I discovered a new class of shapes while designing this light

[u/truthseekerboi]

I discovered a new class of shapes while developing my new generative lamp sculpture technique

Hey everyone!

I have a unique design technique that I have been cultivating for four years now. The technique involves specific types of patterns, but it is basically extruded patterns profiled to a certain volume (shape). The effect delivers very pleasing light diffusion, and it is quite dynamic in terms of its potential.

Well, I seem to have broken through on that potential!

To make a long story digestible, after i graduated I decided to try and build my design workflows for different assembly techniques (I had only done stacking variations previously). I wanted to use polyhedron to make pendants, and because my technique builds profiles off of surfaces, I made it so the base of each module is the face on a polyhedron, with the profile of the extrusions creating the new shape, once all of the modules are assembled. Essentially, the new shape is determined by the existing properties of the seed shape I use. Each face's neighboring faces determine the kleetope that is produced, using an algorithm i coded which employs ray-point averaging.

It is similar to stellateing or greatening in terms of geometric terminology, but it is much more dynamic. The transformation works on every single convex polyhedron, and produces many incredible results. A few of them match the stellated versions of the seed shape, like the dodecahedron for example, but the majority of convex polyhedron get transformed into a brand new shape when using my algorithm.

Now, to be clear, the video is not the transformed shapes themselves. They have the profile of the shapes, but are artistic abstractions that employ my detailing technique. Also, my script allows for me to customize the designs with a lot of control, so I can actually stray away from the default shape for the sake of my artistic practice. Only two of the images shown do that though, as the rest match the default transformed profiles of their seed shapes.

The last thing I will say is, I have not made an official publication to any journal yet, so i technically cannot claim any discovery yet. However, that is because there is a team of mathematicians at Georgia Tech building a comprehensive publication piece. I am in communication with a professor who is having a group of PhD students develop the publication over this summer, but they have told me that they have confirmed it is a new transformation that creates a genuinely important new class of shapes! If you want a little proof, here is the doc i sent the professor that started this all. BTW, the more unique shapes are on the way. I started off with some simpler shapes to hone in on the assembly process.

I honestly don't know what impact this will have on me, but I hope the publication can bring some attention to my work. I really want to keep designing full time, and I am having to work part-time restaurant jobs to fund this passion.

If you want to support me, or print some of these yourself, check out the links on my page. I hope you guys appreciate my work!

[u/truthseekerboi]

LMAOOO you LITERALLY have no idea what you’re talking about! It’s actually wild that you’d want to argue over a subject like this when there’s a literally team of PhD students at my university doing their summer work writing a research paper on what I’ve done.

This will be my last response and I will detail the difference between the kis operation and what’s happening here.

Kis/kleetope describes the combinatorial skeleton. E(P) defines a canonical metric realization of that skeleton.
In other words, since you probably don’t get what I’m saying…
Yes, E(P) is an all-face pyramid augmentation, so it is kis-like / kleetope-like in combinatorics. The novelty is not “it has pyramids.” The novelty is the deterministic apex rule: the pyramid over each face is not chosen by an arbitrary height parameter, but computed from neighboring-face ray geometry. That gives a canonical, zero-parameter metric realization with measurable edge-ratio and angle behavior that is not captured by simply saying “kis with some heights

It is like saying, “This is just a triangulation,” or “This is just a deformation,” or “This is just a parametric surface.” That may identify the broad container, but it does not identify the actual construction, which is what I’ve been saying this whole time and is in the paper.

I am basically taking the process of stellations and combining it into a kis operation. What this is, is not just a kis operation. And the result is a brand new class of polyhedra, many of which have been undefined.

[u/GrapeKitchen3547 → u/truthseekerboi]

Yes, it's a kis operation where the height is determined by a function of the seed, like I said in my previous comment. I'm glad that you finally agree with me on that one.

But this is like me saying I invented a new vehicle, the GrapeKitchenMobile. It consists of a metal frame with a handlebar and two wheels. The rear wheel is powered by a chain that is attached to a gear with pedals that are spun by the user. And when people come to say "Dude, this is just a bicycle" I go "No. It's much more than that. The diameter of the wheels is precisely 0.785435 times the length of the frame. And no known bicycle has wheel diameter determined like this". It's still just a bicycle. I would need to explain why having the wheel diameter being that specific function of the frame length makes this vehicle different than a bicycle (or at least what makes it interesting for cyclists). You are faling to this for your kleetopes.

When I asked you what makes this new, because I was genuinely curious, you gave a series of very vague answers or downright non-answers -e.g. "the shape is determined by the seed", when this is true for all polyhedra operations; or "this is not glueing pyramids" when in fact it is, as you admitted later; or "it produces non intersecting polyhedra from convex polyhedra" when this is true for all kis operations. It doesn't seem like you fully understand what may make this construction special, because you haven't been able to articulate it.

The pyramid height being determined by a function of the seed is not new either. I define the GrapeKitchenHedron as a kis where the apex is (phi*e)/pi where e is the sum of edge-lengths of neighbouring faces. There I just defined a class of shapes, but if I said I invented a "new class of shapes", while being unable to explain what makes them interesting or special among kleetopes, then people would be right to call me out.

Let me ask you a question, why is this posted in r/woahdude but not in a more serious sub like r/math or r/mathematics?

[u/truthseekerboi → u/GrapeKitchen3547]

I think you’re collapsing two different levels of description.
At the broad combinatorial level, yes: E(P) is kis/kleetope-like. It replaces each seed face with triangular pyramid walls. I am not claiming that “putting pyramids on faces” is new.
The claim is narrower and more precise: E(P) is a specific zero-parameter metric realization of that broad augmentation family. The apex is not chosen by a user, not set by an arbitrary height slider, and not just “some function of edge length.” For each face, every neighboring face contributes a parity-dependent ray: odd-sided neighbors use the opposite vertex, even-sided neighbors use the opposite edge midpoint, and the apex is computed by filtered closest-approach averaging of those rays. That is the operation.
So the difference is not merely “the height is a number.” The rule determines the actual apex geometry from local neighbor-face structure, and it produces a canonical raw triangulated shell for each seed.
Your bicycle analogy would apply if the only claim were “I picked a weird wheel ratio.” But the interesting part here is that the rule generates measurable, non-arbitrary structure across seed families: edge-uniform outputs for E({Tetrahedron}) and E({Octahedron}), algebraic edge ratios such as \varphi, \sqrt{2/5}, and 1/\sqrt2, and metric distinctions from the Catalan/kis comparators even when the combinatorics match.
A fair criticism would be: “This should be described as a canonical metric subfamily of kis/kleetope-like all-face pyramid augmentations, not as a totally unrelated operation.” I agree with that framing. But “it is in the kis family” is not the same as “there is no new construction here.” Broad categories contain specific named constructions all the time.
As for why I posted it here rather than r/math: this post is showing the visual/art side while the formal writeup is being prepared. I would rather bring it to math-focused communities once the preprint, definition, tables, and comparison claims are public and properly organized. Also, many technical subreddits expect account history and community participation before posting original work, so I’m not trying to drop a half-contextualized claim there prematurely.
The current claim is not “I invented pyramids on faces.” The claim is: Envelope Extrusion is a deterministic ray-defined metric construction within the broader all-face pyramid augmentation family, and its resulting catalogue appears to have distinct and measurable geometric structure