Dr. Richard Klitzing

Address:
Kantstrasse 23
89522 Heidenheim
Germany
+49 / (0)7 321 / 51 7 54
e-mail


± Last update: 2013 / 7 / 18
 

Polytopes & their
Incidence Matrices

  

Square dance is an other hobby of mine.
- This picture shows a polyhedral mobile with pairs of regular ones dancing (in square dance formation) underneath a cubical truss, which in turn was chosen as a 3 dimensional version of the square dance symbol i.e. two interlinking squares.

Site map

± Polytopes
± spherical space
± Dimensional separation
 •  2D: polygons
± 3D: polyhedra
 •  by point-group-symmetry
 •  by complexity
± by Schwarz triangles
 •  addition list of Schwarz triangles
 •  Visualisation for the 3 elementary ones in a VRML
± 4D: polychora
± by point-group-symmetry
 •  linear Dynkin diagrams
 •  tri-dental Dynkin diagrams
 •  loop Dynkin diagrams
 •  loop-n-tail Dynkin diagrams
 •  two-loop Dynkin diagrams
 •  simplical Dynkin diagrams
 •  (multi)prisms
 •  other non-kaleidoscopical uniforms
 •  by complexity (linear Dynkin diagrams only)
± by Goursat tetrahedra
 •  addition list of Goursat tetrahedra
 •  5D: polytera
 •  6D: polypeta
 •  7D: polyexa
 •  8D: polyzetta
 •  9D: polyyotta
 •  10D: polyxenna
 •  Dihedral angles
 •  Regulars, Quasiregulars, Wythoffians, ...
 •  Uniform polytopes
± Johnson solids
 •  Blind polytopes
 •  CRFs
 •  Deltahedra et al.
 •  Segmentotopes
 •  Axial polytopes
± Uniform compounds
 •  Blends
 •  Vertex regulars (with the tables of D. de Winters)
 •  Noble polytopes
 •  euclidean space (tilings, honeycombs, ...)
 •  hyperbolic space (tilings, honeycombs, ...)
 •  Grünbaum-Coxeter polytopes
 •  polytope products
 •  Incidence Matrices
± Dynkin Diagrams
 •  Overview on Dynkin notation
 •  Symmetry groups
 •  Fundamental domains
 •  Wythoff construction
 •  Snub operations
 •  Lace prisms, lace towers, lace simplices ...
 •  Stott expansions
± Vertex Figures, etc.
 •  Derivation by Dynkin diagrams
± Truncated Polytopes
 •  Subsymmetrical Diminishings
 •  Centers Hulls
± Index of polytopes (alphabetical)
 •  (sorted by dimension)
 •  (sorted by circumradius - if existing)
 •  sets of (d+1)-polytopes, where specific d-polytopes are used as facet
 •  sets of (d+1)-polytopes, where specific d-polytopes are used as vertex figure
 •  Downloads

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

VRML Models
Several pictures bear links to VRML models. Those can be seen for instance with a free browser plug-in from Cortona

Javascript
allowance will not be a must within this site. Even so, the reduction marks (±) in tree-lists (as in the site map above) would not work, nor would some few interactive VRMLs. Further the improved color-softed display of incidene matrices could not appreceated then (but, for sure, 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.


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