| Up | Japanese | Symmetry |
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| 2 dim Space ("Plane") |
3 dim Space ("Space") |
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| Symmetrical position of two points (Hyperplane-symmetry) |
Point-, Line-Symmetry | Point-, Line-, Plane-Symmetry | |
| Symmetrical position of two subsets (Hyperplane-symmetry) |
Point-, Line-Symmetry | Point-, Line-, Plane-Symmetry | |
| Symmetrical figures |
Hyperplane-symmetry | Point-, Line-Symmetrical | Point-, Line-, Plane-Symmetrical |
| Rotationally symmetcal | ♦ | ♦ | |
| Implication of symmetric figures | ♦ | ♦ | |
| Symmetry of primary figures | An Essential Classification of Polygons | | |