IncMats Website Update

[Klitzing]

Thank you for pointing out the copy-n-paste error with bicypdrahi - which indeed lasted for quite long already, undiscovered.

The point about saddid and sidditdid well is correct, as they indeed are different abstract polytopes, i.e. having different 0-1-matrices, while their symmetry-type incidence matrices no longer care about the different hole types involved. Thus in a quite limiting reading of "twins" those well could be considered such. However those still are far away from the very concern to enlist known pairs of polytopes, which are "largely different" and still have the same face vectors. Thence having largely different incidence matrices - even when considered with respect to symmetry types only, and this not only because of considering different (sub)symmetry representations, orientations or gyrations, would rather be the main concern.

--- rk

[Klitzing]

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.)

Version Changes
2023 / 4 / 8

- provided summarized face vectors, both for individual incmat files as well as within some index files
- further polytopal families in dimensional analogs
- emphasizing the matching condition and providing side lengths for all Schwarz triangles too
- some further hyperbolic pentacombs
- further 5D A,B,B-trigonics
- para- and hypercompact Gossetics (up to rank 10)
- truncation and rectification being applied onto abstract Grünbaum-Coxeter polytopes: the 11-cell and the 57-cell
- inserting back-links from individual (Wythoffian) polytope file into dimensional listings
- description and examples of Waterman polytopes
- nearly 90 new incmats files, more than 100 new incidence matrices

--- rk

[mr_e_man]

- description and examples of Waterman polytopes

That reminds me of these sites I found in a search for degenerate CRF polyhedra:

https://watermanpolyhedron.com/dsolids.html
https://polyhedra.doskey.com/DiamondReg ... gular.html
https://www.interocitors.com/polyhedra/Triamonds/
tupelo-schneck.org/polyhedra/

[Klitzing]

Website updates! -> https://bendwavy.org/klitzing/home.htm
- expanded to 4D Waterman polytopes
- major rewrite and huge expansion of complex polytopes with lots of examples
- nearly 120 new incmats files, more than 360 new individual incidence matrices

--- rk

[Klitzing]

next update of my IncMats website https://bendwavy.org/klitzing/home.htm

• ambification further elaborated as well as reverse linked in the individual polytope files
• some more starry, laminate, and other hyperbolics
• some more partially snubbed polypeta
• explanation of sefa derivation process
• bitruncated simplices and bitruncated hypercubes added to the analog listings
• rhombated and quasirhombated hypercubes added to the analog listings as well
• expansion of deltahedra et al. page, now listing homotopal CRFs up to 6D
• adding the (abstract) "tomotope" as well as its truncation and rectification
• T. Ruen's "mystic" x3o6o|x3o substructure of hex
• sadly the previous external pic-refs from http://bulatov.org/polyhedra/ seemingly no longer get resolved any longer,
  accordingly these had to be replaced with still working ones from https://en.wikipedia.org/wiki/ instead
• more than 130 new incmats files, nearly 240 new incidence matrices

--- rk

[Klitzing]

Further IncMats website update.
(For details cf. to https://bendwavy.org/klitzing/version.htm )

--- rk

[mr_e_man]

"triangular tiling antiprism"

Why is it called an antiprism, when it doesn't involve the dual of the triangular tiling, i.e. the hexagonal tiling?

[Klitzing]

"Antiprism" has 2 different readings (i.e. extrapolations from polygons to higher rank elements)!
a) your reading: take the dual (polygon)
b) take a gyrated copy (polygon)

(Sure, the latter is nowadays more specifically known as "alterprism" instead, however, in more classical contexts those most often are dubbed as "antiprisms" none the less.
Esp. when it comes to more wide-spread, aka accepted namings.)

--- rk

[Klitzing]

Further IncMats website update is up!

recent changes include:

- higher-D collection of lace simplices largely expanded, 10D started
- some further ursatopes elaborated
- the theory of amalgamation in general and further examples of
  half-Grünbaum-Coxeter polytopes added
- some more high-D scaliforms elaborated
- fractal dimension
- finally added in quasiperiodicity slot the Socolar tiling
- further Petrie-Coxeter polyhedra
- VRMLs of individual incmat files recovered by means of x-ite (applicable in current HTML5 browsers)
- VRML switching logics implemented eg. for facetins pages (so that alternate ones get represented within same canvas)
- more than 750 existing incmats files changed plus more than 50 new incmats files, more than 140 added incidence matrices

--- rk

[Hugh]

Hi Dr. Richard Klitzing, great site! I hope you don’t mind that I asked ChatGPTo1 to take a look at your site map and suggest any part that might help me explain a 4D/VRI idea I’ve been working on (in the Visualization section of this forum) and it said the Wythoff’s Construction page.

It said: “Wythoff’s construction can be a powerful conceptual tool for explaining 4D-related VRIs because it shows, step by step, how an entire higher-dimensional shape can be generated from a single “seed point” reflected across multiple mirrors (hyperplanes).”

Thanks for this, I hope to develop the idea further.

[Klitzing]

Hi folks,
just want to mention that I just uploaded the next update of the IncMats Website https://bendwavy.org/klitzing/home.htm

Version changes include:

- new explanatory page on twisters / jitterbugs / gyrohedra with VRMLs
- new page for high-symmetrical point structures ("non-lattices") added
- started to introduce external links on explanatory theme pages as well
- starting to enlist the peratope series (i.e. pero based ursatope relatives)
- new page on incidence structures of projective groups, i.e. of PG(n,k)
- cuneprisms and cune twisters added
- started to think about 8D and 9D ursatopes
- more Coxeter-regular polychoral compounds added (acc. to McMullen's 2018 description)
- more than 475 existing incmats files changed with about 70 new incmats files, more than 160 added incidence matrices

Best regards,
--- rk