2013 Fiscal Year Final Research Report
Dividing the space into congruent polyhedral regions and the Kelvin's conjecture
| Project/Area Number |
23540160
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokai University |
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Principal Investigator |
NARA Chie 東海大学, 阿蘇教養教育センター, 教授 (40147898)
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| Co-Investigator(Kenkyū-buntansha) |
ITOH Jin-ichi 熊本大学, 教育学部, 教授 (20193493)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 凸多面体 / 最小性 / 切頂八面体 / 多面体の変形可能性 / 連続的折り畳み / 空間充填立体 |
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| Research Abstract |
Divide the 3-dimensional Euclidean space into infinite regions with equal volume such that the average of surface area is minimal among such divisions. If regions are congruent each other and convex, the modified Kelvin's conjecture says that an optimal figure is a truncated octahedron. Our result says that such conclusion holds among the family of convex simple unfoldings of doubly-covered parallelopipeds. We studied in related topics such as the Hilbert's third problem on transformability among polyhedra with equal volume, and problems on continuous flattening of polyhedra, and we got many results.
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