The icosahedra of edge length 1
Date
2019-05-14Author
Brakhage, K-H
Niemeyer, AC
Plesken, W
Robertz, Daniel
Strzelczyk, A
Subject
math.GR math.GR
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Show full item recordAbstract
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.
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Publisher
Elsevier
Journal
Journal of Algebra
Volume
545
Pagination
4-26
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