How many black and white pentagons of a soccer ball

Solution: 5 white skins are sewn around each black skin, and the white skins have a total (including duplicates): =60 (blocks).

Next to each white skin there are 3 black skins, so it is double-counted 3 times, and the white skins have a total of: =20 (blocks).

Therefore, there are 32 pieces of black and white leather on the surface of the football.

After I was done, I thought: what if I give that there are 20 white skins, and find the number of black skins? Here's how to solve it:

Solution: 3 black skins are sewn around each white skin, and the black skins have a total (including duplicates): =60 (blocks).

There are 5 white skins sewn next to each black skin, so it is double-counted 5 times, and the black skins have a total of: =12 (blocks).

Therefore, there are 12 pieces of black skin on the surface of the football.

Thinking about it further, if you ask: There are 32 pieces of skin, how many black and white skins are there? Here's how to solve it:

Solution: There are x blocks of black skins, then there are (32-x) pieces of white skins sewn around each black skin, and each white skin is double-counted 3 times, and the white skins have a total of: (block).

32-x x=12

Number of white skins: 32-12=20 (blocks).

Therefore, there are 12 pieces of black skin and 20 pieces of white skin on the surface of the football.

So we've figured it out. But some people may ask: why does it have to be 12 pieces of black skin, 20 pieces of white skin?

That's a good question, and in order to prove it, I went to many shopping malls and found that all the soccer balls were made up of 12 black skins and 20 white skins, but they were different in size. Therefore, we can conclude that football is made up of 12 black skins, 20 white skins, and no more or less pieces.

A normal soccer ball is made up of 32 pieces of leather, 12 pieces of black regular pentagons and 20 pieces of white hexagons.

12 pieces of black.

20 pieces of white.

Oh, the Elementary School Olympiad did this.

There are 12 black pentagons and 20 white hexagons.

20 white hexagonal balls and 12 black pentagons Modern football originated in England Sheffield United was the first club to be founded in the history of football.

A total of 12 pentagons and 20 hexagons.

12 pieces of black pentagons.

20 pieces of white hexagons.

32 leathers, 12 pentagons, 20 hexagons.

The pentagon on a soccer ball is as long as the sides of a hexagon, and a soccer ball consists of 20 regular hexagons and 12 regular pentagons.

The inner angle of the regular pentagon is 108 degrees, and the inner angle of the hexagon is 120 degrees. The regular pentagons and hexagons can be divided into five congruent isosceles triangles with a vertex angle of 54 degrees (waist length is side length) and six equilateral triangles, respectively.

These triangular areas and approximations make up the spherical area. Therefore, let the side length be a has (1 2) * a 2 * sin (54 degrees) * 5 * 12 + (1 2) * a 2 * sin (60 degrees) * 6 * 20 = 4 * pai * 2 2

The solution shows that the length of the side a is about equal to meters.

The sides of a pentagon and a hexagon on a soccer ball are the same length.

12 - 6 sides.

20-5 sides.

Let's start with the black skin. How many edges does a child have: 12 5=60. These 60 edges are all sewn together with the white skin, and for the white skin: each piece is white.

Of the 6 sides of the skin, 3 of the edges are sewn together with the edges of the black skin, and the other 3 edges are sewn together with the other white skins, so half of all the sides of the white skin are sewn together with the black skin, so the white skin should have a total of 60 2 = 120 edges, 120 6 = 20, so there are 20 pieces of white skin.

Those who study chemistry should know that C60 is this structure!

The C60 molecule is a stable molecule formed by the combination of 60 carbon atoms, which has 60 vertices and 32 faces, of which 12 are.

Regular pentagon. 20 for.

Regular hexagon. It resembles a football, hence the name "Football".

Soccer olene. Football is also 12.

Pentagon and 20.

hexagonal composition.

The soccer ball has 32 pieces of leather, generally black and white, 12 pentagons and 20 hexagons.

The black ones are regular pentagons, and the white ones are regular hexagons.

Traditional football has 32 pieces of skin, 12 pieces.

Pentagon, 20 hexagons.

The soccer ball has 32 pieces of leather, generally black and white, 12 pieces of pentagons, 20 pieces of hexagons, black is a regular pentagon, and white is a regular hexagon.

Let the black skin x block, then the white skin 32 x block, the number of vertices v, the number of edges e, the column equation:

5x+(32-x)*6=e*2 (two skins for each edge), 5x+(32-x)*6=v*3 (for each vertex, 3 skins), v+32-e=2 (Euler's formula).

The solution is x=12

So the black skin pentagonal is 12 pieces, and the white skin hexagon is 20 pieces.

A soccer ball has 32 pieces of skin, generally black and white, 12 pieces of pentagons, 20 pieces of hexagons Black is a regular pentagon, white is a regular hexagon, set black skin x block, then white skin 32 x blocks, vertex number v, edge number e, column equation: 5x+(32-x)*6=e*2 (each edge is shared by two skins) 5x+(32-x)*6=v*3 (3 pieces per vertex.)

It is composed of 12 regular pentagons and 20 regular hexagons Because there is no regular 60 hexagon geometrically, a football has 32 skins, generally black and white, 12 pentagons, 20 hexagons Black is the old pentagon of Xunzi, and the white is a regular hexagon Set the black skin x block, then the white skin is 32 x blocks, the number of vertices v, the number of edges e, the column equation: 5x+(32-x)*6=e*2 (each edge is shared by two skins) 5x+(32-x)*6=v*3 (each vertex is shared with 3 skins) v+32-e=2 (Euler's formula) x=12 so the pentagons of the black skin are 12 pieces, and the hexagons of the white skin are 20 pieces.

Set the black skin to be 3x, and the white skin to be 5x

3x+5x=32

x=4 black skin is 3*4=12

White skin is 5*4=20

12 - 6 sides.

20-5 sides.

Let's count how many sides there are in the black skin: 12 5 = 60. These 60 edges are all sewn together with the white skin, for the white skin:

Of the 6 sides of each piece of white skin, 3 of the edges are sewn together with the edges of the black skin, and the other 3 edges are sewn together with the edges of the other white skins, so half of all the sides of the white skin are sewn together with the black skin, so the white skin should have a total of 60 2 = 120 sides, and 120 6 = 20, so there are 20 pieces of white skin.

Those who study chemistry should know that C60 is this structure!

The C60 molecule is a stable molecule formed by the combination of 60 carbon atoms, it has 60 vertices and 32 faces, of which 12 are regular pentagons and 20 are regular hexagons, it resembles a football, so it is also called football ene. The soccer ball is also made up of 12 pentagons and 20 hexagons.