expanding the faces

In 1910 Alicia Boole Stott published research [01] on the expansion of 2-, 3- and 4-dimensional polytopes, whose limits are equally moved away from the center (or contracted inwards) until each case, a new uniform polytope is obtained. Ball and Coxeter considered Stott’s method to obtain the achiral Archimedeans “far more elegant” [02: 137] than Kepler’s.

This webpage shows the Grasshopper definitions that I developed [03, 04] to study the expansion e2, which stands for the uniform expansion of the faces of polyhedra (e1 refers to the uniform expansion of the edges, which is dealt with here).

snubbing the cube onto the cuboctahedron

snubbing the cube onto the cuboctahedron (by vera viana)

  1. Stott, A. (1910) Geometrical deduction of semiregular from regular polytopes and space fillings. Verhan-delingen der Koninklijke Akademie van Wetenschappen te Amsterdam, 11(1) 893-2894.
  2. Ball, W., & Coxeter, H. (1987). Mathematical recreations and essays. New York: Dover Publications.
  3. Viana, V. et al. (2018) Interactive Expansion of Achiral Polyhedra. In Luigi Cocchiarella (Ed.). ICGG 2018 – Proceedings of the 18th International Conference on Geometry and Graphics. ICGG 2018. Advances in Intelligent Systems and Computing, 809. Springer. 1116-1128.
  4. Viana, V (2020). Aplicações didácticas sobre poliedros para o ensino da geometria / Didactic Applications on Polyhedra for the teaching of Geometry (http://hdl.handle.net/10348/10337) [Tese de Doutoramento, Universidade de Trás-os-Montes e Alto Douro]. Repositório Científico da UTAD.