User:Jgmoxness

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

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.

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

E8_(mathematics) and Quasicrystals
w:6-cube (w:Hexeract) using 6D w:orthographic_projection to a 3D w:Perspective_(visual) object (the w:Rhombic_triacontahedron) using the w:Golden ratio in the w:basis_vectors (inner edges removed leaving their vertices).
w:6-cube (w:Hexeract) orthographically projected to 3D using the w:Golden ratio. This is used to understand the aperiodic icosahedral structure of w:Quasicrystals.
240 w:E₈ polytope vertices with 1440 w:6-cube (6D) unit edges and w:Golden ratio basis vectors orthographically projected to 3D.
240 w:E8_(mathematics) vertices projected to 2D using w:5-cube w:Petrie_polygon basis vectors
240 w:E₈ polytope vertices projected to 2D using w:5-cube Petrie basis vectors overlaid on electron diffraction pattern of an icosahedral Zn-Mg-Ho w:Quasicrystal.

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

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