Skip to main content

All Questions

Filter by
Sorted by
Tagged with
25 votes
1 answer
3k views

Number of hypercube unfoldings

While writing the code for this answer, I noticed that I not only could calculate the number of unfoldings of the $4$-cube, but also the number of the $n$-cube for more values of $n$. Basically, we ...
Moritz Firsching's user avatar
6 votes
4 answers
2k views

Delaunay triangulations and convex hulls

This is a reference request. I have the impression that those who work in computational geometry are accustomed to the following. You have some locally finite set of sites in $\mathbb{R}^n$ and you ...
Michael Hardy's user avatar
3 votes
1 answer
394 views

Min Bend Orthogonal Knots

I am seeking literature on 3D orthogonal drawings of knots, especially minimum bend drawings. An orthogonal drawing employs segments parallel to the axes of a Cartesian coordinate system. A bend is a ...
Joseph O'Rourke's user avatar
5 votes
2 answers
441 views

Touching-tetrahedra graphs

Have the graphs representable by touching tetrahedra been explored? Let $\cal T$ be a collection of tetrahedra in $\mathbb{R}^3$ with pairwise disjoint interiors. Define a graph $G_{\cal T}$ to have ...
Joseph O'Rourke's user avatar
4 votes
1 answer
646 views

Combinatorial geodesics

[There has been a flaw in my definition - as Sergei and Andreas pointed out. I hope I could fix it.] I want to understand how the concepts of directions, straight (or shortest) lines, and geodesics &...
Hans-Peter Stricker's user avatar