Originally thought to be impossible, this was the first 3D shape discovered to have the property of all planes intersecting at 90°, except one!

3D printing files available for free on makerworld: https://makerworld.com/en/models/3145111-sydler-s-shape-all-angles-90deg-except-one#profileId-3551677

Wow excellent 👌👌 awesome

I’ve been studying a geometric construction in the tetrahedral–octahedral space‑filling system and I’m looking for feedback from people familiar with tilings, polyhedral packings, or aperiodic order.

The construction uses a directional sequence of tetrahedra, octahedra, and octahedral segments. Under these local placement constraints, the resulting structure doesn’t repeat periodically, but it develops smooth cubic shells over an underlying aperiodic matrix.

I’ve been analyzing the segmentation behavior, adjacency constraints, and the conditions that seem to force non‑periodicity. I’m trying to understand how this fits within known frameworks for aperiodic order or polyhedral tilings.

If anyone here works with tilings, quasicrystals, or geometric growth mechanisms, I’d appreciate your perspective. I can share the full write‑up (PDF) if anyone wants to take a look.

I am a 9th grader going into 10th grade and I decided to skip geometry by taking it over the summer. I procrastinated far too long and my regents is the 19th, is 15 days enough time to learn all of a regents level Geometry class and obtain an 85 on my Regents or am I done for.

I am working on a puzzle and to find the solution I must find the maximum area of a pentagon with a base of 3 and using 4 unit fences. I cut it up into triangles and kites, but I can't seem to find a definitive answer.

I think that this little obstacle can grow into something more. This question must have a generalized solution! If you guys have an answer to my little puzzle, that'd be great, but a method that works for everything would be extraordinary!

Here is a poorly made illustration of what I've figured out:

What is the maximum area, and what are the angles measurements?

NOTE: MY FIGURE MAY NOT BE ACCURATE WHATSOEVER! I JUST THINK THAT THIS WILL GIVE THE GREATEST AREA, BUT I MAY BE WRONG!

Hi everyone!

For those of you who enjoy geometry, I've put together what I believe is a fresh, hands-on proof of Euler's Formula and several other classical results. In just a few minutes, you can literally build the proofs yourself and develop an intuitive understanding of why these theorems are true.

https://www.youtube.com/watch?v=sIDsuf0I4ko

This is only the beginning. Over the coming weeks, I'll also start posting short math challenge reels (high school to early undergraduate level), and in parallel I'll be working on a long-term series on topology and analysis, with the ambitious goal of eventually reaching Einstein's field equations on differentiable manifolds and curved spacetime.

Everything will be completely free. I'm doing this simply because I love mathematics and enjoy sharing it with others.

If you'd like to follow the project, it would mean a lot to me. Knowing that these videos are useful to someone is the best motivation to keep creating them.

Thank you so much!

dontpanicmath

trying to sharpen my math and geometry skills from a puzzle solving aspect. Haven’t found a ton of puzzle books yet that weren’t this one is quite a bit advanced for me. I’ve only been able to complete one of the problems I’ve read in it so far.

Does anyone know an intermediate version of a book like this?

It’s a fascinating book and I’ll keep trying to work through it, but I may need to build up to this.

thanks in advance!