User:Jgmoxness

• 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

E8 421 Petrie Projection

E8 241 Petrie Projection

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

• more detail on projections

120-Cell Hulls

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

Triakis icosahedron Hulls

600-Cell Hulls

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

• 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

• Klein Quartic Curves
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• 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

• 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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• 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

• 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

• 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

• Fano Planes.
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CoPrime graph

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