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The name does not imply regular by default. For regular ones, you should say "regular polytope".
Convex hull of all (Cartesian product power) D-tuples, e.g. in 3D:
( 1, 1, 1)
( 1, 1, -1)
( 1, -1, 1)
( 1, -1, -1)
(-1, 1, 1)
(-1, 1, -1)
(-1, -1, 1)
(-1, -1, -1)Ciro Santilli is very fond of this result: the beauty of mathematics.
How can so much complexity come out from so few rules?
How can the proof be so long (thousands of papers)?? Surprise!!
And to top if all off, the awesomely named monster group could have a relationship with string theory via the monstrous moonshine?
The classification contains:
- cyclic groups: infinitely many, one for each prime order. Non-prime orders are not simple. These are the only Abelian ones.
- alternating groups of order 4 or greater: infinitely many
- groups of Lie type: a contains several infinite families
- sporadic groups: 26 or 27 of them depending on definitions
Simple Groups - Abstract Algebra by Socratica (2018)
Source. Good quick overview.Besides the understandable Wikipedia definition, Video "Simple Groups - Abstract Algebra by Socratica (2018)" gives an understandable one:
Given a finite group and a simple group , find all groups such that is a normal subgroup of and .
We don't really know how to make up larger groups from smaller simple groups, which would complete the classification of finite groups:
In particular, this is hard because you can't just take the direct product of groups to retrieve the original group: Section "Relationship between the quotient group and direct products".
Basically the same as classical mechanics.
Ciro Santilli's hardware House 2018-01 Aluminium extractor filter by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16This is the exact model: shop.elica.com/en/accessori/filtro-grassi-in-alluminio-cod-gf03fc.html | web.archive.org/web/20190707053526/https://shop.elica.com/en/accessori/filtro-grassi-in-alluminio-cod-gf03fc.html
Searching by th epart name "GF03FC" leads to other sellers besides Elica however, which could reduce shipping costs: www.cookerhoodsupplies.co.uk/filters-and-lamps/188-metal-grease-filter-gf03fc.html
Brand on filter itself: "ARMA Filtre a.s." based on markings: www.armafiltre.com.tr/uygulamalar/7/3/en/Home-Appliances.html Cannot find any model on website however... looks like Elica's B2B supplier only.
July 2019 message:
Aluminium extractor filter for 208298104403Hi there,I'm trying to buy a spare aluminium extractor filter for an Elica extractor, but I can't find the right size on the website.My 12NC is : 208298104403My filter looks a lot like this: shop.elica.com/en/accessori/filtro-grassi-in-alluminio-cod-GRI0077330A.html but the dimensions are different: I measured 45.9cm x 17.6cm on my old one.Do you have that for sale?
Brand according to documents: SMEG.
Most similar models I an find: www.smeguk.com/products/UKC8173N1F and www.smeguk.com/products/UKC81721F, the keyword are "built-in" and "integrated", other very similar ones: www.smeguk.com/refrigerators/built-in
Looks like this: www.youtube.com/watch?v=4c_LBVnU4ec and that's how to unclog the drain.
2020-11-28: defrost. Some small Styrofoam was broken lose from top, noticed small burn or rust marks on top grid nearby.
Looks a lot like: Bristan Monza EF Sink Mixer Chrome www.bathroomsensations.co.uk/Bristan-Monza-EF-Sink-Mixer-Chrome.html
How to open: www.youtube.com/watch?v=oHTpOG1Uhzw
2023-07: one of the sides broke near center, rebuying.
2021-07: wire half broke near connector, only works in some positions. The funny thing is: only voices seem to be blocked out! Rebuying.
2021-06: a small bottom piece of the left earpiece broke. Wire seems find, that is like a little extension to protect wire. Let's see for how long.
2020-20: wires at one of ears broke, not sure how.
Look they looked exactly like: "Skullcandy Smokin' Buds 2 In-Ear Audio Earbud Headphones with In-Line Microphone - Black".
Re-buying that one 10 pounds:
Tech specs:
Connection Type: 3.5mm AUX CableImpedence: 32 ohmsDriver Diameter: 9mmSound Pressure Level: 95 dB (1mW/500Hz)Frequency Response: 20kHz - 20HzHeadphone Type: In-Ear
Bought: 2022.
