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There are many ways to flatten polyhedra continuously. In this paper, we focus on the maximum number of rigid faces, as well as rigid edges, in continuous flattening motions for a given polyhedron. First, we give some lower and upper bounds of those numbers for general polyhedra, based on the results described in the literature. Moreover, we provide three folding methods that keep more edges rigid. Then, we discuss the respective numbers for each regular polyhedron.

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Maximum Numbers of Rigid Faces and Edges in Continuous Flattening of Regular Polyhedra

  • 会议论文

  • 发表日期：

    2026年

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  • Kazuki Matsubara,
  • Chie Nara

摘要

There are many ways to flatten polyhedra continuously. In this paper, we focus on the maximum number of rigid faces, as well as rigid edges, in continuous flattening motions for a given polyhedron. First, we give some lower and upper bounds of those numbers for general polyhedra, based on the results described in the literature. Moreover, we provide three folding methods that keep more edges rigid. Then, we discuss the respective numbers for each regular polyhedron.