The icosahedra of edge length 1

2019/03/19 by Karl-Heinz Brakhage, Alice C. Niemeyer, Brakhage, Karl-Heinz +7 · 2 citations
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1903.08278

arxiv created 2019/03/19 · arxiv updated 2019/03/21

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.

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