MATHS Answer the following (2 mark each) :

self

Yes, regular hexagons can fit together around a point without any gaps or overlaps. Three hexagon fit perfectly around one central point, like pieces of a puzzle. They touch each other neatly without any empty spaces in between, and they don’t pile up on top of each other.

Row 1 — 2 over, 1 under, 2 over, 1 under, … (repeat).
Row 2 — 1 under (do not repeat), 3 over, 3 under, 3 over, 3 under, … (repeat).
Row 3 — 2 under, 1 over, 2 under, … (repeat).
Row 4 — 1 over (do not repeat), 3 under, 3 over … (repeat). Continue weaving in this order.

Let us try to understand how this mat is woven by looking at the pattern in the first two rows.
Row 1 — 2 over, 1 under, 2 over, 1 under, …
Row 2 — 2 under, 1 over, 2 under, 1 over, …
You can use strips of the same colour or 2 different colours, one for each row.

self

Yes, there are a few other types of shapes where all faces are identical. These are known as platonic solids. Besides the icosahedron and dodecahedron, the other platonic solids are:
→ Tetrahedron: 4 faces, all are equilateral triangles.
→ Cube: 6 faces, all are squares.
→ Octahedron: 8 faces, all are equilateral triangles.

14

5

yes

zero

many

4

20

octagon

rhombus

12

8

6

6

(a) 2
(b) 2

more faces-icosahedron.

self

Square, hexagon

Hexagon

Rhombus

Equilateral triangle

No, it cannot fit without overlap.