User:Tomruen/uniform polytopes and tessellations

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This user subpage is an attempt to index articles related to uniform polytopes and tessellations.

Contents 1 Symmetry 2 Polytopes 3 Tessellations 4 Categories 5 Templates 6 Terminology, operations, properties 7 Space 8 Polygons 9 Polyhedra 9.1 Uniform polyhedra 9.2 Uniform polyhedra duals 10 Tilings 11 Uniform polychora and duals 12 Uniform 3d honeycombs

[edit] Symmetry

• List of spherical symmetry groups
  • Tetrahedral symmetry
  • Octahedral symmetry
  • Icosahedral symmetry
  • Dihedral group
• Orbifold notation
• List of planar symmetry groups
• Crystallographic point group
• Wallpaper group
• Frieze group
• Coxeter group
• Weyl group
• Symmetric group
• Fundamental domain
• Wythoff construction
• Schwarz triangle

[edit] Polytopes

• Polytope
  • Simplex
  • Measure polytope
  • Cross-polytope
  • Regular polytope
    • List of regular polytopes
  • List of polygons, polyhedra and polytopes
• Convex hull

[edit] Tessellations

• Tessellation
  • Uniform tessellation

[edit] Categories

• Category:Geometry stubs
• Polygon
  • Category:Polygons
• Polyhedra
  • Category:Platonic solids
  • Category:Archimedean solids
  • Category:Kepler-Poinsot polyhedra
  • Category:Uniform polyhedra
  • Category:Prismatoid polyhedra
  • Category:Tiling
  • Category:Quasiregular polyhedra
  • Category:Johnson solids
  • Category:Pyramids and bipyramids
  • Category:Polyhedral stellation
  • Category:Polyhedral compounds
  • Category:Deltahedra
  • Category:Chiral polyhedra
  • Category:Zonohedra
  • Category:Self-dual polyhedra
  • Category:Catalan solids
  • Category:Polyhedra templates
• Tilings
  • Category:Tiling
  • Category:Honeycomb image
• Polytope
• Category:Polytopes
• Category:4-dimensional geometry
• Polyhedron images
  • Category:Periodic tiling image
  • Category:Polyhedral image

[edit] Templates

• Template:Polyhedron types

[edit] Terminology, operations, properties

• Notations
  • Schläfli symbol
  • Vertex configuration
  • Vertex figure
  • Face configuration
  • Root system#Dynkin diagrams
• Operations
  • Truncation (geometry)
  • Rectification (geometry)
  • Runcination (geometry)
  • Omnitruncation (geometry)
  • Snub (geometry)
  • Dual polyhedron
• Properties
  • Euler characteristic
  • Genus (mathematics)
  • Chirality (mathematics)
  • Orientability
  • Defect (geometry)
  • Convex
  • Nonconvex
• Definitions
  • Vertex
  • Face (geometry) - polygon in 3-space
  • Ridge (geometry) (n-2)-polytope in n-space
  • Peak (geometry)
  • Facet (mathematics) (n-1)-polytope in n-space
  • Cell (geometry) - polyhedron in 4-space
  • Dihedral angle

[edit] Space

• Topology
• Graph (mathematics)
  • Graph theory
  • Dual graph
• Manifold
• Euclidean geometry
• Non-Euclidean geometry
• Elliptic geometry
• Riemannian geometry
• Spherical geometry
• Hyperbolic geometry
• Euclidean space
• Riemannian manifold

[edit] Polygons

• Polygon
  • Star polygon
  • Simple polygon
  • Convex polygon
  • Complex polygon
• Triangle
• Quadrilateral
  • Square (geometry)
  • Rectangle
  • Rhombus
  • Parallelogram
  • Geometric kite
  • Isosceles trapezoid
  • trapezoid
  • Cyclic quadrilateral

[edit] Polyhedra

• Polyhedron
• Polyhedron model
  • Zonohedron
  • Stellation
  • Johnson solid Convex
    • Near-miss Johnson solid
  • List of rotational symmetry polyhedral sets
  • Deltahedron Triangles
• Net (polyhedron)

[edit] Uniform polyhedra

• Polyhedron
  • Uniform polyhedron
    • Platonic solid
    • Kepler-Poinsot solid
    • Archimedean solid
      • Semiregular polyhedra
  • Prism (geometry)
  • Antiprism
    • Polyhedral compound
  • List of uniform polyhedra
  • List of Wenninger polyhedron models
  • List of uniform polyhedra by Wythoff symbol
  • List of uniform polyhedra by spherical triangle
  • Snub polyhedron
  • Self-dual polyhedron
  • Prismatoid
  • Pyramid (geometry)
  • Cupola (geometry)

[edit] Uniform polyhedra duals

• Duals
  • Catalan solid
  • Trapezohedron
  • Bipyramid

[edit] Tilings

• Uniform tilings
  • Tiling by regular polygons
  • List of uniform planar tilings

[edit] Uniform polychora and duals

• Polychoron
  • Uniform polychora
    • Regular polychora
      • Convex regular 4-polytope
      • Nonconvex regular polychora
    • Uniform polychoron
      • Semiregular 4-polytopes
    • Uniform polyhedral prism
    • Duoprism
    • Uniform Polychora Project

[edit] Uniform 3d honeycombs

• • Honeycomb (geometry)
  • Uniform honeycombs
    • Andreini tessellation