| Symmetry_and_Pattern__The_Art_of_Oriental_Carpets Resources compiled by the Math Forum. |
| Symmetry_and_the_Shape_of_Space With interactive demos using Geometer's Sketchpad (requires Macintosh). |
| Symmetry_and_the_Shape_of_Space Chaim Goodman-Strauss, Arkansas. With interactive demos using Geometer's Sketchpad (requires Macintosh). |
| TESS Tessellation software. 11 rosette, all 7 frieze and all 17 wallpaper groups included. |
| Tessellated,_Interlocking_Concrete_Pavers_and_Molds Pictures of some concrete tilings. |
| Tessellating_Wallpaper_Patterns Original tessellating desktop wallpaper tiles. |
| Tessellation_and_Photography A study for the endless possibilities of tessellating the plane based on the work of Dutch graphic artist M.C. Escher. |
| Tessellation_Links Compiled by Suzanne Alejandre for the Math Forum. |
| Tessellation_Tutorials_by_Suzanne_Alejandre Tutorials and templates for making tessellations using ClarisWorks, the Geometer's Sketchpad, HyperCard, HyperStudio, and straightedge and compass, including step-by-step instructions for classroom |
| Tessellations A company selling foam puzzles, many based on planar tessellations (tilings) and fractals. |
| Tessellations__Technology_and_Culture Examples and Java applets. |
| Tessellations_Using_Geometer\'s_Sketchpad Description of a class project. |
| Tessellations_with_Java Examples and source code. |
| Tiling_Plain_and_Fancy Tiling from the mathematical and historical viewpoint by Steve Edwards. Provides a number of examples of various types of tiles that tile the plane and includes periodic tiling plus Penrose's aperiod |
| Tilings_and_Geometric_Ornament Applying principles of computer graphics to the creation of geometric ornament, as a continuation of the tradition of ornamental design using modern tools and algorithms. |
| Totally_Tessellated An introduction to tessellations explaining the basic underlying mathematics, and with many examples from real life. |
| 17_Wall_Paper_Symmetry_Groups_to_Create_a_Regular_Division_of_the_Plane Graphics. |
| Wallpaper_Groups Images and descriptions of the 17 plane symmetry groups. |
| William\'s_Geometric_Construction_Page Activities to create patterns using simple resources, such as making equilateral triangle from a circle. Suitable for upper primary and lower secondary ages. |
| Aanderaa_Instruments Instruments and Sensors for Land, Sea and Air |
| Adcon_Telemetry_GmbH Provide meteorological sensors, but specialty is wireless telemetry. |
| Advanced_Designs_Corp_ Doppler Weather Radar and Weather Data Displays, Doppler Radar, Weather Radar, Doppler, Radar |
| Advanced_Sensing_Products ASP is a manufacturer standard PRTs, precision RTDs, and different types of thermocouples. |
| Alltec_Corp_ A manufacturer of lightning protection and grounding systems. |
| AllWeatherInc A source of weather sensors, environmental monitoring systems, data collection products, and display and recording devices. |
| Applied_Technologies,_Inc_ Manufacturer and supplier of scientific instrumentation, software, and systems for meteorological and atmospheric research. |
| Atmospheric_Radar_Systems_(ATRAD) Atmospheric Radar systems for scientific and commercial applications. |
| Axinum_Innovations_&_Technologies Manufacture of Siphoning Rain Gauges and Data Loggers |
| B__K__Consimpex_Meteorological_Systems Satellite remote sensing & metereological system integrators in India. |
| Belfort_Instruments Offer a variety of weather instruments for the measurement of Wind, Precipitation, Temperature, Humidity, Pressure, and Visibility. |
| BOLTEK A leader in affordable thunderstorm tracking technology and Lightning Detection Systems. |
| Campbell_Scientific_Ltd_ Professional weather monitoring products, including a full line of automated, research-grade weather stations. |
| Casella_CEL Manufacturer and supplier of meteorological equipment, weather stations, rain gauges, solar equipment and wind speed and direction. |
| Climatronics_Corp_ Meteorological systems for ambient surface and upper air weather stations and networks. Offering sensors for wind, temperature, humidity, rainfall, pressure, solar, ice, clouds and visibility. |
| Coastal_Environmental_Systems Coastal Environmental designs and manufactures weather stations, meteorological, environmental monitoring instrumentation, and data acquisition systems. |
| Columbia_Weather_Systems Makers of the Capricorn weather stations. Systems include wind speed and direction, temperature, barometric pressure, humidity, rainfall, leaf wetness, solar radiation and soil moisture. |
| Comptus_Inc_ Manufacturer of meterological instruments for measuring wind, rain, snow and other weather elements. |
| Corr-Tek_Idrometria Environmental Monitoring: Products for Sampling and Monitoring Water |
| Davis_Instruments_Corp_ Weather instrumentation for amateur and commercial boaters, farmers, meteorologists, hobbyists. Introductory Flash option. |
| Diplex_Instruments Manufacture, import and distribute meteorological and scientific instruments. Specialist in thermometers. |
Here are more solutions, boring ones that you get by subdividingmore common tiles. (I think these are old, I'm not sure.)
Angles 120-60-180-60-120, all sides equal. This is definitely old, butit forms some patterns that no other tile forms. The first pattern shownis a "reptile": 4 tiles form a larger tile of the same shape, and 4 of thoseform yet a larger tile, and so on recursively. (It's a pentagonbecause there are five points at which tiles meet. It doesn't matterthat the angle at one of the points is 180 degrees.)
Here are the solutions I found. (I have about 2000 more candidatenew solutions, but I haven't developed the tools to judge them.Probably about 6 will be real solutions.)Angles 45-270-22.5-112.5-90, four sides equal. This forms onlyone pattern.
Angles 100-140-60-160-80, all sides equal. The tile and its mirrorimage are required for this tiling. I just learned the circle iscalled a "Hisrchhorn Medallion", and was first found by MikeHirschhorn in the 1970's. I tiled the floor of my half bath with this tiling. Mathematician Ed Pegg, Jr. manufactured a game (sort of like dominoes) out of this tile and another that he found. (I had to geta set to show my support for mathematicians actually building things.)
Angles 108-36-252-36-108, all sides equal. This is easy to derivefrom a pentagram. It forms many interesting tilings. I've seen it insome of David Eppstein's tilings, so I didn't find it first. Ipainted it on the ceiling of my half bath.
Angles 60-90-150-30-210, all sides equal. It would be easy to layfloor tiles or linoleum made with this.
Here is another solution by Mike Korn:
Here's the recipe I'm using in my search.David Eppstein's tilingrelated linksDavid Eppstein's generally geometriclinksEd Pegg's Chaotic Tiling combinesthe 160-60-140-100-80 tile with another to produce chaotic tilings.PatWehrman is a ceramics artist who has an interest in unusualtilings of the plane.I decorated my half bath with thesetiles.Here's a gallery of my mom's art.Table of Contents