Let $P$ be a regular $n$-gon, and erect on each edge toward the inside a regular $k$-gon, with edge lengths matching. See the example below for $n=12$ and $k=3,\ldots,11$. Two ...
I'm having trouble putting this into a fully coherent question, so I'll give the broad question, then a few bullet points to give you a better idea of what I'm asking. I'm looking for a line of ...
Definition: A $n$-gon is simple if it has no self intersection and is in general position if no pair of its edges are parallel. It is clear that by extending the edges of each simple $n$-gon in ...
What interesting properties of convex sets are retained by star-convex sets?
I remember seeing something like the following problem in the past and would like to know if it has a solution (or if I can find a source for it). Problem Given a finite set of points in the plane in ...
I am seeking a listing of the distinct Hamiltonian cycles following the edges of the icosahedron and the dodecahedron. By distinct I mean they are not congruent by some symmetry of the icosahedron or ...