Polytope is our data-access system for extracting specific features directly from large datasets. It can substantially reduce transfer volumes & simplify workflows, changing the user experience.
https://www.ecmwf.int/en/about/media-centre/focus/2026/polytope-making-access-weather-and-climate-data
https://www.ecmwf.int/en/about/media-centre/focus/2026/polytope-making-access-weather-and-climate-data
September 27, 2026 at 7:00 AM
Polytope is our data-access system for extracting specific features directly from large datasets. It can substantially reduce transfer volumes & simplify workflows, changing the user experience.
https://www.ecmwf.int/en/about/media-centre/focus/2026/polytope-making-access-weather-and-climate-data
https://www.ecmwf.int/en/about/media-centre/focus/2026/polytope-making-access-weather-and-climate-data
Quaternionic Polytope, Priest of the Eightfold Path, ya-Tsatsa
November 9, 2023 at 6:41 AM
Quaternionic Polytope, Priest of the Eightfold Path, ya-Tsatsa
Ok, I will wait. Whilst I do not admire the musicality of Polytope de Cluny so far, it must be noted that at 24:26 in duration it does offer excellent value for money at 99p for the, audiophiles favourite, .m4a on iTunes
September 25, 2026 at 6:32 PM
Ok, I will wait. Whilst I do not admire the musicality of Polytope de Cluny so far, it must be noted that at 24:26 in duration it does offer excellent value for money at 99p for the, audiophiles favourite, .m4a on iTunes
Jon Lee
Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
https://arxiv.org/abs/2609.25981
Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
https://arxiv.org/abs/2609.25981
September 23, 2026 at 1:23 PM
Jon Lee
Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
https://arxiv.org/abs/2609.25981
Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
https://arxiv.org/abs/2609.25981
Happy to see the new #DestinE simulations out in the open!
I’d strongly recommend trying the new Jupyter example notebooks, including lazy browsing: github.com/destination-...
Looking forward to seeing what people will build and discover with this next generation of #ClimateDT simulations!
I’d strongly recommend trying the new Jupyter example notebooks, including lazy browsing: github.com/destination-...
Looking forward to seeing what people will build and discover with this next generation of #ClimateDT simulations!
May 19, 2026 at 5:45 AM
Happy to see the new #DestinE simulations out in the open!
I’d strongly recommend trying the new Jupyter example notebooks, including lazy browsing: github.com/destination-...
Looking forward to seeing what people will build and discover with this next generation of #ClimateDT simulations!
I’d strongly recommend trying the new Jupyter example notebooks, including lazy browsing: github.com/destination-...
Looking forward to seeing what people will build and discover with this next generation of #ClimateDT simulations!
Mathematicians trying to invent a relationship status: imagine a polytope
May 15, 2026 at 3:56 AM
Mathematicians trying to invent a relationship status: imagine a polytope
this has fun consequences for issues where policy positions are represented as booleans or integers. if you inscribe a hypersphere-approximating gaussian inside a high-dimensional polytope almost all the probability mass will be in the corners; almost none will be inside the hypersphere.
hypercubes are pointier than you’d expect
October 20, 2025 at 10:18 PM
this has fun consequences for issues where policy positions are represented as booleans or integers. if you inscribe a hypersphere-approximating gaussian inside a high-dimensional polytope almost all the probability mass will be in the corners; almost none will be inside the hypersphere.
Excited to share our preprint: Polytope, an epitope barcoding system, generating up to 512 unique color codes for in vivo lineage tracing. 🌈🧬 This tech enables spatial fate-mapping with unprecedented clonal and spatial resolution! doi.org/10.1101/2024... #SpatialBiology #LineageTracing #Polytope
Polytope: High-resolution epitope barcoding for in vivo spatial fate-mapping
Tracing the fate of individual cells and their progeny remains a challenging task. While imaging-based fate-mapping provides spatial information, it generally lacks complexity due to limited label div...
doi.org
December 3, 2024 at 9:41 AM
Excited to share our preprint: Polytope, an epitope barcoding system, generating up to 512 unique color codes for in vivo lineage tracing. 🌈🧬 This tech enables spatial fate-mapping with unprecedented clonal and spatial resolution! doi.org/10.1101/2024... #SpatialBiology #LineageTracing #Polytope
📚 New Arxiv Paper
Title: Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
Authors: Jon Lee
Read more: https://arxiv.org/abs/2609.25981
Title: Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
Authors: Jon Lee
Read more: https://arxiv.org/abs/2609.25981
September 23, 2026 at 8:02 AM
📚 New Arxiv Paper
Title: Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
Authors: Jon Lee
Read more: https://arxiv.org/abs/2609.25981
Title: Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
Authors: Jon Lee
Read more: https://arxiv.org/abs/2609.25981
One formula to rule them all!
P(d, F) = 4d / ((d+1) F)
In d-dimensional space, d≥2, given a regular polytope with F faces that come in opposite pairs, if you pick two points at random from the interior of the polytope and draw the line that contains them …
P(d, F) = 4d / ((d+1) F)
In d-dimensional space, d≥2, given a regular polytope with F faces that come in opposite pairs, if you pick two points at random from the interior of the polytope and draw the line that contains them …
August 26, 2025 at 3:31 AM
One formula to rule them all!
P(d, F) = 4d / ((d+1) F)
In d-dimensional space, d≥2, given a regular polytope with F faces that come in opposite pairs, if you pick two points at random from the interior of the polytope and draw the line that contains them …
P(d, F) = 4d / ((d+1) F)
In d-dimensional space, d≥2, given a regular polytope with F faces that come in opposite pairs, if you pick two points at random from the interior of the polytope and draw the line that contains them …
6-dimensional polytope ✌️👍✅🙋♂️
December 28, 2024 at 12:17 PM
6-dimensional polytope ✌️👍✅🙋♂️
Attention mathematicians!!
