Accidents of small $n$

big-list examples-counterexamples

You might enjoy the article The Strong Law of Small Numbers by Richard K. Guy.

He has other publications in which he partly recycles the title.


Another accident of small dimension: in all dimensions $\gt 4$, there are only three regular polytopes: the simplex, hypercube, and cross-polytope (the dual of the hypercube). In two dimensions there are infinitely many (all of the $n$-gons); in three dimensions you have two additional polyhedra, the dodecahedron and icosahedron; and in four dimensions there are three additional ones, the 120-cell and 600-cell (which are dual to each other) and the 24-cell (which is self-dual).

Related

Are there any other methods to apply to solving simultaneous equations?
Are Mersenne prime exponents always odd?
If $A$ and $B$ are matrices such that $AB^2=BA$ and $A^4=I$ then find $B^{16}$.
Reasoning that $ \sin2x=2 \sin x \cos x$
A family has three children. What is the probability that at least one of them is a boy?
Why is every answer of $5^k - 2^k$ divisible by 3?
Connecting three houses to three utilities [duplicate]
Math olympiad 1988 problem 6: canonical solution (2) without Vieta jumping
Are there intersection theoretic proofs for Ham-Sandwich type theorems?
Universal binary operation and finite fields (ring)
Rigidity of the category of fields
Examples of transcendental functions giving almost integers