 | Acta Crystallographica Section A Acta Crystallographica Section A FOUNDATIONS AND ADVANCES |
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![[Figure 11]](uv5024fig11mag.jpg)
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Figure 11
(a) A planar square unit-distance graph that is flexible in 2D as vertices 1 and 2 can be moved in the plane of the square to produce a unit-distance graph that is geometrically distinct from the original unit-distance graph (a rhombus rather than a square) while retaining equal edge lengths. (b) The square unit-distance graph in (a) viewed in the plane of the page. This unit-distance graph is also flexible in 3D as vertex 2 can be moved out of the plane of the square to produce a geometrically distinct unit-distance graph while retaining equal edge lengths. (c) A triangular unit-distance graph that is rigid in 2D and 3D as no vertex (or combination of vertices) can be moved to produce a geometrically distinct unit-distance graph without forcing edges to be of unequal length. (d) A unit-distance graph that is rigid in 2D but (e) flexible in 3D. (f) A tetrahedron unit-distance graph that is rigid in 2D and 3D. Dashed black lines and arrows show the movement of vertices 1 and 2 in (a) and vertex 2 in (b) and (e). |
![[Figure 11]](uv5024fig11.jpg)
| FOUNDATIONS ADVANCES |
ISSN: 2053-2733
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