ToE Framework

Some of the works on this site can be custom made into personalized artwork for sale. See the “E8 Math, Science and Art” Gallery Sales at: 

Some info on my creative work is here. See also my Nature, Abstract, and Astro Photography on Flickr.
The_Isomorphism_of_3-Qubit_Hadamards_and_E8.pdf 11/20/2023. (12Mb) My latest ToE paper here,
The_Isomorphism_of_H4_and_E8.pdf 10/28/2023. (28Mb) My latest ToE paper here,
3D & 4D Solids using​ Quaternion Weyl Orbits from Coxeter-Dynkin ​Geometric Group Theory​.pdf 02/17/2023. A PowerPoint version is here, with a cloud based one here. These show code and output from my VisibLie-E8 tool generating all Platonic, Archimedean and Catalan 3D solids (including known and a few new 4D polychora from my discovery of the E8->H4 folding matrix) from quaternions given their Weyl Orbits.
ToE_Demonstration.nb Latest: 05/30/2022 (135 Mb). This is a Mathematica version 13 demonstration (or as an interactive web page) (130 Mb) takes you on an integrated visual journey from the abstract elements of hyper-dimensional geometry, algebra, particle and nuclear physics, Computational Fluid Dynamics (CFD) in Chaos Theory and Fractals, quantum relativistic cosmological N-Body simulations, and on to the atomic elements of chemistry (visualized as a 4D periodic table arranged by quantum numbers). It requires the free Mathematica CDF plugin.
ToE_Demonstration-Lite.nb Latest: 05/30/2022 (11 Mb). This is a lite version of the full Mathematica version 13 demonstration. It only loads the first 8 panes and the last UI pane which doesn’t require the larger file and load times. It requires the free Mathematica CDF plugin.
3D_Polytope_Hulls_of_E8-421-241-142.pdf 05/19/2020 (40 Mb). 3D Polytope Hulls of E8-4_21, 2_41, and 1_42
Unimodular-Rotation-of-E8-to-H4.pdf 10/19/2019 (4 Mb). A recent paper-Unimodular rotation of E8 to H4 600-cells
E8 Particle Assignment Symmetry 03/24/2015. An .html version of a .ppt (or .pps or .pdf) that explains the detail of the particle assignment symmetries contained in MyToE. A complete algorithmically assigned particle list is here.
E8toH4fold.pdf Latest: 12/19/2014. This paper presents detail on the matrix I found several years ago (as shown on the Wikipedia Quasicrystal and Rhombic Triacontahedron pages), which relates the crystallographic E8 to the non-crystallographic H4 (600 cell). It also presents various techniques for visualizing a split real even E8 representation in 2 and 3 dimensions using this E8 to H4 folding matrix. It shows its importance in the analysis of theoretical physics models and grand unified theories that are related to these structures.
Integrated E8, Binary, Octonion An .html version of a .ppt (or .pps or .pdf) (15MB) that explains the detail of the content of Fano.pdf. It outlines the relationships in the integration of E8 with Octonions, Binary, Particles, NKS, and the Periodic Table of Elements.
splitFano.pdf Latest: 12/25/2015. A 241 page pdf file (15MB) with the 480 octonion permutations with Fano planes and multiplication tables, including the split octonion. These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices. octonionG2-nonNull.pdf is a 481 page (15MB) file available that adds the G2 automorphisms for each multiplication table (including splits).
Octonion.nb A small Mathematica notebook for octonion math. It also has the ability to compare/contrast the more limited Mathematica based Quaternion logic as it applies to using the Cayley-Dickson doubling procedure for octonions.
DynkinParticleReductions.pdf Fully interactive paper discussing the potential to reduce the Standard Model to 8 elemental particles. This requires the free Mathematica CDF plugin (50Mb). If you don’t want to use CDF, here is a DynkinParticleReductions.pdf (25Mb).
ToEsummary.pdf A .pdf of the Mathematica notebook that summarizes how my ToE integrates the latest results from both the Planck spacecraft survey and the LHC Higgs discovery. It highlights minor changes to the original papers from ’98-’07 which predict an expanding (Hubble) and accelerating universe, as well as the Higgs boson.
ToE.pdf My ToE paper – full detail of a framework for a ToE based on a new look at fundamental constants, units-of-measure, and the dimensionality of time, mass, and charge. This version ToEnb.pdf. Here is the same paper above validated w/Mathematica
VisibLie_E8 vs. EPE Feature set comparison of Lisi’s Elementary Particle Explorer (EPE) and ToE_Demonstration (above, aka. VisibLie_E8, E8Viewer, or E8Flyer). This is also a good source of instruction for interacting with the main VisbLie E8 demo for pane 5- E8 Representation Theory (
E8Favorites.pdf “E8 Math, Science and Art” Gallery Exhibit. (10Mb) or on the web at E8 Art Prints. See Gallery.pdf for more “E8 Math, Science and Art” Gallery images. (6Mb)

9 thoughts on “ToE Framework”

  1. Really beautiful and complex multifaceted pictures. Generaly, simplification is the better course when defining a TOE. No matter what you may see out there the more convoluted it is the less accurate.
    If, at the bare-bones-level it doesn’t make sense and cannot be defined in a few succinct paragraphs then chances are it’s wrong.

    Michael Gary Jordan

  2. ■ Grand Unified Theory: The New Natural Perspective in the Mathematical & Scientific Unification of 4 Forces of the Universe – Bernard Rementilla.

    A New GUT Scientific & Mathematical Configuration(s) – The Riemann-Rementilla Non-Euclidean [Vector Duality Field Hyperdensity Matrix] Mathematics! – Bernard Rementilla

  3. Until Gravity is understood, matter will not be defined. Gravity is not a ‘pull’, it is a ‘push’. It is an electro-dynamic response influenced by electromagnetism. It is a by-product of matter’s reality.

  4. Hello, Gregory,
    I downloaded your Mathematica program, and used it to create a 3D model of the Gossett polytope 4 21. (E8 roots projected from 8D to 3D). Unfortunately, the data points do not seem to be correct: there are distortions. I can email you an stl file and a screen shot showing the issue. Could you please contact me at
    You can see the model here in 3D:
    Thanks, Rick R

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