Here is a beautiful 3D visualisation by ChatGPT of a 10-dimensional polytope 🤩🙋♂️
Here is a beautiful 3D visualisation by ChatGPT of a 10-dimensional polytope 🤩🙋♂️
December 26, 2024 at 12:07 PM
Attention mathematicians!!
Here is a beautiful 3D visualisation by ChatGPT of a 10-dimensional polytope 🤩🙋♂️
Here is a beautiful 3D visualisation by ChatGPT of a 10-dimensional polytope 🤩🙋♂️
I finally learned Dollman's backstory. 😔
July 4, 2026 at 9:57 AM
I finally learned Dollman's backstory. 😔
Our preprint of Polytope is featured in the ISEH preprint watch
The first Preprint Watch for 2025 is plentiful: 9 preprints focusing on Acute Myeloid Leukemia, but also spatial fate mapping meets barcoding, how cell fate decisions occur in hematopoietic progenitors, and more! Read now➡️ simplyblood.org
January 10, 2025 at 1:14 PM
Our preprint of Polytope is featured in the ISEH preprint watch
Today we celebrate the birthday of two important mathematicians - Tripos trailblazer, algebraic geometrist, and Bryn Mawr legend Charlotte Angas Scott (born 1858) and polytope pioneer Alicia Boole Stott (born 1860)!
#WomenInSTEM #MathSky #HistSci #BookSky 🧮
#WomenInSTEM #MathSky #HistSci #BookSky 🧮
June 8, 2025 at 3:08 PM
Today we celebrate the birthday of two important mathematicians - Tripos trailblazer, algebraic geometrist, and Bryn Mawr legend Charlotte Angas Scott (born 1858) and polytope pioneer Alicia Boole Stott (born 1860)!
#WomenInSTEM #MathSky #HistSci #BookSky 🧮
#WomenInSTEM #MathSky #HistSci #BookSky 🧮
That Coxeter polytope is so cool but also almost impossible to photograph well
June 13, 2025 at 9:16 PM
That Coxeter polytope is so cool but also almost impossible to photograph well
Here's a mathematical fact which I find amazingly counter-intuitive:
There exists a polytope (=the convex hull of a finite set) in ℝ⁴ which is not combinatorially equivalent to one with rational vertex coordinates (=the convex hull of a finite subset of ℚ⁴)!
🤯
•1/4
There exists a polytope (=the convex hull of a finite set) in ℝ⁴ which is not combinatorially equivalent to one with rational vertex coordinates (=the convex hull of a finite subset of ℚ⁴)!
🤯
•1/4
January 13, 2026 at 6:38 PM
Here's a mathematical fact which I find amazingly counter-intuitive:
There exists a polytope (=the convex hull of a finite set) in ℝ⁴ which is not combinatorially equivalent to one with rational vertex coordinates (=the convex hull of a finite subset of ℚ⁴)!
🤯
•1/4
There exists a polytope (=the convex hull of a finite set) in ℝ⁴ which is not combinatorially equivalent to one with rational vertex coordinates (=the convex hull of a finite subset of ℚ⁴)!
🤯
•1/4
三浦大知 (Daichi Miura) / Polytope -Conceptual Film-
YouTube video by Daichi Miura
youtu.be
December 5, 2025 at 10:24 PM
back in the old days it was enough to just know about the attention mechanism. attention was all anybody needed. now if you wanna have a good llm you have to constrain your residual hyperconnection mappings to a birkhoff polytope and cook up a bespoke hybridized approach to attention compression
July 31, 2026 at 3:21 PM
back in the old days it was enough to just know about the attention mechanism. attention was all anybody needed. now if you wanna have a good llm you have to constrain your residual hyperconnection mappings to a birkhoff polytope and cook up a bespoke hybridized approach to attention compression
三浦大知 - Polytope
music.youtube.com/watch?v=hRc_...
music.youtube.com/watch?v=hRc_...
Polytope
YouTube video by Daichi Miura - Topic
youtu.be
June 25, 2025 at 1:44 PM
三浦大知 - Polytope
music.youtube.com/watch?v=hRc_...
music.youtube.com/watch?v=hRc_...
yes-ish. This explains what I'm working towards: elliot.website/editor/updat...
Polytope editor
Polytope editor
elliot.website
November 19, 2024 at 10:53 PM
yes-ish. This explains what I'm working towards: elliot.website/editor/updat...
The associahedron, hands down. I even wrote an article about it for my school’s magazine! www.reed.edu/reed-magazin...
Positive Associations
Students in Math 113 investigate a curious polytope.
www.reed.edu
October 3, 2025 at 4:34 PM
The associahedron, hands down. I even wrote an article about it for my school’s magazine! www.reed.edu/reed-magazin...
In dimension 3 (or less!), it is true by a theorem of Steinitz (dating 1922) that any 3-polytope is combinatorially equivalent to one with rational vertex coordinates (and, I think, arbitrarily close to the given polytope). But in dimension ≥4, this is no longer the case. •3/4
January 13, 2026 at 6:38 PM
In dimension 3 (or less!), it is true by a theorem of Steinitz (dating 1922) that any 3-polytope is combinatorially equivalent to one with rational vertex coordinates (and, I think, arbitrarily close to the given polytope). But in dimension ≥4, this is no longer the case. •3/4