Monday February 24
Continued discussion of Regular and Semiregular Tilings of the plane.
A tiling is a regular tiling if
(i) it has a single tile shape that is a regular polygon and
(ii) the vertices and edges of the tiles coincide (no overlapping edges)
A tiling is a semi-regular tiling if
(i) each tile shape is a regular polygon,
(ii) the vertices and edges of the tiles coincide (no overlapping edges) and
(iii) every vertex has the same polygon types arranged around it.
Continued explorations - classification of semiregular tilings.
Wingeometry download! and demonstrate tesselations.
The numbers represent the number of sides in the polygons.
The order indicates the order in which the polygons are arranged about a vertex.
Semiregular Tilings: global results!
Look at the results using wingeometry.
(Math Forum) a place for further explorations on-line.
Reflective symmetry: BI LATERAL SYMMETRY
T C O 0 I A
Folding line: "axis of symmetry"
This kind of symmetry is hard to describe in Flatland where a "flip: is not possible.
Symmetries of playing card.... classify the cards by having same symmetries.
Notice symmetry of clubs, diamonds, hearts, spades -
the layout of the visuals on the cards
Now... what about finding all the reflective and rotational symmetries of a single figure?
6 Symmetries of an equilateral triangle.
Symmetries of an equilateral triangle:
Activity on the composition of symmetries for an equilateral triangle.