Tangrams can be mixed up to make many different shapes, or reassembled into a square.
TangramsĪ tangram is a Chinese puzzle made up of a square sliced into a seven shapes (or tans) that fit together – a smaller square, five triangles and a rhombus. Try creating a repeating tessellation using an irregular shape. M C Escher, an artist, made tessellations using identical irregular shapes, often of living things – there are pictures using fish, dogs, frogs, flying horses and many others.
Were there any shapes that would not fit at all? Work out what kind of extra shapes would be needed to make these tessellate – are these regular shapes? They can also be made using other shapes, including trapeziums and rhombuses. Tessellations don’t always have to use regular shapes. These can use equilateral triangles, squares, hexagons, octagons and dodecahedrons. Patterns that repeat but use more than one kind of regular shape are called semi-regular tessellations. These can only be made using three shapes – equilateral triangles, squares, or hexagons. Patterns using only one regular shape are called regular tessellations. Are there any that won’t create patterns of one kind of shape? Are there any that won’t create patterns of two or three kinds of shape? Try fitting these together, first using only one kind of shape, and then using repeating patterns of two or three different shapes. rhombuses (a diamond or a four-sided shape with four equal sides).trapeziums (four sided shapes with one pair of parallel sides).dodecahedrons (12 sides the same length).equilateral triangles (three sides the same length).Polygon, Interior Angle SumThe Magical 900: Making TessellationsĬarefully and accurately, cut out some regular shapes (shapes where all the sides are the same length) from paper or cardboard (it might make it clearer if different shapes are in different colours):
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