Symmetry, Crystals and Polyhedra

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay

---

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)
• Interactive Page for Drawing the 17 Plane Space Groups       htmL5 Version (faster, better)
• Symmetry around a point in three dimensions (3-dimensional point groups)
• The "Best" Representations of the 3-D Point Groups
• Interactive Page for Plotting Stereonets of the 3-Dimensional Point Groups       htmL5 Version (faster, better)
• 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
  • Toward a More Perfect Pyritohedron
  • Tetragonal Crystal Forms
  • Trigonal and Rhombohedral Crystal Forms
  • Hexagonal Crystal Forms
  • Orthorhombic, Monoclinic and Triclinic Crystal Forms
• Miller Indices

---

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
• Create Your Own Log Spiral Tesselations (Javascript)      htmL5 Version (faster, better)
• 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

Return to Physical Geology Index
Return to Crustal Materials (Mineralogy-Petrology) Index
Go to Recreational Mathematics Index

Return to Professor Dutch's Home Page

Created 15 September 1997, Last Update 9 July 1999