Site Map Polytopes Dynkin Diagrams Vertex Figures, etc. Incidence Matrices Index

Version Changes

2018 / 7 / 4

- new page on Bistratic Lace Towers
- new page on several round shapes
- many more reverse links from incmats pages back to explanatory theme pages
- started to collect convex segmentozetta, segmentoyotta and  and segmentoxenna
- providing explicite general stacking rules for n-rectified crosspolytopes under simplicial symmetry, 
  demihypercubes under simplicial symmetry, n-rectified crosspolytopes under hypercubic symmetry
- revisiting jak = 221, naq = 321, and fy = 421 once more, adding several deeper insights
- started to collect scaliform polyzetta, esp. kadify as initiated by D. Halitsky
- about 70 new incmats files and about 200 new, sometimes quite huge incidence matrices

2017 / 9 / 19

- new page on Catalan solids and their 4D counterparts
- ursatopes and tutsatopes added to axials page
- found one further (ico-wise) 24-diminishing and added also several (spid-wise) 20-diminished CRFs
- finally got around to evaluate the huge incidence matrix of gotanq, 
  which is the omnitruncated form of the 7D Gosset polytope 32,1
- cross-refs to several known diminishings of the various EKFs
- more than 80 new incmats files, more than 130 new incidence matrices

2017 / 5 / 19

- outline on rectify vs. ambo
  esp. its application to the Catalans oPmQoRo, resulting in the Gévay polychora
- research in area of C4nRF,
  esp. those occuring within Partial Stott Expansions when allowing additionally for the "diagonally expanded square"
- expanded section on non-convex Wythoffian polytera
- expanded section on "non-convex" Wythoffian honeycombs (i.e. including non-convex cells, retrograde cells, or 2D tilings)
- elaboration of the main hexacombs and their relation to lattices
- more than 100 new incmats files, more than 200 new incidence matrices

2016 / 12 / 3

- started to collect convex segmentoexa
- separate page on skew polytopes
- a small subsection on skeletal polytopes added
- added a further page for asorted other polytopes – meant to host temporarily so far otherwise nowhere else linked polytopes
- more than 80 new incmats files, more than 120 new incidence matrices
- esp. matrices for 2 further bi-cyclopentadiminished figures: bicypdrox, bicypdrahi (in addition to bicypdex)

2016 / 7 / 3

- separate page on the dimensional behaviour of convex unit-edged lace prisms
- separate page on scaliform polytopes
- separate excel spreadsheet listing the known 4D CRFs by their different cell counts added to the download area
- more than 100 new incidence matrix files

2016 / 1 / 3

- new page on quasiperiodic tilings & according projection methods
- further own article papers linked in download area
- new pages on lattices and on the Gosset polytopes
- page on euclidean tesselations now extended to enneacombs
  and all missing OBSAs up to here are now provided too
- elaborated the gyrotrigonisms and some higher CRFs related to the Dutour polytopes
- started to collect convex segmentopeta
- section on EKFs further extended
- several further quite huge subsymmetric IncMats descriptions of already described polychora and higher dimensional polytopes
- some cell count corrections included into the convex segmentochora paper, as finally found by J. Roth
- marked external links now in a separate color

2015 / 5 / 2

- section on non-convex euclidean honeycombs added
- section on decompositions largely extended (esp. at 4D)
  with lots of new incmats files, belonging here
- recent research results on Some Hyperbolic Tiling Classes with Specific Local Configuration Types added
- several incmats added for 5D alternated facetings which become Wythoffian again
- more than 100 new incidence matrix files

