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This
web site was built to show some results of my 20 plus years of research
on the close packing of spheres. At the origin, these results were
examined purely from a mathematical standpoint. Later on, unexpected
findings emerged, connecting these equations with observable physical
realities. As I expanded this investigation, it eventually lead to the
generation of a different way to link together the fundamental concepts
of space, time, matter and light. It even goes further by re-defining
each of these basic components. I hope you will enjoy exploring these concepts ... as well as the many associated observations presented on this site. Feedback is certainly welcomed.
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my email address is swaterman@watermanpolyhedron.com
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Mathematics
Mensuration tables -
Platonic Archimedean Johnson
rhombic inclusive polyhedron ( shortest edge = 1)
Waterman polyhedron - integer grid based - with some 5000 rotatable depictions.
complete with 3d graphics; polyhedra, lattice, symmetry, Conway, dual, geodesic, zonohedron.
Radial sweeps were taken from 0,0,0 as well as those itemized to the right of the lattice involved.
bcc* 1,0,0 1,0.5.0 1,0.5,0.5 1,1,0 1,1,0.5 1.5,1.5,0.5
cuboctahedron and octahedron* 1,0,0 1,1,0* 1,1,0.5 1,1,1 2,1,0.5 2,2,0.5 2,2,1
diamond** 1,1,0 1,1,0.5 2,0,0**
fcc* 0.5,0.5,0 0.5,0.5,0.5** 1,0,0* 1,1,0.5
hcp 0.5,0.5,0.5 1,1,1 2,0.5,0.5 2,2,0.5 0.25,0.25,0.25* 1,0.5,0
hcp diamond 1,1,0 2,0,0 0,0,0.5
rhombic dodecahedral* 1,0,0 1,0.5,0.5 1,1,0 1,1,0.5 1,1,1* 2,2,0.5
simple cubic* 0.5,0,0 0.5,0.5,0 0.5,0.5,0.5*
truncated octahedron 1,0,0 1,1,0 1,1,1 2,2,0.5 2,2,1 0.25,0,0* 1.5,1.5,1.5
truncated tet and tet* 0.5,0.5,0.5 1,0,0 2,1,1 1.5,1.5,0 1.5,1.5,0.5 1.5,1.5,1 1.5,1.5 1.5**
truncated tet and truncated octahedron and cuboctahedron* 1.5,1.5,0 1.5,1.5,1.5**
* Oh symmetry ** Td symmetry
4-Fold and 5-fold [ includes some phi related; non-integer x,y,z, points ]
Waterman polyhedron applications or write up
applet - Mark Newbold's [ over 20,000 polyhedron with no inventory required ]
Great Stella - software by Rob Webb [ even draws exact pieces for constructions ]
Maurice Starck's - pages with various graphics
Paul Bourke's - pages on-line generator for sphere clusters and polyhedron
Antiprism - sofware by Adrian Rossiter
Magnus Wenninger stellations
Wikipedia
ccp sphere based packs - aka fcc
cubic close packing
Cartography
Waterman World map - new 2010 Atlantic and Pacific centered versions
2d projections - maps projected onto Waterman solids
3d globe projections - globe projected onto Wateman solids
other
Lineal - conversion tables for the tetrahedron, cube and octahedron
Volumetric - conversion tables for the tetrahedron, cube and octahedron
71 diamond-regulars
Ramsey predictions
phi
suggested universal concepts
math vs physical - a conceptual overview applied to topics below
my 17 postulates
fixed point space
fixed interval time
fixed quanta mass
fixed wavelength light
math derived values for fundamental physical constants
over 100 fundamental physical constant values. -
Nist / Waterman
suggested individual concepts
Periodic table - aligned by valence
Lyman wavelengths - related to Rydberg
Fine Structure constant - as a variable
Ionization Potentials
suggested EMR wave
suggested FTL effect
my Relativity challenge
Galilean Challenge - x' = x-vt
2 observer math - Einstein
4 observer math - aka multilateration
Personal
jukebox 1 [ my Dad's tunes ]
"classical honky-tonk jazz" from the Juliard School musicians
juke 2 [ my tapes of 1978 ] Montreal; Rainbow Bar ( back room ) Yellow Door Coffee house
original poems
various links
polyhedron toys geometry ( some links may no longer be working )
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The contents of this web site are © Copyright Steve Waterman or a third
party contributor where indicated. You may print or save an electronic
copy of parts of this web site for your own personal use. Permission
must be sought for any other use. |
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