which is equal to (N * N + N)/2, where N=1,2,3,... This is collapsed lattice counting, where mass = 1, 3, 6, 10, 15, 21,... VI A six sided regular polygon has a mass of 1 + 6 * (N * N + N)/2, where mass = 7, 19, 37, 61, 91, 127,... IV Given a square of sides N, it has a mass of N * int(2 * N/sqrt(3)) - int(N/sqrt(3)), where N=8, 9, 10,... For N=1, 2, 3,...,7 mass = N * N. The main series has mass = 68, 85, 105,.. All 10 structures in phase I are combinations of these three equations.