2014 / 10 / 28

- expanded kaleido-facetings extracted from (partial) Stott expansions
  resp. from CRFs into a new own subpage
- several new according EKF-CRFs have been found
- closed finite flat complexes largly extended and lots of according incmats added
- major revision of section on Partial Stott Expansions
- lots of non-convex polytera incidence matrix files added 
  (thanks to the recently updated listing resp. pictorial groundworks of HedronDude!)
- all irreducible convex Wythoffian polyzetta now having acronyms
- noble page now including the (so far elaborated) euclidean and hyperbolic ones
- opened the challange for compounds beyond 4D as well
- due to EKF research several more subsymmetrical representations of the hexacosachoron (ex) have been added
- because of several quite huge incidence matrices in a single file the soften script for their zeroes might run rather long;
  therefore an interactive skipping possibility now has been added to some of the most extremal cases
  (both, soften script and its skipping are available only if javascript execution is being allowed)
- tegum sum defined and contrasted to the tegum product,
  incl. providing its relation to the degenerate zero-height lace prisms with pseudo bases
- several further incidence matrices according to tegum sum representations added
- neerly 150 new incidence matrix files / neerly 800 edited ones

2014 / 3 / 30

- cross-links added between alternated facetings (i.e. snubs) and their starting figures
- new page added for collecting closed finite flat complexes
- section on Coxeter domains now revised due to several deeper insights
- started to add 2-sided infinite lace tower descriptions for euclidean tesselations
- |,>,O devices introduced
- internal broken links (typos) fixed (based on 404 error logs)
- cross-refs to HDDB changed into perma links (in advance before a there being announced thread splitting)
- more than 125 new incidence matrix files (with 25 for 3D, 80 for 4D, 40 for 5D)

2013 / 10 / 17

- section on euclidean star tilings added
- lot more hyperbolic tesselations added (of various dimensions, both compact and non-compact)
- incmats-files for hyperbolic tilings with Coxeter domains added 
- a listing added providing now some more such 2D ones
- providing (purely imaginary) circumradii for hyperbolics too
- several further uniform polytera added, esp. those of hedrondude's "Polyteron of the day"
- some of the formers needed extra files for their intricate vertex figures
  (for calculating their circumradii a formula shows rather useful, 
  which relates that of the original figure to that of its verf!)
- redesign of site map
- more than 150 new incidence matrix files
- more than 500 old ones got additions

2013 / 7 / 18

- new page on (partial) Stott expansion,
  together with many new corresponding incmats files of any geometry (curvature)
- new page on dihedral angles
- started to add dihedral angles within incmats-files
- incmats pages for J.McNeill's elementary honeycombs added,
  within those (and some applicable others too): cross-links to his website mcneill added
- several new cross links to meanwhile added wiki pages
- incmats display optimized through javascript based content depending text-coloring (within ie only supported from ie9 on)
- several technical improvements on cross-browser support (incl. the new ie10)
- nearly 120 additional incidence matrix files

2013 / 3 / 13

- started to collect convex segmentotera
- started to collect 4D CRFs, providing lot of recently found examples
- throughout incmats files: cross-links to hedrondude's hedrondude and quickfur's quickfur websites (if applicable)
- links inserted in this version history
- started to group unsorted "confer"-lists now into contexts
- new page to collect noble polytopes
- extending the section on subsymmetrical diminishings
- inclusion of a section on Green's family of supersemicupolae to the axials page
- full table of convex segmentochora included
  and conversely added in incmats files the Klitzing numbers of segmentochora
- more than 100 additional incidence matrix files (with 90 therefrom for 4D)

2012 / 11 / 27

- version history included
- download page added (incl. the there provided spreadsheets)
- lace cities moved to more prominent positions
  several of those ASCII-art pics with according true projection pics complemented
  several additional ones
- several additional lace towers incmats
- vertex layers according to subsymmetries added
- some own incmats files for general variations like a3b3c
- incmats-files with table-border switched on for more clarity at property separations
- prism-symmetric segmentochora added
- some youtube videos added
- extra page on axial polytopes added, also refering the EEAs and EEBs!
- segmentochoron pdf updated (with footnotes)

2012 / 7 / 28

- added list of simplicial CD permutations for polychora
- added list of quasiregular polycombs of irreducible groups for 5D to 8D
- an own segmentochoron page
- "Segmentochoron display" (if applicable) added
- pdf-documents of publications of the author added
- reduction marks on site map
- favicon
- link to olchevsky's panoploid tetracomb pdf 
  (being contained on bendwavy.org outside of the IncMats-website)
- link to bowers' category A & B pages as well as his new scaliforms list
- lots of broken picture links to wikipedia recovered
- over 100 additional polytopes, getting the total count already above 2000!

