# 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.
• Naming tilings (Math Forum)
• 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.
• Student lesson (Math Forum) a place for further explorations on-line.

• Symmetry Ideas

• Reflective symmetry: BI LATERAL SYMMETRY
T  C  O   0    I   A
• Folding line: "axis of symmetry"
• The "flip."
• The "mirror."
• 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.