Polytopes & their
Incidence Matrices

Last update
2018 / 7 / 4   –   Cf. also the version history.

Total count of actually available polytopes: 3309
Total count of contained incidence matrices: 7911

Author
Dr. Richard Klitzing
Kantstrasse 23, 89522 Heidenheim, Germany
(+49 / 0) 7 321 / 51 7 54
richard (dot) klitzing (at) t (minus) online (dot) de

Link lists to individual polytope pages

• Spherical ones   –  
      2D
      3D   (by point-group-symmetry   /   by complexity   /   by Schwarz triangles   /   addition list of Schwarz triangles)
      4D   (by point-group-symmetry   /   by complexity   /   by Goursat tetrahedra   /   addition list of Goursat tetrahedra)
      5D
      6D
      7D
      8D
      9D
      10D
• Euclidean ones
• Hyperbolic ones   –   Simplicial fundamental domains   /   Coxeter domains
• Elliptical ones (just some so far)

Main explanatory pages

• Polytopes   –   esp. introductions to:   regular   /   quasiregular   /   Wythoffian   /   Grünbaumian   /   uniform   /   scaliform   /   orbiform   /   skeletal
• Incidence Matrices
• Dynkin Diagrams   –   Symmetry groups   /   Fundamental domains   /   Wythoff construction   /   Snub operations   /   Lace prisms, lace towers, lace simplices ...
• Vertex figures   –   general Truncations   /   general Rectifications   /   subsymmetrical Diminishings   /   Centers hulls   /   Voronoi cells
• Quasiperiodic tilings (projection methods)   –   Lattices

Subordinate theme pages

• Dihedral angles
• Johnson solids, etc.   –   Johnson solids   /   Blind polytopes   /   CRF (convex, regular faced)
• Isohedra with regular facets   –   Deltahedra   /   Tetrahedrochora   /   Pentachorotera   /   etc.
• Noble polytopes   –   Scaliform polytopes
• Vertex regulars (with the tables of D. de Winters)
• Coxeter-Elte-Gosset polytopes   k_m,n,..
• Axial polytopes   –   Dutour's Delone cells   /   Bistratic Lace Towers
• Segmentotopes   –   dimensional behaviour of fundamental Lace Prisms
• Stott expansions   –   Partial Stott expansions   /   EKF (expanded kaleido-facetings)
• Closed finite flat complexes
• Uniform compounds   –   Blends
• Polytope products   –   |,>,O devices
• Abstract polytopes and modwraps   –   Grünbaum-Coxeter polytopes   /   skew polytopes
• Catalan solids, etc.

For Reference

• Overview on Dynkin notation
• Indices of polytopes   –   alphabetical   /   sorted by dimension   /   sorted by circumradius   /   used as facet   /   used as vertex figure
• Asorted other polytopes (so far otherwise nowhere else linked)
• Some round shapes
• Downloads   –   some publications of the author   /   excel spread sheets   /   etc.

Color Code of Links
Used color code of links within this and all subsequent pages: unvisited & internal to site - unvisited & external to site - visited - hover - internal to page

VRML Models
Several pictures bear links to VRML models. Those can interactively be viewed by means of a free browser plug-in, e.g. Cortona3D.
It should be noted however, that some Browsers like the new Microsoft Edge or Google Chrome (since version 42) don't support any add-ons!

Javascript
allowance will not be a must within this site. Even so, some few of the VRMLs might not work, Further the improved color-softed display of incidene matrices could not appreceated then (but, for sure, all the matrices would be completely visible nevertheless).

Impressum
For contents of external websites no warrenty can be provided. Any site administrator himself is responsible for the there provided contents. At the moment of link assignment those appeared appropriate. Any awareness of no longer appropriate contents or broken links would be appreciated and according necessary changes would be included in the following update.

Other web presences of the author
  Square Dance Club magic moments   –     Dr. Richard Klitzing at facebook   –     Dr. Richard Klitzing at LinkedIn   –     Dr. Richard Klitzing at ResearchGate