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I can confirm j.c.'s list of 6-tuples of integers less than or equal to 7 which are edge lengths of tetrahedra -- up to the tuple (6,6,6,5,3,2), for which I obtain a negative Cayley-Menger determinant …

Question: Given three positive integers $a$, $b$ and $c$ such that the sum of any two of them is bigger than the third, how difficult is it algorithmically to determine the kissing number of triangle …

There are indeed other such polygons. -- For example there is one for $n = 11$, as follows (the origin is in the lower left corner): Also there is one for $n = 15$: Further there are $21$ such p …

Let $n$ be a positive integer, and let $n = \ell_1 + \dots + \ell_k$ be a partition of $n$. Then there exists a convex polygon with side lengths $\ell_1, \dots, \ell_k$ if and only if all of the $\ell …

Let $d$ be a positive integer, and let $\mathbb{R}^d$ be endowed with the Euclidean metric. Given an infinite set $S \subset \mathbb{R}^d$ without limit points and a positive integer $n$, is there alw …

Is there a set $P \subset \mathbb{R}^2$ of points in the Euclidean plane whose intersection with every convex subset of $\mathbb{R}^2$ of area $1$ is nonempty but finite? If the answer is yes, can $P …