User:Jgmoxness

Archimedean and Catalan solid hulls with their Weyl orbit definitions

File:E8_Maximal_Embeddings.svg|E8 Maximal Embeddings

File:E8_MaximalEmbeddings_with_Weyl_Orbit_and_Coxeter-Dynkin_Diagrams.svg|E8 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams

File:E7_Maximal_Embeddings_with_Weyl_Orbit_and_Coxeter-Dynkin_Diagrams.svg|E7 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin

File:E6_Maximal_Embeddings_with_Weyl_Orbit_and_Coxeter-Dynkin_Diagrams.svg|E6 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin

File:D8_Maximal_Embeddings.svg|D8 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams

File:C8_Maximal_Embeddings.svg|C8 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams

File:B6_Maximal_Embeddings.svg|B6 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams

File:A7_Maximal_Embeddings.svg|A7 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin Diagrams

File:F4_Maximal_Embeddings_with_Weyl_Orbit_and_Coxeter-Dynkin_Diagrams.svg|F4 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin

File:G2_Maximal_Embeddings_with_Weyl_Orbit_and_Coxeter-Dynkin_Diagrams.svg|G2 Maximal Embeddings with Weyl Orbits and Coxeter-Dynkin

E8 421 Petrie Projection

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E8 241 Petrie Projection

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

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File:E8_241-3D_Concentric_Hulls.png

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• [http://theoryofeverything.org/theToE/2020/05/04/nested-lattices-of-e8/ more detail on projections]

120-Cell Hulls

[[File:120-Cell showing the individual 8 concentric hulls and in combination.svg|thumb|400px|

Orthogonal projection of the 120-cell using any 3 of the 4 dimensions forms an outer hull of a Truncated icosahedron of Norm={{radic|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 each Rhombicosidodecahedrons.]]

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

File:Snub_decahedron_comparing_regular_vs_quasi-regular.svg

[[File:Truncated_icosidodecahedron_comparing_regular_vs_quasi-regular_overlay_of_regular_and_quasi-regular_constructions.svg|thumb|200px|

Overlay of regular and quasi-regular truncated icosidodecahedra]]

Triakis icosahedron Hulls

File:Triakis_icosahedron_hulls.svg

600-Cell Hulls

File:E8 as H4 and H4 phi 600-Cells concentric hulls.svg

24-Cell to 600-Cell H4 Animation

File:24CellLΦ2H4Anim8.gif

600-Cell to 120-Cell Animation

File:H42JLΦAnim8.gif

T alternate of the 120-cell

File:T-120-cell with 600 vertices.png

DualSnub24Cell

File:DualSnub24Cell.png

Snub24Prime

File:Snub24Prime.png

Snub24CellPrime-hulls

File:Snub24CellPrime-hulls.png

120Cell-M

File:120Cell-M.png

Snub24Cell

File:Snub24Cell.png

File:DualSnub24Cell-2D-all-projections.svg

H4Phi-Snub24Cell-4hulls-each

File:H4Phi-Snub24Cell-4hulls-each.png

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File:A_collection_of_named_attractors.svg|A collection of named 3D chaotic attractors

File:A_collection_of_named_fractals.svg|A collection of fractals named by their generating function

File:A_collection_of_3D_fractals_named_by_their_generating_functions.png|A collection of 3D fractals named by their generating function

File:A_collection_of_fractals_named_by_their_generating_expression.svg|A collection of fractals named by their generating expression

File:A_collection_of_named_surfaces.svg|A collection of named 3D parametric surfaces

File:TrottCurveBiTangents7.svg

File:TrottCurveBiTangents28.svg

File:FanoLegendre-1024x682.jpg

File:D4HasseData.svg|D4 Hasse

File:C5_Hasse.svg|C5 Hasse

File:F4HassePoset.svg|F4 Hasse

File:E6HassePoset.svg|E6 Hasse

File:E7HassePoset.svg|E7 Hasse

File:E8HassePoset.svg|E8 Hasse

File:Stowe-Janet-Scerri PeriodicTable.svg

File:Stowe-Janet-Scerri Periodic Table.jpg

File:Periodic Table 3Ds.jpg

File:Periodic Table 2D.jpg

File:4DPeriodicTable.png

File:2D_Spherical_Harmonic_Orbitals.png

File:E8-2D.png|2D Polygons

File:E8-3D-Platonic-2.png|3D Platonic Solids

File:E8-4D-Polychora.png|4D Polychora

File:E8-5D-Polytopes.png|5D Polytopes

File:E8-6D-Polytopes.png|6D Polytopes

File:E8-7D-Polytopes.png|7D Polytopes

File:E8-8D-Polytopes.jpg|8D Polytopes

File:RhombicTricontrahedron.png|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).

