Jul 27, 2013 · Formula for pentagonal numbers Ask Question Asked 12 years, 4 months ago Modified 6 years, 6 months ago

Aug 5, 2011 · While there is a lot of value to the different bijective proofs known for Euler's pentagonal theorem, perhaps the proof that's easiest to see without having to draw pictures is Euler's original idea.

A polyhedron has all its faces either pentagons or hexagons. Show that it must have at least $12$ pentagonal faces. I can show that it has exactly $12$ pentagonal faces when exactly $3$ faces meet at

Apr 30, 2020 · I agree with you. The type 8 pentagon tiling has one degree of freedom, and although you can choose it so that clusters of four tiles form a large hexagonal shape similar to that seen in …

Feb 10, 2025 · Thank you for your comment! Indeed, all convex pentagonal tilings have been mapped, and the list is believed to be complete. However, for concave pentagons, there are infinitely many …

Dec 30, 2020 · Is there a pentagonal tiling composed of only one shape of pentagon so that each pentagon touches exactly 5 other pentagons? Two pentagons are in touch if they share at least one …

Sep 11, 2023 · This is a 13-edged polyhedron that fills space. I don't yet have any solutions for 10, and it isn't clear to me if there are any (though I suspect so); a restricted question that seems interesting is …

Finding triangular numbers that are also pentagonal Ask Question Asked 8 years, 9 months ago Modified 8 years, 9 months ago

May 3, 2023 · Then he defines the pentagonal numbers as being the number $\omega (n)$ and $\omega (-n)=\frac {3n^2+n} {2}$. I don't get what $\omega (-n)$ here represents, I need help …

Jun 12, 2019 · Commonly used $10$ -sided dice are pentagonal trapezohedrons, as opposed to pentagonal bipyramids. Given that bipyramids are a more "obvious" shape for a fair die with an even …