Noticeably worse than the Skullcandy Smokin' Buds 2 for a similar price.
~8GB,
lsblk reports 7796176 * 1KB = 7983284224 bytes.They are shaped like bicornes, which is super cool, but also super impractical!
Markings: "AX ÉCOLE POLYTECHNIQUE PROMOTION X2009"
From Ubuntu 20.04 on an ext4 formatted one:With Linux Unified Key Setup + ext4 the results are similar, maybe hdparam bypasses it?
/dev/sdb:
Timing cached reads: 28656 MB in 1.99 seconds = 14421.31 MB/sec
SG_IO: bad/missing sense data, sb[]: 70 00 05 00 00 00 00 0a 00 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Timing buffered disk reads: 42 MB in 3.03 seconds = 13.88 MB/sec/dev/sdb:
Timing cached reads: 28326 MB in 1.99 seconds = 14251.55 MB/sec
SG_IO: bad/missing sense data, sb[]: 70 00 05 00 00 00 00 0a 00 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Timing buffered disk reads: 38 MB in 3.11 seconds = 12.23 MB/secgnome-disks LUKS + ext4 benchmark with default params also gives about 14 MB/s.In degrees Celsius:
- 25+
- 18-25
- "dhb Aeron Short Sleeve Jersey"
- XGC Men's Cycling Shorts
- 2020-04 Giro Rumble VR Off Road Shoe
- 15-18:
- "dhb Aeron Short Sleeve Jersey"
- "dhb Lightweight Mesh Long Sleeve Base Layer"
- XGC Men's Cycling Shorts
- 2020-04 Giro Rumble VR Off Road Shoe
- 10-15:
- dhb Classic Thermal Bib Tights 10 and under. TODO this is a bit too warm for the upper range, need something more intermediate
- "dhb Lightweight Mesh Long Sleeve Base Layer"
- Castelli Perfetto RoS Long Sleeve - Cycling jersey. TODO this is a bit too warm for the upper range, need something more intermediate
- "Karrimor X Lite Run Black Headband"
- "Nike academy hyperwarm gloves"
- "Nevica Skuff". A bit too hot on upper range, but easy to take off.
- 0-10:
- dhb Merino Long Sleeve Base Layer
- Castelli Perfetto RoS Long Sleeve - Cycling jersey
- dhb Classic Thermal Bib Tights 10 and under
- dhb Dorica MTB Shoe (2020-12)
- "Karrimor X Lite Run Black Headband". Head a bit cold on lower range.
- "dhb Neoprene Nylon Overshoes". Feet a bit cold on lower range.
- "Extremities XDRY gloves". Hands a bit cold on lower range.
- "Nevica Skuff"
Bought SM-SH56 cleat to accompany.
When it arrived, it felt a bit too long, around 2cm maybe free space after toe, and when I walk and the front part touches ground, heel comes off a bit, which is annoying. But I was too lazy to give it back and take the risk of a second try, also it felt correctly tight on sides. During first test ride it felt good.
Ciro Santilli's hardware 2020-04 Giro Rumble VR Off Road Shoe by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-162021-01-28: used this show for the first time after wearing dhb Dorica MTB Shoe (2020-12) exclusively for a while. It felt much much more comfortable, the Dorica is too narrow. Also this one is much more recessed, and walking with it is much easier. Also, I notice that the intentional asymmetry I had put on cleats is not necessary anymore now that my saddle height is not way too high
At 5C feet are too cold. Compatible overshoes are basically impossible to find: bicycles.stackexchange.com/questions/73589/what-kind-of-overshoes-can-i-use-with-a-large-touring-spd-cycling-shoe-such-as-t
It is not possible to do long walks with this, unlike some websites suggests, especially on hard surfaces like rock, that would be very dangerous because the cleat area will slip. But it is good for shorter walks on grass/mud, and that does open up some good short walk exploration possibilities compared to a road shoe.
Color "Black/Red 20" (but it's actually orange), size 46 www.wiggle.co.uk/giro-rumble-vr-off-road-shoe (archive). Manual says to use Loctite 243 medium strength, first 2.4 Nm bolt torque to test it out and find good position, and then final bolt torque 5-6 Nm unless cleat says less. Starting with Shimano SM-SH56 cleats (archive), which also says provisional torque 2.5 Nm, tightening torque 5-6 Nm.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact