There are a lot of six sided pieces on the soccer ball, white and black

It is made up of 12 regular pentagons and 20 regular hexagons Because there are no regular 60 hexagons geometrically. A soccer ball has 32 skins, usually black and white, 12 pentagons, 20 hexagons Black is a regular pentagon, white is a regular hexagon. Let the black skin x block, then the white skin 32 x blocks, the number of vertices v, the number of edges e, the column equation: 5x+(32-x)*6=e*2 (two skins per edge) 5x+(32-x)*6=v*3 (3 skins per vertex) v+32- e=2 (Euler's formula) The solution gives x=12 so the black hexagon is 12 and the white hexagon is 20.

Trouble, thanks!

There are 32 pieces of leather on the surface of the football; 20 regular hexagons, 12 regular pentagons; The two polygons have equal side lengths; The area of a regular hexagon is comparatively larger; There are many different patterns to put together a football, not just black and white, you can get it.

Take a look at the top 10 classic match balls in world football.

The pentagonal shape is surrounded by hexagons, then there are 60 points on a football, and they participate in the formation of 12 pentagons and n hexagons, and each point extends three lines, so there are a total of 60*3 2=90 from Euler's theorem 60+12+n-90=2 to get n=20, so there are 20 pieces of white skin.

If you look at football today, you won't have that question.

The white one is hexagonal, and the black one is pentagonal.

If the soccer ball has x black pentagons, then there is a white hexagon.

32-x) pcs.

Football Stitching Rules:

All 5 sides of the pentagonal shape are stitched with the hexagon, and only 3 sides of the hexagon are stitched with the pentagon.

So: the number of splits in a pentagon multiplied by 5 should be equal to the number of hexagons multiplied by 3

i.e.: 5x = 3 (32-x).

5x=96-3x

8x=96x=12

Answer: The soccer ball has 12 pieces in the shape of a black pentagonal ode and 20 pieces in a white hexagon.

Categories: Sports Sports >> Football.

Problem description: There are two kinds of black and white in football, black five-sided, white six-sided, black twelve, how many white pieces?

Analysis: 20 pieces of white noodles!

According to Euler's theorem, for each polyhedron, the number of edges = the number of vertices + the number of faces - 2.

There are x white blocks. Then the number of sides is (12*5+6x) 2, black is 5 sides, 12 blocks, a total of 60 vertices, and the number of faces is (x+12).

Substituting the above formula.

12*5+6x) 2=60+(x+12)-2 to get x=20

Of course, you can also think of it this way: each black block is surrounded by 5 white blocks, and each white block is surrounded by 3 black blocks, and their ratio is 3; 5. The white block is 20 pieces.

If the soccer ball has x black pentagons, then there are white hexagons (32-x) soccer ball stitching rules:

All 5 sides of the pentagon are stitched to the hexagon, and only 3 sides of the hexagon are stitched to the pentagon.

So: the number of pentagons multiplied by 5 should be equal to the number of hexagons multiplied by 3

i.e.: 5x = 3 (32-x).

5x=96-3x

8x=96x=12

Answer: The soccer ball has 12 black pentagons and 20 white hexagons.

The black block is pentagonal and the white block is hexagonal, and the five sides of each black skin are sewn together with one side of the five white skins. The three sides of each white skin are sewn together with the three black skins. Therefore, the 12 pieces of black skin on the surface of the closed football are closely connected with several pieces of white skin, and there will be no remaining or missing sides of the white skin and black skin.

If there are x blocks in the white skin, then it has a total of 6x edges, and in the 6x edges, one of the sides is the white skin and the white skin is connected to the white skin, and the other part is the white skin and the black skin are connected, obviously, there are 3x edges connected to the black skin. Solution: If the white skin has x blocks, then it has 6x edges.

The number of edges stitched together with the black skin is 3x. It has been counted that there are 12 black skins, and each black skin has 5 sides, so the black skin has a total of 5 12 = 60 sides. According to the title, it is called:

3x=60.Solve this equation and get x=20Therefore, there are a total of 20 pieces of white skin.

Black is a pentagon, white is a hexagon, let black be x, white is y, there are a total of 32 footballs, i.e.: x+y=32 Since there are five hexagons around each pentagon, 5x is counted as the number of blocks of the hexagon, and there are duplicates of each hexagon connected to three pentagons, i.e. each hexagon is counted three times, so 5x=3y is solved x=12, y=20

It's 20 pieces. There are 5 pieces of white skin around a black skin, and one piece of white skin is shared by three pieces of black skin, so a simple calculation can be 20 pieces.

Let there be x white blocks, and the black edges are 12 5 = 60 (bars), and each white block has three sides that must be connected to the black edges, then there must be 60 white edges first, because the white block has six sides, so there are three sides that are not connected to the black edges, so the white edges are a total of 60 2 = 120 (strips), then the white block is a hexagon, that is, 6x=120, then x=20, I think the arithmetic method can come out, and the equation is really this, that is, 20 white blocks.

Black is a pentagon, white is a hexagon, let black be x, white is y, there are a total of 32 footballs, i.e.: x+y=32 Since there are five hexagons around each pentagon, 5x is counted as the number of blocks of the hexagon, and there are duplicates of each hexagon connected to three pentagons, i.e. each hexagon is counted three times, so 5x=3y is solved x=12, y=20

Let the black leather block be an x block, then the white leather block is a (32-x) block, and according to the black leather block is a regular pentagon.

The white leather block is a regular hexagonal trapped judgment to give way.

It can be seen that the black leather block has a total of 5x edges, and the white leather block has a total of 6 (32-x) smooth edges. According to the appearance of the football, it can be seen that some of the edges of the white leather and the white leather are sewn together.

So: 2 5x = 6 (32-x).

Solution: x=12, so 32-12=20, 12 black leathers, 20 white leathers.