Half turn or quarter turn?

In your book, Maths Mela (Chapter 10), there is a square cut into four equal smaller squares. The top-left and bottom-right parts are green; the top-right and bottom-left parts are pink. So matching colours sit in opposite corners.

Turn it 1/2 a turn. The top-left part goes to the bottom-right, and the top-right part goes to the bottom-left. Green lands on green and pink lands on pink, so the design looks the same. Now turn it just 1/4 of a turn. The top-left green part moves to the top-right corner, where pink used to be. The colours do not match, so it looks different. This design looks the same after 1/2 a turn but not after 1/4 of a turn. In one full turn it looks the same 2 times: after 1/2 a turn and after the full turn.

The book also shows a square cut by its two diagonals and its two middle lines into 8 equal triangles. Colour the triangles going round the centre: green, pink, green, pink, and so on. A 1/4 turn moves each triangle two places round, so green lands on green and pink on pink. This design looks the same after every 1/4 turn: after 1/4, 1/2, 3/4 and a full turn. That is 4 times in one full turn.

In the book's 'Making Designs', there is a circle in the middle. Above it and below it are two triangles, both pointing in towards the circle. To its left and right are two triangles, both pointing outwards. And there is one more circle further out, on the right side only. After 1/2 a turn, that extra circle would be on the left, where there is nothing, so the design has no rotational symmetry. If we add a circle further out on the left too, the design looks the same after 1/2 a turn.