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Hexeract - 6D Cube (Skeleton Structure)

Type: Image (jpg)

Submitter: [anonymous]

Category: Nature

Exhibition Date: 2018-05-11 11:17:29 MST

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Submitter's Comment
A related projection of a 6D 6-Cube (Hexeract) into a perspective 3D object using the Golden Ratio [Phi]. This particular projection is used to understand the structure of QuasiCrystals. The specific basis vectors are:
x = {1, [Phi], 0, -1, [Phi], 0}
y = {[Phi], 0, 1, [Phi], 0, -1}
z = {0, 1, [Phi], 0, -1, [Phi]}
There are 64 vertices and 192 unit length edges forming pentagonal symmetry along specific axis (as well as hexagonal symmetries on other axis).

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

It has Schläfli symbol {4,34}, being composed of 3 5-cubes around each 4-face. It can be called a hexeract, a portmanteau of tesseract (the 4-cube) with hex for six (dimensions) in Greek. It can also be called a regular dodeca-6-tope or dodecapeton, being a 6-dimensional polytope constructed from 12 regular facets.

Keywords: Sacred Geometry Shape Dodeca-6-Tope Dodecapeton 6 Dimensional Polytope Constructed 12 Regular Facets

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