ALLISTARSymmetric Field Physics

Allistar Center · Geometry Atlas · Study

One figure, three dimensions, then a wall

Divide a circle into five and the golden ratio appears whether you want it or not. That same ratio carries upward into three dimensions as the icosahedron, and into four as the 600-cell — the same object wearing three different dimension counts. Then it stops. There is no five-fold figure in five dimensions or above, and none will ever be found.

2D

Where the numbers come from

Every figure here is computed in the page from its definition, not drawn by hand. The 600-cell's 120 vertices are generated from the φ coordinates, its 720 edges found by distance, its 12 decagonal rings built as cosets of an order-10 quaternion subgroup, and its 30-fold shadow taken on the H4 Coxeter plane. Rotate anything; the relationships hold because they are the construction, not a rendering of one.

The five-divisioned grid follows the drawing procedure in the source framework's chapter on communication: circle, equal divisions, radii extended past the rim, a circle at each division point, then every point joined to every other point.

Continue in the Geometry Atlas

Take the 600-cell further: rotate it with the 120-cell, merge the two as one dual pair, flatten both into their thirty-fold shadows, and read every rod length needed to build them.

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