Escape from Boxland

A library of common geometric shapes can be used to train our brains for understanding data structure in high-dimensional Euclidean space. This article describes the methods for producing cubes, spheres, simplexes, and tori in multiple dimensions. It also describes new ways to define and generate high-dimensional tori. The algorithms are described, critical code chunks are given, and a large collection of generated data are provided. These are available in the R package geozoo, and selected movies and images, are available on the GeoZoo web site (

Barret Schloerke , Hadley Wickham , Dianne Cook , Heike Hofmann

CRAN packages used

geozoo, tourr, bitops, geozoo, geozoo

CRAN Task Views implied by cited packages



Text and figures are licensed under Creative Commons Attribution CC BY 4.0. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".


For attribution, please cite this work as

Schloerke, et al., "The R Journal: Escape from Boxland", The R Journal, 2016

BibTeX citation

  author = {Schloerke, Barret and Wickham, Hadley and Cook, Dianne and Hofmann, Heike},
  title = {The R Journal: Escape from Boxland},
  journal = {The R Journal},
  year = {2016},
  note = {},
  doi = {10.32614/RJ-2016-044},
  volume = {8},
  issue = {2},
  issn = {2073-4859},
  pages = {243-257}