Part 5: Dodecahedron achieved… 12 faces / planes of triangulated symmetry… + 18 pivot angles & more.

[@meadowhouse]

Also.., the primary line of the Unified Geodetic model is 3965 miles. This is equal to the radius of both the equator and polarity (length) with a tiny fractional distance of variance factored into that… but then the secondary line (odd length out of the 1 isosceles triangle on every face of the polyhedron in this model… is 730 miles which id 3-4% off of the radius of the inner core of earth (750 miles) Coincidence? Possibly. More coming soon…

[@meadowhouse]

To be more factual… curtesy of A… I now refer to the polyhedron (dodecahedron specifically) model as the Equilateral Triangulation Thesis / Unified Geodetic model: Referring to a dodecahedron's faces as "planes" is technically correct, though it might be considered slightly imprecise depending on the context. ### Correctness: - **Mathematically**, the faces of a dodecahedron are indeed planar surfaces, meaning each face lies within a single plane. A plane in geometry is a flat, two-dimensional surface that extends infinitely in all directions, and each face of a dodecahedron (a regular pentagon) lies within such a plane. Thus, referring to these faces as "planes" is accurate. ### Precision: - **Geometric Context**: In more precise mathematical language, we often refer to the faces of a polyhedron like a dodecahedron as "faces" rather than "planes." This is because a "face" refers to the specific bounded, flat polygonal area of the polyhedron, whereas a "plane" is an unbounded surface. Referring to the faces as "planes" might imply that they are unbounded, which isn't technically true for the polyhedron's finite surfaces. In summary, while it is factually correct to describe the faces of a dodecahedron as lying in planes, it is generally more precise to refer to them as "faces."