User:Jgmoxness

[1]jgmoxness or Special:Emailuser/Jgmoxness
See also:

• www.TheoryOfEverything.org

See below for my content:

Images of the Archimedean and Catalan Solids

Images of maximal subgroup embeddings of Lie Algebras

• Images of maximal subgroup embeddings of Lie Algebras
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  E8 Maximal Embeddings
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  E8 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams
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  E7 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin
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  E6 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin
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  D8 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams
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  C8 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams
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  B6 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams
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  A7 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams
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  F4 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin
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  G2 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin

Images of higher order orbits of E8 (421, 241, 142)

E8 421 Petrie Projection

E8 241 Petrie Projection

E8 142 Petrie Projection (53% of inner edges culled)

• more detail on projections

Images of various orbits of H4 hulls

120-Cell Hulls

Orthogonal projection of the 120-cell using any 3 of the 4 dimensions forms an outer hull of a Truncated icosahedron of Norm=√8.
Hulls 1, 2, & 7 are each overlapping pairs of Dodecahedrons.
Hull 3 is a pair of Icosidodecahedrons.
Hulls 4 & 5 are each pairs of Truncated icosahedrons.
Hulls 6 & 8 are pairs of Rhombicosidodecahedrons.

Overlay of regular and quasi-regular constructions of Snub Dodecahedra and Truncated Icosidodecahedra

Overlay of regular and quasi-regular snub decahedra

Overlay of regular and quasi-regular truncated icosidodecahedra

Triakis icosahedron Hulls

600-Cell Hulls

This shows the non-zero concentric hulls of E8 rotated to H4 and H4 phi 600-Cells

24-Cell to 600-Cell H4 Animation

600-Cell to 120-Cell Animation

T alternate of the 120-cell

DualSnub24Cell

Snub24Prime

Snub24CellPrime-hulls

120Cell-M

Snub24Cell


H4Phi-Snub24Cell-4hulls-each

Images of fractals, 3D chaotic attractors, and 3D parametric surfaces

• of fractals, 3D chaotic attractors, and 3D parametric surfaces
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  A collection of named 3D chaotic attractors
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  A collection of fractals named by their generating function
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  A collection of 3D fractals named by their generating function
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  A collection of fractals named by their generating expression
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  A collection of named 3D parametric surfaces

Images of Quartic Curves and Octonions as they relate to Electron Spherical Harmonic Legendre Functions and their Dual Quark-Gluon Nucleons

• Klein Quartic Curves
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Images of Hasse Diagrams

• Hasse Diagrams
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  D4 Hasse
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  C5 Hasse
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  F4 Hasse
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  E6 Hasse
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  E7 Hasse
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  E8 Hasse

Images of Stowe-Janet-Scerri Periodic Table

• Stowe-Janet-Scerri Periodic Table organized by the Psi{n,l,+/-m} and +/-s quantum number symmetries and includes cutaway views of the spherical harmonics of the 3D orbital electron cloud probabilities.
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Images of E8 (and its subgroups)

• E8 (and Subgroups) Visual Catalog of Regular Symmetries with Projections to 2D and 3D
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  2D Polygons
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  3D Platonic Solids
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  4D Polychora
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  5D Polytopes
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  6D Polytopes
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  7D Polytopes
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  8D Polytopes

Images related to Quasicrystals

• E8_(mathematics) and Quasicrystals
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  6-cube (Hexeract) using 6D orthographic_projection to a 3D Perspective_(visual) object (the Rhombic_triacontahedron) using the Golden ratio in the basis_vectors (inner edges removed leaving their vertices).
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  6-cube (Hexeract) orthographically projected to 3D using the Golden ratio. This is used to understand the aperiodic icosahedral structure of Quasicrystals.
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  240 E₈ polytope vertices with 1440 6-cube (6D) unit edges and Golden ratio basis vectors orthographically projected to 3D.
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  240 E8_(mathematics) vertices projected to 2D using 5-cube Petrie_polygon basis vectors
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  240 E₈ polytope vertices projected to 2D using 5-cube Petrie basis vectors overlaid on electron diffraction pattern of an icosahedral Zn-Mg-Ho Quasicrystal.
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  5 cell to hull of the Rhombic 20 Hedron
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  5 cell in H3 projection (all vertices and edges)
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  4 cell to hull of the Rhombic 2-hedron
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  4 cell in H3 projection (all vertices and edges)
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  D6 to H3 icosadodecahedron
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  6 Demicube (even) to dodecahedron
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  6 Demicube (odd) to icosahedron
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  E8 in H4 projection and orthonormal to 3D to STL and 3D printed
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  E8 concentric hulls in H3 projection
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  E7 concentric hulls in H3 projection
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  E6 concentric hulls in H3 projection
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  6-cube to concentric hulls in H3 projection
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  H4 concentric hulls in H3 projection

E8 with Lisi Particle Assignments
Petrie Projection	E8 embedding	E8 embedding with particle labels	F4 (outer=Quarks, inner=Bosons/Leptons) w/Triality Edges	F4 with particle labels	Modified E6 projection showing Fermions in groups w/Boson rings	Mathematical representation of the physical Zome model isomorphic (?) to E8.
Hasse diagrams of selected E8 subgroups
A7 Hasse	F4 Hasse	C5 Hasse	D5 Hasse	E6 Hasse	E7 Hasse	E8 Hasse
Petrie Projections of the n-Cubes (C3 to C7, E8)
3D 4-cube	3-cube	4-cube	5-cube	6-cube	7-cube	E8
Column (Pascal Triangle) Projections of the n-Cubes (C2 to C7, E8)
2-cube	3-cube	4-cube	5-cube	6-cube	7-cube	3D E8
Coxeter Plane (Petrie) Projections of D3 to D8
D3	D4	D5	D6	D7	D8 in D7	D8
Coxeter Plane Projections
G2	Cell 24 in D5	Cell 24 in E6	F4 in E6	E6	E7	E8 in E6
Cell 600 Projections
3D	Petrie	Square	Pentagon	Hexagon
Cell 120 Projections
3D	Petrie	Orthogonal	Pentagon	2Pi/3 basis
Other Projections
Rectified F4 with Triality	Birectified F4	Rectified E8 with F4 Triality	E8 with 6720 Sqrt(6) edges	E8 in D8

Images Dynkin Diagrams

• Assorted Dynkin Diagrams
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  Rank 3 Compact Hyperbolic Dynkin Diagrams (1-5 of 238)
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  Rank 3 Compact Hyperbolic Dynkin Diagrams (6-10 of 238)
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  Finite Dynkin Diagrams
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  Affine Loop Dynkin Diagrams
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  Hyperbolic and very extended affine Dynkin Diagrams
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  Folding Dynkin Diagrams
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  Folding Dynkin Diagrams
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Cell8+Cell16=Cell24

Tesseract (Left frame orthogonal, Right frame perspective)	Anaglyph for depth cueing(Red left eye, Cyan right eye) (Left frame orthogonal, Right frame perspective)
Penteract Hexeract	Hepteract
16 Cell	24 Cell
120 Cell	600 Cell

Images of Fano Planes

• Fano Planes.
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CoPrime graph

(talk) 02:52, 6 April 2010 (UTC)