Polytopes & their
Incidence Matrices

Site map

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)
• Complex polytopes

Main explanatory pages

• Polytopes   –   esp. introductions to:   regular   /   quasiregular   /   Wythoffian   /   Grünbaumian   /   uniform   /   scaliform   /   orbiform   /   skeletal
• Incidence matrices   –   twins
• Dynkin diagrams   –   symmetry groups   /   fundamental domains   /   Wythoff construction   /   snub operations (note on multisnubs)   /   lace prisms, lace towers, lace simplices ...
• Vertex figures   –   general Truncations   /   general Rectifications   /   Ambifications   /   general Rhombation   /   general Expansion   /   subsymmetrical Diminishings   /   centers hulls   /   Voronoi cells
• Quasiperiodic tilings (projection methods)   –   lattices   /   Waterman polytopes

Subordinate theme pages

• Dihedral angles
• Johnson solids, etc.   –   Johnson solids   /   Blind polytopes   /   CRF (convex, regular faced)
• Homohedra 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,..   –   dimensional analogs
• Axial polytopes   –   Dutour's Delone cells   /   bistratic lace towers
• Segmentotopes   –   dimensional behaviour of fundamental lace prisms
• Lace simplices   –   simple Wythoffians   /   simple lace prisms   /   simple Trigonics   /   etc.
• Stott expansions   –   partial Stott expansions   /   EKF (expanded kaleido-facetings)
• Polytope products   –   |,>,O devices   /   Hanner polytopes   /   volume & density   /   roundness measure for polytopes
• Ridge-facetings   –  
      of oct + co
      of sirco
      of gocco
      of ike
      of id + gid
      of srid
      of sidtid
      of siid
      of sissid
      of did
      of raded
      of gaddid
      of gidrid
• Closed finite flat complexes
• Uniform compounds   –   blends
• Catalan solids, etc.   –   isogonal polytopes
• Abstract polytopes and modwraps   –   Grünbaum-Coxeter polytopes   /   Coxeter-Moser polytopes (regular maps)   /   skew polytopes

For Reference

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

Index