Apple-Peel Fold-Outs of Four-Dimensional Polytope {3,4,3} and Its CG Image Generation

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  • KIMURA Yuta
    National Institute of Technology, Sendai College, Hirose Campus
  • KAINO Keimei
    National Institute of Technology, Sendai College, Hirose Campus
  • OKUMURA Toshiaki
    National Institute of Technology, Sendai College, Hirose Campus

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Other Title
  • ４次元正24胞体のリンゴの皮むき展開図とCG表現

Description

Regular polyhedron is regarded as an approximate figure of a sphere. Apple-peel fold-out (AF) nets of regular polyhedra have symmetric S-shaped figures and the net of a sphere a symmetric S-shaped spiral half of which consist of Archimedes' spiral and the lituus. There are six regular polytopes in the four-dimensional (4-D) space. AF nets of regular polytopes, regular 4-cube, 16-cell are obtained by using their axonometric projection diagrams. From this fact, two types of AF nets of 24-cell are shown to consist of 3-D spirals on both ends and central nets of S-shaped figure on a 2-D plane derived from their axonometric projection diagrams. These AF nets will give us a good algorithm to obtain AF nets of 120-cell and 600-cell.

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