Tag Archives: H4

Playing around visualizing non-crystallographic DNA/RNA

I’ve got interaction between the DNA/RNA protein visualizations (e.g. “1F8V- PARIACOTO VIRUS REVEALS A DODECAHEDRAL CAGE OF DUPLEX RNA) with the VisibLie_E8 projections of crystallographic E8 to non-crystallographic H4 (and to dodecahedral H3 in 3 dimensions, of course).

These pics are a simple (naive) merge of the D6 projected using the E8 to H4 folding matrix and the Protein DB at http://www.rcsb.org/ for 1F8V).

outE80prot

DNAscreen

outDNA

outDNAprot

E8, H4, Quasi-Crystals, Penrose Tiling, Boerdijk-Coxeter Helices and an AMS blog post on the topic

This pic is an overlay of an image from Greg Egan on the AMS blog VisualInsight on top of one I created several years ago for the quasicrystal wikipedia page.

It uses my E8-H4 folding matrix to project E8 vertices to several interesting objects. The 5 dimensional 5-cube (Penteract) and the related 3D the Rhombic-Triacontahedron, as well as this 2D overlay on the Ho-Mg-Zn electron diffraction pattern.

Ho-Mg-Zn_E8-5Cube-baez-egan-overlay

E8 vertices projected to 2D pentagonal projection
E8-5Cube

5-cube in 3D
5-cube-2

6-cube edges projected to the Rhombic-Triacontahedron using 3 of 4 rows of my E8-H4 folding matrix.
6Cube-QuasiCrystal-low

Rhombic-Triacontahedron with inner edges removed
RhombicTricontahedron

The Boerdijk-Coxeter helix is also related to these structures through the Golden Ratio.

Edges on the outer ring of the E8 Petrie projection related to Boerdijk-Coxeter helix.
helix2Db

Same as above in 3D with the tetrahedral cell faces and 3D vertex shape-color-size based on quantum particle parameters from a theoretical physics model.
cells6004b

Same as above also showing the inner E8 ring Boerdijk-Coxeter helix.
inner-outerP
Platonic solids
E8-3D-Platonic-2

Analyzing individual Fermi 4 particle "cell interactions" in 3D on Boerdijk–Coxeter helix rings

cell-interaction

inner-outerP

The Boerdijk–Coxeter helix is a 4D helix (of 3D tetrahedral cells) that makes up the vertices on 4 of the concentric rings of E8 Petrie projection (or the H4 and H4φ rings of the 2 600 cells in E8).

Outer (Ring 4) of H4 in 2D with non-physics vertices of all 8 rings of E8 in the background

helix2Db

Outer (Ring 4) of H4 in 3D with physics vertices

cells6004b

Ring 3 of H4 in 3D with physics vertices

cells6003b

Ring 2 of H4 in 3D with physics vertices

cells6002b

Inner (Ring 1) of H4φ in 3D with physics vertices

cells6001a

Combined 4 rings of H4 in 3D with physics vertices

cells6001234-small

Outer (Ring 4) of H4φ in 3D with physics vertices
cells6004phib

Ring 3 of H4φ in 3D with physics vertices

cells6003phib

Ring 2 of H4φ in 3D with physics vertices

cells6002phib

Inner (Ring 1) of H4φ in 3D with physics vertices

cells6001phib

Combined 4 rings of H4φ in 3D with physics vertices

cells6001234phi-small

Combined 8 rings in 3D with physics vertices

cells6001234-phi-small

Boerdijk–Coxeter helix

The Boerdijk–Coxeter helix is a 4D helix (of 3D tetrahedral cells) that makes up the vertices on 4 of the concentric rings of E8 Petrie projection (or the H4 and H4φ rings of the 2 600 cells in E8).

Outer (Ring 4) of H4 in 2D with non-physics vertices of all 8 rings of E8 in the background

helix2Db

inner-outerP

Outer (Ring 4) of H4 in 3D with physics vertices

cells6004b

Ring 3 of H4 in 3D with physics vertices

cells6003b

Ring 2 of H4 in 3D with physics vertices

cells6002b

Inner (Ring 1) of H4φ in 3D with physics vertices

cells6001a

Combined 4 rings of H4 in 3D with physics vertices

cells6001234-small

Outer (Ring 4) of H4φ in 3D with physics vertices
cells6004phib

Ring 3 of H4φ in 3D with physics vertices

cells6003phib

Ring 2 of H4φ in 3D with physics vertices

cells6002phib

Inner (Ring 1) of H4φ in 3D with physics vertices

cells6001phib

Combined 4 rings of H4φ in 3D with physics vertices

cells6001234phi-small

Combined 8 rings in 3D with physics vertices

cells6001234-phi-small