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Results tagged with rigidity
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user 108884
5
votes
3
answers
675
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Alexandrov's generalization of Cauchy's rigidity theorem
Alexandrov generalized Cauchy's rigidity theorem for polyhedra to higher dimensions.
The relevant statement in the article is not linked to any source. …
- 13.6k
13
votes
0
answers
358
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Is a convex polyhedron determined by its edge lengths and angular defects?
Let's consider 3-dimensional convex polyhedra $P\subset\Bbb R^3$.
The angular defect at a vertex $v$ is $2\pi$ minus the sum of the interior angles of the incident faces at $v$.
Question:
Is a conve …
- 13.6k
20
votes
0
answers
423
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Is the dodecahedron flexible (as a polytope with fixed edge-lengths)?
Consider the (regular) dodecahedron $D\subset\Bbb R^3$. I want to continuously deform it so that throughout the deformation
it stays a convex polytope,
it stays a combinatorial dodecahedron (i.e. its …
- 13.6k
11
votes
1
answer
614
views
How to correctly state Cauchy's rigidity theorem?
Cauchy's rigidity theorem is often stated briefly as
Any two (convex, 3-dimensional) polyhedra with pairwise congruent faces are themselves congruent. … To deal with this contradiction in my knowledge, I looked up the common proofs of Cauchy's rigidity theorem for polyhedra. …
- 13.6k