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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.02049 |
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| _version_ | 1866909766058508288 |
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| author | Honda, Atsufumi Koiso, Miyuki |
| author_facet | Honda, Atsufumi Koiso, Miyuki |
| contents | Pillow boxes are surfaces used for gift boxes, packaging, and even architectural applications. By definition, a pillow box is isometric to a double rectangle consisting of two copies of a rectangle. If the crease pattern is allowed to change, there exist continuous isometric deformations from a pillow box to a double rectangle. However, practical applications often require preserving the crease pattern. In this paper, we classify isometric deformations from a pillow box to a double rectangle among curved foldings that preserve the crease pattern. As a corollary, we prove that such an isometric deformation necessarily changes the topology of a pillow box. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isometric deformations of pillow boxes Honda, Atsufumi Koiso, Miyuki Differential Geometry Primary 53A05, Secondary 51M15 Pillow boxes are surfaces used for gift boxes, packaging, and even architectural applications. By definition, a pillow box is isometric to a double rectangle consisting of two copies of a rectangle. If the crease pattern is allowed to change, there exist continuous isometric deformations from a pillow box to a double rectangle. However, practical applications often require preserving the crease pattern. In this paper, we classify isometric deformations from a pillow box to a double rectangle among curved foldings that preserve the crease pattern. As a corollary, we prove that such an isometric deformation necessarily changes the topology of a pillow box. |
| title | Isometric deformations of pillow boxes |
| topic | Differential Geometry Primary 53A05, Secondary 51M15 |
| url | https://arxiv.org/abs/2509.02049 |