Triangle simulated sphere

Use a triangle to simulate a sphere. The degree of all nodes is 5 or 6, and the degree of 12 nodes is 5.

Proof:

There are x nodes with a degree of 5 and Y nodes with a degree of 6.

Number of vertices: X + Y.

Number of edges: (5x + 6y)/2 (handshake theorem. The sum of degrees is twice the sum of edges)

Use a triangle to simulate the characteristics of a sphere: each side is shared by two sides, so each side is divided into 1.5 sides. That is:

1.5 * number of sides = number of sides, so the number of sides: (2.5x + 3y) * 2/3

Using Euler's theorem: F + V-E = 2 (number of faces + number of vertices-Number of edges = 2), x = 12 can be obtained.

 

Note: football uses a positive Pentagon and a hexagonal shape to simulate a sphere.

Football has 32 skins, generally black and white, 12 pentagons, 20 hexagonal

Black is the positive Pentagon, white is the positive hexagonal

Set black skin x blocks, white skin 32-x blocks, number of vertices V, number of edges E, column equation:

5x + (32-x) * 6 = E * 2 (each side is shared by two skins)

5x + (32-x) * 6 = V * 3 (each vertex shares three skins)

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

X = 12

Therefore, the black Pentagon is 12 blocks, and the white hexagonal is 20 blocks.

In the above question, place the triangle in the Pentagon and hexagonal of the football, which is equivalent to 6 in the center of the hexagonal, and 5 in all other vertices.