Question

The cover of a soccer ball consists of interlocking regular pentagons and regular hexagons. Why can't they be interlocked in this pattern to tile a floor?

Answer 1

Answer: Because of gaps between the vertex of Pentagons and hexagon.

Step-by-step explanation:

The Pentagon has 5 sides and 5 vertex angles. While hexagon has 6 sides and six vertex angles

The sum of the angle of polygon is equal to ( n - 2 )180

Sum of the angle of a Pentagon will be: (5 - 2)×180 = 540

Each vertex angle of a Pentagon = 540/5 = 108

Sum of the angle of hexagon will be: (6 - 2)×180 = 720

Each vertex angle of a hexagon =

720/6 = 120

To interlock Pentagon and hexagon, the sum of the combination of vertex angles of both must be equal to 360 ( sum of the angles at a point = 360)

Since there is no number of combinations that can be equal to 360, there will surely be a gap.