Trinity Basics — Geometry Museum

Fundamentals

Triangle

Atomic

The fundamental unit. Three points define a plane, creating the atomic building block of the Trinity system.

3 vertices equilateral △

Hexagon

Composite

Six triangles united around a center. The most efficient shape for tessellation — nature's choice for honeycombs.

6 triangles tessellation ⬡

Diamond

Dual

Two triangles mirrored. A rhombus formed by joining up and down orientations along their base.

2 triangles mirror ◇

Triforce

Recursive

Four triangles in perfect hierarchy. One center void defined by three surrounding solids.

3+1 triangles hierarchy △△△

True OEG

Only three regular polygons tile the plane. 6 × 60° = 360° (triangle). 4 × 90° = 360° (square). 3 × 120° = 360° (hexagon). The ancient Greeks proved it — crystallography confirmed it.

IVM

60°

Isotropic Vector Matrix — the triangle grid. 6 × 60° at every vertex. Nature's preferred lattice.

6 × 60° isotropic △▽

Simple Cubic

90°

4 × 90° at every vertex. Pure horizontal and vertical lines — simple, but nature rejects it. No crystal prefers the cubic grid.

4 × 90° orthogonal □

Hexagonal

120°

3 × 120° at every vertex. Six triangles per hex, zero gaps — the omniequivalent honeycomb.

3 × 120° honeycomb ⬡⬡

The Unchosen Palette

Beyond command and control

The 369-Dichte constraint — only hex digits 3, 6, 9. Sacred geometry encoded in color.

Mittel

#3369B6

Hell

#3696E9

Steel

#336699

Dunkel

#163996

Trinity

Three points define a plane