Jul 27, 2013 · Formula for pentagonal numbers Ask Question Asked 12 years, 4 months ago Modified 6 years, 5 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 …

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 $3$ …

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 …

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 …

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 …

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 …

Sep 1, 2019 · The recursive formula for generalized pentagonal numbers characteristic function Ask Question Asked 6 years ago Modified 4 years, 9 months ago

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

Sep 17, 2023 · What must be the angles for this kite to be used for my polyhedron? Indicate if you're answering for a pentagonal or heptagonal trapezoihedron 2.- Now let's think I have the …