IncMats Website Update

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Re: IncMats Website Update

Postby Marek14 » Mon Jun 24, 2019 9:20 am

Klitzing wrote:Just 2 months later the next update of my IncMats website is up already! 8)

2019 / 6 / 22
- added an own page on ridge facetings as well as several according sub-pages
- added an own page on lace simplices, listing all the easiest cases each
- added a section on the Dehn-Summerville equations for simplicial polytopes
- several broken links, esp. on the pages for hyperbolic tilings and to pics of polyterons, now got fixed
- exactly 50 new incmats files as well as nearly 150 additional incidence matrices, many of them for various segmentotera, thus summing up to the following totals:

Total count of actually available polytopes: 3448
Total count of contained incidence matrices: 8256

--- rk


Speaking of hyperbolic tilings, I made some new hi-def images of some, thanks to new HyperRogue features that allow for displaying of general Archimedean tilings. If you want, we could update their page :)
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Re: IncMats Website Update

Postby Klitzing » Sat Nov 23, 2019 9:06 pm

Next IncMats website update got uploaded.

Changes 2019 / 11 / 23:

- completed the list of all possible up to 5D lace simplices, which use links marked 2 or 3 only
- further downloadable excel spreadsheets, eg. in order to calculate the circumradius of lace prisms and of trigonics respectively
- several new uniform compounds, some with ex components:
  spohi (5) and sody (10), kepisna (6) and pedisna (12), kidisna (10) and ditusna (20);
  others with ico components: kitapna (4) and bitapna (8), kitefa (6) and bitefa (12)
- added a section on the Coxeter-Moser polytopes, a.k.a. regular maps
- even more broken links, esp. to pics of polyterons, now got fixed
- cross-linking to Nan Ma's page on regular stars
- nearly 60 new incmats files as well as nearly 150 additional incidence matrices, many of them in 5D


(Sorry @Marek14 for not having replied to you so far. I did get your provided pics. But still hadn't enough time to exchange them one by one.)

--- rk
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Re: IncMats Website Update

Postby Klitzing » Wed Jul 01, 2020 10:01 am

Hi,

just want to inform you about the recent update of my incmats website http://bendwavy.org/klitzing/home.htm .
(In case don't miss to hit the reload button to get the newed pages and not those from your cache...)

Some of the recent changes:

- many more 4D uniform compounds listed, even started to collect 7D & 8D compounds
- also extended to 7D combinations of extrusions and taperings, cf. |,>,O devices
- the notion of alterprisms is being added (thereby elaborating various further scaliform examples),
  as well as introducing according acronym shortenings (X-al-X becoming now simply X-a)
- some more polychora investigated wrt. EKF constructions therefrom
- hidicau pretasto, a further outstanding CRF has been found after a long time of silence in this resort
- section on the hypersine function for hypersolid corner angles
- cross-linking to a new polytopewiki
- over 80 new incmats files as well as 160 additional incidence matrices

Have a look!

--- rk
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Re: IncMats Website Update

Postby Klitzing » Tue Dec 22, 2020 9:15 am

Hi,

just want to inform you about the recent update of my incmats website http://bendwavy.org/klitzing/home.htm .
(In case don't miss to hit the reload button to get the newed pages and not those from your cache...)

Some of the recent changes:

- added a page on isogonal polytopes with quite a lot of according stuff from a current research project
- noticed that firp in fact is a 4D cuploid and found a further such: co retro-cuploid
- found a new scaliform honeycomb with vertex configuration 5 Y4 + 3 T + 3 Q3 + 1 T3
- continued cross-linking of the still quite fast growing polytopewiki
- started to collect some twins
- major xhtml-reworking: erasing lots of html-allowed, but not well-defined xml
- finally providing OBSAs for the polygons as well
- started to provide OBSAs for hyperbolics as well
- started to collect compounds of euclidean tilings as well
- nearly 200 new incmats files as well as more than 250 additional incidence matrices

Have a look!

--- rk
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Re: IncMats Website Update

Postby Marek14 » Tue Dec 22, 2020 9:18 am

Me and Zeno have been collecting my tilings at https://zenorogue.github.io/tes-catalog/ . I started in tilings many years ago by researching uniform (a,a,a,b) tilings, and now I have finished the classification of 2-uniform (a,a,a,b) as well :)
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Re: IncMats Website Update

Postby Klitzing » Tue May 04, 2021 10:57 am

Just want to announce that even before Jonathan' polychoron website
my own IncMat website https://bendwavy.org/klitzing/home.htm has got an update!
Go and check out! - (You might want to hit [F5] if the cache displays the old content still.)

