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41 votes
2 answers
2k views

Can we find lattice polyhedra with faces of area 1,2,3,...?

I asked this question two months ago on MSE, where it earned the rare Tumbleweed badge for garnering zero votes, zero answers, and 25 views over 61 days. Perhaps justifiably so! Here I repeat it with ...
2 votes
0 answers
100 views

Sequence of numbers related to line-segment intersections

Question: what is known about the sequence $\mathbb{X}\subset \mathbb{N}_0$ such that for each $k\in \mathbb{X}$ there exists a set of $n$ points in general position in the Euclidean plane such that ...
1 vote
0 answers
67 views

Counting pieces when an object is cut n ways

I was reading a passage from an old essay by Martin Gardner on the calculus of finite differences, and it seems to me that there is more that can and should be said about seemingly anomalous values of ...
4 votes
0 answers
206 views

Generating a Penrose tessellation around a given tile

Given a starting Penrose tile, I need to build a "spiraling" tessellation around it. The following picture illustrates the request: In this example, the starting tile is a "thin rhombus" (the pink ...
7 votes
2 answers
964 views

Maximal number of edges and triangular cells for n points in a triangular lattice

Consider a subset of $n$ points in an equilateral triangular lattice. Draw all the edges between nearest-neighbor points. What is the maximum, over all such subsets, of the number of edges? This ...