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Results tagged with polyhedra
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user 39495
40
votes
Accepted
Which unfoldings of the hypercube tile 3-space: How to check for isometric space-fillers?
Answer to Q1: All of the 261.
I looked at this question because of a video of Matt Parker and wrote an algorithm to find solutions. See here for an example of how a solution would look like. I dumped …
- 10.7k
19
votes
On maximal regular polyhedra inscribed in a regular polyhedron
The same optimization ansatz will also work in other dimensions and even for non-regular polyhedra. …
- 10.7k
15
votes
3D models of the unfoldings of the hypercube?
I used sage to make a 3d animation of all 261 unfoldings.
Here is a screenshot of the first few:
The file cube-unfoldings.txt contains all the unfoldings, each line contains a list of 8 points.
…
- 10.7k
11
votes
Accepted
The $32$-deg polynomial for the tetrahedron inscribed in the icosahedron?
I guess it would be difficult to prove that the answero your question is "no", since proving that "no a priori reason exists" might be hard.
More modestly, I can say that I don't really know a good r …
- 10.7k
9
votes
Put P inside Q! polygons/polyhedra
To make sense of this question one has to say first what you mean by "copy of $P$".
For example one could image to allow translations, rigid motions and/or dilations.
The answer also depends on how t …
- 10.7k
6
votes
Convex polyhedra, combinatorial types and Symmetry
Yes, this is true for all polyhedral graphs. See the following reference:
P. Mani, Automorphismen von polyedrischen Graphen, Mathematische Annalen Volume 192, Issue 4, pp 279-303, August 1971
My tran …
- 10.7k