Abstract
Retaining the combinatorial Euclidean structure of a regular icosahedron, namely the 20 equiangular (planar) triangles, the 30 edges of length 1, and the 12 different vertices together with the incidence structure, we investigate variations of the regular icosahedron admitting self-intersections of faces. We determine all rigid equivalence classes of these icosahedra with non-trivial automorphism group and find one curve of flexible icosahedra. Visualisations and explicit data for this paper are available under http://algebra.data.rwth-aachen.de/Icosahedra/visualplusdata.html.
DOI
10.1016/j.jalgebra.2019.04.028
Publication Date
2019-05-14
Publication Title
Journal of Algebra
Publisher
Elsevier
ISSN
0021-8693
Embargo Period
2024-11-22
Additional Links
http://arxiv.org/abs/1903.08278v1
Keywords
math.GR, math.GR
Recommended Citation
Brakhage, K., Niemeyer, A., Plesken, W., Robertz, D., & Strzelczyk, A. (2019) 'The icosahedra of edge length 1', Journal of Algebra, . Elsevier: Available at: https://doi.org/10.1016/j.jalgebra.2019.04.028
