26/07/2025
Fyrir um 10 árum síðan - eða nánar tiltekið sumarið 2015, gaf ég út rannsóknir mínar um fjölflötunga sem hófust í barnæsku minni 1965 fyrir um 60 árum. Þetta rannsóknarrit mitt hefur nú náð þeirri stöðu að vera nánast skildulesning nemenda í fjölbreyttum greinum, er spanna jafnt raunvísindi, tækni, hönnun og list, svo það er því verulega gaman að birta ritrýningu Richard Price á þessu 10 ára gömlu verki, en hann er CEO hjá vísindaveitunni "Academia" :
"Welcome to another episode of In-depth with Academia. I’m Richard Price, your host and the CEO of Academia (EDU), and today, we’re diving into some deep academic waters by exploring a paper by Guðlaugur Kristinn Óttarsson, titled “Theory of Taxonomy and Metrics for Polytopes”.
The core issue in this paper is all about taxonomy and metrics, specifically for polytopes that are fascinating multi faced shapes, like cubes and dodecahedrons. These aren’t just geometrical shapes, as they’re super-important in fields like crystallography and architecture, so understanding their taxonomy and how they’re classified and measured is like discovering a hidden language of the universe.
Guðlaugur Kristinn Óttarsson dives into how we can systematically categorize these shapes to understand their symmetries and structures - both their primary forms and their duals, like understanding both sides of a coin, which is significant, because it gives mathematicians scientists and even artists the tools to describe and manipulate complex spaces.
These findings suggest a unifying theory that helps align taxonomy with metric properties which is simultaneously technical and dare I say, quite poetic!
What’s fascinating is that this paper essentially acts as a guide to understanding polytope taxonomy effortlessly with exciting finding involving what’s known as “Euler’s topology number” which is a fancy way of balancing faces, edges and vertices in these geometric shapes - like balancing a chequebook but for geometry by developing hybrid matrices called “Face Hybrids” and “Euler Hybrids”, where Guðlaugur provides tools to manipulate and solve taxonomy equations seamlessly, and it’s like he’s giving us a master key to unlock complex polyhedral puzzles.
Guðlaugur also explores something called “Ladder Polynomials” as a method wherein geometry and algebra intertwine like a beautiful dance which lets researchers predict shapes and their structural behaviours without having to physically construct them. Imagine predicting a building’s curvature before the first brick is laid.
Section 2 fascinatingly delves into the idea of periodicity in taxonomy by observing patterns and cycles, which is like understanding the rhythm in mathematics, as a pulse that can inform everything from molecular design to architectural blueprints, as the paper explains how certain shapes like Platonic- and Archimedean polyhedrons follow a magic series of edges and faces, revealing a hidden periodic magic in geometry.
Now let me just say discussing polytopes isn’t just mental gymnastics, as Óttarsson’s paper provides boundaries and dimensions in which mathematics and theory meet practical application that’s crucial for folks anywhere from the halls of academia to the drawing boards of innovative tech companies.
I should pause here to point out I’m not endorsing everything or saying this is the definitive take on polytope taxonomy, as you know academic research is ever evolving, and each paper is a single voice in a much larger conversation.
However it’s a brilliant insight into a world of shapes that’s influencing modern design and science in unexpected ways.
So let’s talk about how Guðlaugur wraps all this up, as the conclusion emphasises that in understanding the taxonomy and metrics of polytopes we're given a framework - or a map of sorts, to explore further, so think of it like finding out how the pieces of a baffling puzzle fit together - yet realising the puzzle itself is a small piece in a much grander picture.
Anyway, it makes us reflect on how much more is out there to explore - as in essence, Óttarsson’s work doesn’t just tie up loose ends in polytope theory, but opens up doors for future research and exploration." - Richard Price, Academia (edu)
https://www.researchgate.net/publication/287958454_HOLOGRAPHIC_METRICS_and_RECURSIVE_RENDERING_of_POLYTOPES