Shapes that tessellate

In your book, Maths Mela (Chapter 7, Shapes and Patterns), we cover a floor or a wall with tiles. A pentagon is a shape with 5 sides. When all its sides are equal, it is a regular pentagon. Shapes whose sides are all equal are called regular shapes.

Put 3 regular pentagons around a point, corner to corner. A gap is left, but the gap is too small for a fourth pentagon. Pentagons cannot cover a floor without leaving gaps, so we say regular pentagons do not tessellate. To tessellate means to fit together around a point with no gap and no overlap.

A triangle with all three sides equal is an equilateral triangle, or regular triangle. 6 equilateral triangles fit around a point with no gap and no overlap, so equilateral triangles tessellate. Squares tessellate too: 4 squares fit around a point, because each corner of a square is a right angle and 4 right angles make a full turn. A fifth square cannot fit, because the 4 squares already go all the way round.

A regular hexagon has 6 equal sides. 3 regular hexagons fit around a point with no gap, so regular hexagons tessellate. A regular octagon has 8 equal sides. Regular octagons leave gaps between them, so they do not tessellate.