# Proton 6: 2nd Degree (P6-30)

 A second degree solution set for P6. The first three images are side views, the fourth & fifth are views of the polar triangles, and the sixth is shown without the balloon inserted to demonstrate the symmetry of the shell. As you can see, this model for P6 is more spherically symmetric in its structure than the polar star shells shown below, all of the structural circlets also qualify as equatorial circlets. These spherical shells are extremely difficult to model from scratch using the glue-gun and wire techniques I am forced to use. The 6-particle spherical shells presented here are the result of a great deal of frustrating trial and error. Look at the pictures of the shell and note that all the filler circlets can be replaced by a single sinusoidal string wrapped once around the particle. This sinusoidal string can be calculated exactly by virtue of the fact that the peaks of the sine correspond to the fixed position of a quark on the shells surface. (Figures for the sinusoidal solution are not given.)

## Stereograms of P6-30 Shell

 Required Snap Points: 60 Available Snap Points: 60 Pinned Vector Bosons: 0 L1 = 32.60432506" (Structural) L2 = 32.60432506" (Structural) L3 = 18.39567494" (Filler) Model Diameter: 10.378279" Loop Ratios: (1:2): 1 (1:3): 1.772390802 (2:3): 1.772390802 Loop Equation: 3(L1) + 3(L2) + 6(L2) = 306" Snap Point Equation: 3(6) + 3(8) + 6(3) = 60 R.S.P.

# Proton 6: 3rd Degree, Polar Star (P6-30PA)

 This Proton Shell of 6 is built from 13 hadron strings. Six of the strings are structural, six are filler circlets, and one is a polar circlet. The polar circlet has six snap points, and a different loop value than the filler circlets. All the down quarks are found at one pole of the shell, making for a highly polarized charge structure.

## Stereograms of P6-30PA Shell

 Required Snap Points: 60 Available Snap Points: 60 Pinned Vector Bosons: 0 L1 = 29.75263657" (Structural) L2 = 17.94151492" (Filler) L3 = 19.83509105" (Polar) Model Diameter: 10.93566267" Loop Ratios: (1:2): 1.658312395 (1:3): 1.5 (2:3): 0.904534034 Loop Equation: 6(L1) + 6(L2) + 1(L3) = 306" Snap Point Equation: 6(6) + 6(3) + 1(6) = 60 R.S.P.

# Proton 6: 3rd Degree, Polar Star (P6-30PB)

## Stereograms of P6-30PB Shell

 Required Snap Points: 60 Available Snap Points: 60 Pinned Vector Bosons: 0 L1 = 28.40477376" (Structural) L2 = 32.79901906" (Equatorial) L3 = 17.12872306" (Filler) Model Diameter: 10.44025202" Loop Ratios: (1:2): 0.8660251 (1:3): 1.658312395 (2:3): 1.914854887 Loop Equation: 6(L1) + 1(L2) + 6(L3) = 306" Snap Point Equation: 6(6) + 1(6) + 6(3)= 60 R.S.P.

# Proton 6: 4th Degree, Polar Star (P6-40PS)

 A fourth degree sinusoidal solution set for P6. Because there are an even number of facets to this shell, the sinusoidal string only wraps once around the shell before closing on itself. A more conventional equatorial string cohabits the equator with the sinusoidal string. The sinusoidal string is estimated, and the length of this string will affect the lengths of the other strings in the model, but the loop ratios for the non-sinusoidal strings will remain unchanged. Knowing that, it is possible to substitute values for the sinusoidal string and recalculate the dimensions of the other loops so as to satisfy the loop equation. I have not yet been able to determine any concrete rules or laws which govern the amplitude of the sinusoidal strings, making it difficult to get concrete values for most shells containing sinusoidal strings.

## Stereograms of P6-40PS Shell

 Required Snap Points: 60 Available Snap Points: 60 Pinned Vector Bosons: 0 L1 = 29.9410405" (Structural) L2 = 51.8594216" (Sinusoidal) L3 = 34.5729478" (Equatorial) L4 = 19.9606937" (Polar) Model Diameter: 11.00491108" Loop Ratios: (1:2): 0.577350067 (1:3): 0.8660251 (1:4): 1.5 (2:3): 1.5 (2:4): 2.598077123 (3:4): 1.732051415 Loop Equation: 6(L1) + 1(L2) + 1(L3) + 2(L4) = 306" Snap Point Equation: 6(6) + 1(6) + 1(6) + 2(6) = 60 R.S.P.

Copyright 1997 by Arnold J. Barzydlo
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