The classic version of soccer has several white faces and a few black faces

The soccer ball is made up of 32 black and white cowhides, the black blocks are pentagonal, the white blocks are hexagonal, the black blocks are 12, and the white blocks are 20.

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

A soccer ball has 32 pieces of skin, black and white, 12 black pieces are regular pentagons, and 20 white pieces are regular hexagons.

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 per edge).

5x+(32-x)*6=v*3 (3 skins per vertex).

v+32-e=2 (Euler's formula).

The solution is x=12

So 12 pieces of black skin and 20 pieces of white skin.

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.

A soccer ball has 32 pieces of skin, generally black and white, 12 pentagons, 20 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, bai12 pentagonal du, 20 hexagons.

The one that is black is positive. The five-sided zhi shape dao, and the white one is the 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

Each rib is shared by two pieces of skin).

5x+(32-x)*6=v*3

Each vertex is shared with 3 pieces of skin).

v+32-e=2

Euler's formula) is x=12

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

The soccer ball is made up of 12 black facets.

It is composed of 12 regular pentagons and 20 regular hexagons.

Because geometrically there is no regular 60 hedron in place.

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

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

Each rib is shared by two pieces of skin).

5x+(32-x)*6=v*3

Each vertex is shared with 3 pieces of skin).

v+32-e=2

Euler's formula) is x=12

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