3D cuboid: Research on spatial geometric similarity scaling in conformal mapping

Abstract

Abstract: This paper investigates the problem of self‑similar fractal proportions in three‑dimensional space and derives the unique aspect ratio (approximately 1.5874:1.2599:1) for a cuboid that satisfies the property of "shape invariance after bisecting the longest edge." Cuboids conforming to this ratio are collectively termed RFW cuboids, which are instances of the N-dimensional RFW orthotope in three‑dimensional space. We analyze five intrinsic properties of the RFW cuboid: shape‑preserving (self‑similar fractal) property, regularity, low‑loss property, aesthetics, and harmonic property. It is concluded that the RFW cuboid, as a mathematical tool for equal‑ratio cutting with shape preservation, can be applied to material cutting, jewelry processing, 3D display, acoustic design, and also to fundamental theoretical physics research such as string theory.