The Dehn invariants of the Bricard octahedra

2009/01/20 by Victor Alexandrov · 12 citations
Computer Science · Mathematics · #Combinatorics #Computer science #Conjecture #Constant (computer programming) #Crystallography #Dehn surgery #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics #Octahedron #Polyhedron #Pure mathematics #math.MG #msc:52C25 #semigroups and automata theory

paper · pdf · doi:10.1007/s00022-011-0061-7

published in Journal of Geometry 99(1-2), 1-13 (Birkhäuser) · 13 pages, 10 figures

arxiv created 2009/01/20 · openalex publication_date 2010/12/01 · arxiv updated 2011/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.

Citations

• The Algebra of Polyhedra and the Dehn-Sydler Theorem.
• Conditions nécessaires et suffisantes pour l’équivalence des polyèdres de l’espace euclidien à trois dimensions
• On Hilbert’s third problem

Cited by

• Flexible suspensions with a hexagonal equator
• The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in \mathbb R^d does not always remain unaltered during the flex
• Dehn invariant [wikipedia]
• Flexible polyhedron [wikipedia]
• Polyhedron [wikipedia]

Related

• Flexible suspensions with a hexagonal equator
• Extending Bricard Octahedra
• Flexible Polyhedra and Their Volumes
• Metric description of flexible octahedra
• On Flexible Prismatic Polyhedra