2012 / 1 / 1

- about nearly 100 new polychora files
- made additions to more than 300 polytope files
- polychora main page now splitted into several subpages
- several more polychoral compounds (if not elaborated so at least) listed
- lots of broken picture links to wikipedia recovered
- links to wikichoron webpage clearly don't work for now (as mentioned lately)

2011 / 9 / 7

- "Polyhedra derived by Schwarz triangles" moved closer into 3D range, including better cross-linkages 
- Addition list for Schwarz triangles added
- "Polychora derived by Goursat tetrahedra" (new, still filling up with examples)
- Addition list for Goursat tetrahedra added (complete)
- Accordingly major changes for 4D range
- Page on hyperbolic space tessellations extended
- Subsymmetrical diminishings added (mainly based on recent list discussions)
- Besides to the existing listing of d-dim elements being used as facets of d+1-dim structures, 
  now a similar listing of d-dim elements being used as vertex figures of d+1-dim structures is available 
  (both, like the 3 types of indexes, are just distilled from the so far available incidence matrix files)
- nearly 80 additional incidence matrix files (mainly for 4D)

2011 / 4 / 27   (now at http://bendwavy.org/klitzing/)

- latest change esp. in hyperbolic space
- about 16% of files was changed or is new

2011 / 1 / 15   (in those days at http://ogre.nu/klitzing/)

- nearly 100 more polytopes (50 of those being further polychora or 4d compounds)
- lot others having got additional incidence matrices, given according to further symmetries
- starting with (some first) non-convex 5d polytopes
- Jonathan's new concept of "lieutenants" incorporated
- several newer OBSA (and their related longer names) name changes by Jonathan included / changed
- additional tabulation page for reverse incidences: within which polytopes some given polytope would be used for facet?
- back links to sitemap within the head bar
- several more cross references to wikipedia (also some lately broken picture links updated)
- the tabulation of Dik de Winter on vertex regular inclusions (not new, just to mention, as that was a topic recently)

2010 / 9 / 30   (in those days at http://ogre.nu/klitzing/)

- added all the A7,B7,D7,E7 family CD permutations
- over 50 further uniform polychora
- fixed lots of links to wiki

2010 / 4 / 23   (in those days at http://ogre.nu/klitzing/)

- dimensions 9 + 10 added
- euclideans expanded, OBSAs for 4D ones added
- hyperbolics added
- broken links to wiki pics are fixed
- about 120 further polytopes

2009 / 12 / 7   (in those days at http://ogre.nu/klitzing/)

- further external crosslinks added: those to the wikichoron pages
- additions within index: dimensionalities
- extra dimensional sorted index
- for dim 3+4: army generals and regiment colonels (beyond only convex ones so far)
- compounds
- page on vertex regularity
- over 130 new polytopes (and plenty ones have changed)

2009 / 7 / 21   (in those days at http://ogre.nu/klitzing/)

- Grünbaum-Coxeter polytopes (kind of abstract 11-cell, 57-cell etc.)
- and all the starry polychora with linear Dynkin diagrams are now completed as well 
  (as long as not being a-priori Grünbaumian multicovers)

2009 / 3 / 12   (in those days at http://tinyurl.com/polytope/)

- some more polytopes done, esp. added all 20 non-convex quasiregular polychora
- included hedrondude's cross-section figures (plus link) for polychora (as far as he provides them)

project started in 2004


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