Excerpts from the new stuff:
  • hidlin and idinaq, 2 newly found 7D convex scaliforms
  • sissiddow, a 7D non-convex noble scaliform
  • quite a few newly found 6D convex scaliforms
  • major rewrite and extension of skew page while finding infinite skew polychora
  • further isogonal doubling cases elaborated
  • started to collect non-convex non-Wythoffian polypeta, polyexa, and polyzetta
  • started with isogonal polytera
  • elaborated a further 3D lace hyper city for the 8D 2_4,1
  • starting to provide a small intro on Shephard-Coxeter Polytopes (aka complex polytopes),
    giving additionally their relations to the according twice-dimensional real space polytope,
    from which it is just the abstract polytopal subset of (some of) its even-dimensional elements
  • reached the limit of 4000 html files in the whole IncMats website,
    providing more than 100 new polytope files and above 175 additional incidence matrices
--- rk
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Re: IncMats Website Update

Postby mr_e_man » Fri May 21, 2021 4:33 am

Lots of good information there. :) I didn't know what the Gosset polytopes km,n were until I found it on your site.

Do you think any of my results on CRF honeycombs are worthy to be mentioned there? They can be summarized thus: Any CRF honeycomb, other than cube-doe-bilbiro, has only cells which can be decomposed into P3,P4,P8,T,Y4,Q4 . In particular, decagons cannot be used, for example.
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
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Re: IncMats Website Update

Postby Klitzing » Sat May 22, 2021 5:46 pm

mr_e_man wrote:Do you think any of my results on CRF honeycombs are worthy to be mentioned there? They can be summarized thus: Any CRF honeycomb, other than cube-doe-bilbiro, has only cells which can be decomposed into P3,P4,P8,T,Y4,Q4 . In particular, decagons cannot be used, for example.

Is that statement of yours a mere observation based on the known ones,
or is it a rigorously proven result, valide also for any future being found honeycomb?
--- rk
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Re: IncMats Website Update

Postby mr_e_man » Sun May 23, 2021 7:59 pm

The latter: I have proven to my own satisfaction that other honeycombs cannot possibly exist.

In other words, the statement is valid for any honeycomb found in the future.

That linked page is supposed to be an outline of the proof. Anyone who wants to follow what I did there can point out any unclear parts that I should explain, or any cases that I missed.
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
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Re: IncMats Website Update

Postby mr_e_man » Fri Jun 11, 2021 2:58 am

How should I respond to no response? :sweatdrop:

Is this result just not very interesting? Or is my "proof" totally incomprehensible? Or are you taking your time to figure it out?
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
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Re: IncMats Website Update

Postby Klitzing » Fri Jun 11, 2021 9:49 pm

When I read your starting article here I can get the followings

  • 2D convex tilings with regular polygons only can use 3-, 4-, 6-, 8-, and 12-gons,
    as any other being used regular convex polygon ultimatly results in a non-continuable configuration
  • morover there is only a single 2D convex tiling with regular polygons only using 8-gons: the uniform 4.8.8-tiling
  • occurances of 6-gons variously might be decomposed into 6 3-gons each (6-pyramid)
  • occurances of 12-gons variously might be decomposed into 6 3-gons, 6 4-gons, and 1 6-gon each (6-cupola),
    in fact within 2 different orientations.
  • 3D convex tilings with regular polygons should similarily be restricted to use 3-, 4-, 5-, 6-, 8-, 10-, and 12-gons only,
    as any other being used regular convex polygon ultimatly results in a non-continuable configuration
  • morover usages of 12-gons only can occur within infinite stacks of according 2D tilings.
  • sevaral CRF cells can also be excluded for similar reasons:
    4-ap, n-ap with n>5, 7-p, 9-p, 10-p, 11-p, n-p with n>12, J52-53, J84-90, J92, snic, snid, grid
About further restrictions on the usage of 10-gons - at least therein - you still seem unfixed.
Within a later post of that very thread you show up a configuration with a tid, but I don't get exactly why it isn't continuable.
Still, that one alone doesn't rule out any other 10-gon usage.

A bit later in that thread you further observe the (non-new) facts of degenerate segmentochora
  • tic || cube
  • toe || oct
  • co || point
  • girco || sirco
as well as the obvious decomposition of sirco into the lace tower squacu || op || squacu.

From that you now deduce that ANY 3D convex tiling with regular polygons should be decomposable into P3 (trip), P4 (cube), P8 (op), T (tet), Y4 (squippy), and Q4 (squacu)
- except for the single case of Weimholt's cube-doe-bilbiro honeycomb.

First of all I don't see the final 10-gon exclusion. But esp. I don't see why that mentioned exception should be the only possible 5-gon usage.

--- rk
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Re: IncMats Website Update

Postby mr_e_man » Sun Jun 13, 2021 10:44 pm

Let's discuss this over there, and not clutter your Update page too much. :arrow:
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
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Re: IncMats Website Update

Postby Klitzing » Thu Sep 09, 2021 2:12 pm

Just want to announce that the IncMat website https://bendwavy.org/klitzing/home.htm has got a further update!
Go and check out! - (You might want to hit [F5] if the cache displays the old content still.)

Excerpts from the new stuff:
  • worked out the lace city of riffy under A2×E6 subsymmetry
  • setup of an own page on dimensional analogs, providing various counts and measures in a general form
  • accordingly filled in the missing infos for the there contained polytopes in their individual pages as well
  • started for hyperbolic compounds
  • added further complex polytopes
  • above 120 additional incidence matrices
--- rk
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