English

Representation of Geometric Objects by Color

History and Overview 2022-11-01 v1 Metric Geometry

Abstract

By introducing various actions involving color to geometrical objects, we represent a cube and simplex in four or fewer dimensions, the geometrical net of a cube and simplex in five or fewer dimensions, hyperprisms, truncated polytopes, stellated polytopes, and fractals such as Cantor dust and Menger sponge, and propose the "four-dimensional" Menger sponge whose volume is infinite.

Keywords

Cite

@article{arxiv.2210.16722,
  title  = {Representation of Geometric Objects by Color},
  author = {Yusuke Imai},
  journal= {arXiv preprint arXiv:2210.16722},
  year   = {2022}
}

Comments

38 pages, 45 figures

R2 v1 2026-06-28T04:46:54.377Z