Symmetry, Crystals and Polyhedra

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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References and Links

Symmetry and Crystals

Symmetry Concepts

• Symmetry around a point in the plane
• Repeating patterns on a strip (one-dimensional space groups)
• Repeating patterns in the plane (two-dimensional space groups)
• Symmetry around a point in three dimensions (3-dimensional point groups)
• Repeating patterns in space (three-dimensional space groups)

Crystals

• The crystallographic point groups
• The 48 special Crystal Forms
• Bravais Lattices
• Building crystal forms with unit cells
  • Hexoctahedral Crystal Forms
  • Other Isometric Crystal Forms
  • Tetragonal Crystal Forms
  • Trigonal and Rhombohedral Crystal Forms
  • Hexagonal Crystal Forms
  • Orthorhombic, Monoclinic and Triclinic Crystal Forms
• Miller Indices

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Tilings and Polyhedra

Tilings

• Tiling Terms
• General Facts about Tilings
• Regular and Archimedean Tilings
• Uniform Tilings
• Polypolygon Tilings
• Rep-Tiles
• Radial and Spiral Tilings
• Logarithmic Spiral Tilings
• The Heesch Tile: An Interesting Non-Tiler
• Aperiodic Tilings

Polyhedra

• Data on Polyhedra
• Platonic Solids
• Archimedean Solids
• Archimedean Duals
• Kepler-Poinsot Solids
• Uniform Polyhedra
• Compounds of Uniform Polyhedra
• Johnson Polyhedra (Convex polyhedra with regular polygon faces)
• Stellations of Simple Polyhedra
• "Hyperbolic" Tesselations
• Stewart Toroids (Toroidal Solids with regular polygon faces)
• Stellations of the Icosahedron
• Polar Zonohedra and Extended Zonohedra
• Other Interesting Polyhedra
• Enumeration of Polyhedra
• Geometry of the Tetrahedron

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Created 15 September 1997, Last Update 9 July 1999

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