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± 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

• 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

• Overview on Dynkin notation

• Symmetry groups

• Fundamental domains

• Wythoff construction

• Snub operations

• Lace prisms, lace towers, lace simplices ...

• Derivation by Dynkin diagrams

± Truncated Polytopes

• Subsymmetrical Diminishings

• Centers Hulls

• (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

Dr. Richard Klitzing

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