TESSELLATIONS c Definition c A tessellation is a
- Slides: 13
TESSELLATIONS
c. Definition c A tessellation is a tiling of a plane with a shape or shapes without creating any gaps or overlaps
Periodic d A periodic tessellation is one on which you can outline a region that tiles the plane by translation, that is, by shifting the position of the region without rotating or reflecting
Periodic: Regular d d d A regular tessellation is a tiling in which only one shape is used The shape must have congruent sides and congruent angles There exists exactly three regular tessellations
Periodic: Semiregular d d d A semi-regular tessellation is when more than one regular shape is used to tile a plane Every vertex has the same combination of shapes There are only eight such tessellations
Periodic: Not Semiregular d The vertices do not have the same combination of shapes A B A (3. 4. 6. 4) B (3. 3. 4)
Periodic: Irregular d d d An irregular tessellation is one in which nonregular shapes are used An infinite number of shapes tile periodically Any quadrilateral will tessellate
Escher d M. C. Escher, the Dutch artist, is famous for his many pictures of periodic tilings with shapes that resemble living things
Aperiodic d d d In an aperiodic (nonperiodic) tessellation translation alone is not used to cover the plane. Shapes are rotated and reflected as well. An infinite number of shapes tile only periodically An infinite number of shapes tile both periodically and aperiodically
Penrose d d Roger Penrose found a pair of tiles that force aperiodicity. In other words, they can not tile by translation alone. As the patterns expand, they seem to strive to repeat but as you continue out they are not the same
Tessellations d d Periodic – Regular – Semiregular – Not Semiregular – Irregular Aperiodic
Credits Produced by Dottie Feinstein © 1997 (2007) Conti, Shrines of Power, HBJ Press, 1978 Gardner, Penrose Tiles to Trapdoor Ciphers, W. H. Freeman & Co. , 1989 Tessellation Poster: Teaching Notes, Dale Seymour, 1987
For more information see http: //www. Science. U. com/geometry/articles/tiling/ http: //library. thinkquest. org/
- Square triangle tessellation
- Tessellation regular
- Who is the father of tessellation
- Escher ghosts
- Examples of tessellations in nature
- Sun and moon tessellation
- Glide reflection tessellation examples
- Dilation tessellation
- Tessellation 1
- Tessellation using 2 regular polygons
- The word tessellation comes from the root word
- Famous tessellation artists
- Pentominoes tessellation
- Tessellation town