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Results tagged with rigidity
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user 108884
13
votes
0
answers
358
views
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
5
votes
3
answers
675
views
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