Jul 27, 2013 · Formula for pentagonal numbers Ask Question Asked 12 years, 6 months ago Modified 6 years, 8 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.

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 …

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

Finding triangular numbers that are also pentagonal Ask Question Asked 8 years, 11 months ago Modified 8 years, 11 months ago

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 …

Aug 26, 2015 · Pentagonal Numbers Ask Question Asked 10 years, 5 months ago Modified 10 years, 5 months ago

Aug 3, 2025 · But if you raise the center point (turning it into a pentagonal pyramid), it gets closer to having all triangular faces equilateral. How tall does it need to be so that every triangular face is …

Mar 13, 2025 · I am a high school student, and while learning about figurate numbers, I came up with a relationship between pentagonal numbers, square numbers, and triangular numbers. I’m wondering …

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 …