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

Version Changes

2022 / 2 / 9

- theme index to the main page
- adding the Witting polytope as well as Shephard's generalised hypercubes to the complex polytopes
- adding several more polytopal families to the dimensional analogs
- starting to consider non-convex polyyotta as well
- some rewording of the truncation and rhombation cycles and the addition of the expansion cycle
- added the quartersnub derivation of ike (s3s4s')
- page on Hanner polytopes added
- started to evaluate some 5D partial Stott expansions
- 98 new incmats files, bringing the count up to 9300 individual incidence matrices

2021 / 9 / 9

- 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

2021 / 5 / 3

- 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 24,1
- 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

2020 / 12 / 21

- 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 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

2020 / 7 / 1

- 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 polytopewiki
- over 80 new incmats files as well as 160 additional incidence matrices

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

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

2019 / 4 / 24

- started to collect 6D noble polytopes
- found the second scaliform polyzetton: codify
- first lace hyper cities, e.g. 3D ones for naq = 321, laq = 231, lin = 132, hax = 131,
  and 4D ones for rek, codify
- some general thoughts on a roundness measure of polytopes
- added a (non-unit-edged) toroidal polyhedron, which allows to tile 3D-space without gaps and overlaps
- about 90 new incmats files and exactly 200 new, mostly quite huge incidence matrices

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 segmentoxenna
- providing explicit 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 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

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

2011 / 1 / 15   (in those days at

- 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

- 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

- 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

- 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

- 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

- 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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