File:6Cube-QuasiCrystal.png|6-cube (Hexeract) orthographically projected to 3D using the Golden ratio. This is used to understand the aperiodic icosahedral structure of Quasicrystals.

File:E8-6Cube.jpg|240 E₈ polytope vertices with 1440 6-cube (6D) unit edges and Golden ratio basis vectors orthographically projected to 3D.

File:6-cell-to-Rhombic-30-Hedron.png

File:E8-5Cube.svg|240 E8_(mathematics) vertices projected to 2D using 5-cube Petrie_polygon basis vectors

File:Ho-Mg-Zn_E8-5Cube.jpg|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.

File:5-cell-to-Rhombic-20-Hedron.png|5 cell to hull of the Rhombic 20 Hedron

File:5-cube-Phi-projection.png|5 cell in H3 projection (all vertices and edges)

File:4-cell-to-Rhombic-12-Hedron.png| 4 cell to hull of the Rhombic 2-hedron

File:4-cube-Phi-projection.png| 4 cell in H3 projection (all vertices and edges)

File:D6-to-H3-hulla.png|D6 to H3 icosadodecahedron

File:6demicube-even-dodecahedron.png| 6 Demicube (even) to dodecahedron

File:6demicube-odd-icosahedron.png|6 Demicube (odd) to icosahedron

File:E8-3Dprint-b.png|E8 in H4 projection and orthonormal to 3D to STL and 3D printed

File:4_21 E8_to_3D_H3_symmetry_concentric_hulls.png|E8 concentric hulls in H3 projection

File:3_21_E7_to_3D_H3_symmetry_concentric_hulls.png|E7 concentric hulls in H3 projection

File:1_22 E6_to_3D_H3_symmetry_concentric_hulls.png|E6 concentric hulls in H3 projection

File:6-cube_to_3D_H3_symmetry_concentric_hulls.png|6-cube to concentric hulls in H3 projection

File:Hulls_of_H4only-orthonormal.png|H4 concentric hulls in H3 projection

File:Rank3Compact1-5.svg|Rank 3 Compact Hyperbolic Dynkin Diagrams (1-5 of 238)

File:Rank3Compact6-10.svg|Rank 3 Compact Hyperbolic Dynkin Diagrams (6-10 of 238)

File:DynkDiagFinite.svg|Finite Dynkin Diagrams

File:DynkDiagAffineLooped.svg|Affine Loop Dynkin Diagrams

File:DynkDiagExtended.svg|Hyperbolic and very extended affine Dynkin Diagrams

File:DynkDiagFolded1.svg|Folding Dynkin Diagrams

File:DynkDiagFolded2.svg|Folding Dynkin Diagrams

File:DynkinE6Full.svg

File:DynkinE7Full.svg

File:DynkinE8Full.svg

File:DynkinA2Affine.svg

File:DynkinC2Affine.svg

File:DynkinG2Affine.svg

File:DynkinA3Affine.svg

File:DynkinB3Affine.svg

File:DynkinC3Affine.svg

File:DynkinA4Affine.svg

File:DynkinB4Affine.svg

File:DynkinC4Affine.svg

File:DynkinD4Affine1.svg

File:DynkinF4Affine.svg

File:DynkinA5Affine1.svg

File:DynkinB5Affine.svg

File:DynkinC5Affine.svg

File:Cell24Construction.ogvCell8+Cell16=Cell24

File:Fano_plane_for_7-D_cross_product.svg

File:FanoPlane.svg

File:SplitFanoPlane.svg

CoPrime graph

File:Coprime8.svg

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