Geometric triangles, quadrilaterals, pentagons, hexagons, octagons, etc., are the earliest figures we know in school, and they are also geometric shapes that we often see in our daily lives, and we call them polygons. And polygons with equal lengths for each side and equal size for each corner are called regular polygons. Such as: regular triangle, square, regular pentagon, regular hexagon, regular octagon, etc.
Theoretically, such regular polygons, which are equal in length per edge and equal in size in each corner, can be infinitely numerous, but as the number of edges increases, they get closer and closer to a circle.
When discussing regular polyhedra, each face on a regular polyhedra must be equal, in addition to the edges and angles being equal. Unlike regular polygons, the types of regular polyhedra are not infinite.
According to Euler's formula number of faces + number of vertices - prismatic number = 2. It can be rigorously proved that there are and only five types of regular polyhedra: regular tetrahedron, regular hexahedron, regular octahedron, regular dodecahedron, and regular icosahedron.
Four equal regular triangles form a regular tetrahedron;
6 equal squares make up a regular hexahedron;
8 fully equal regular triangles form a regular octahedron;
12 fully equal regular pentagons form a regular 12-sided body;
The 20 equal positive triangles form a regular 20-sided body.
For example, the crystals of table salt are regular hexahedron, the crystals of alum are regular octahedron, and the new coronavirus is regular icosahedron.
Some of the special properties of regular 6-sided, regular 8-sided, regular 12-sided, and regular 20-sided are listed below:
1。 The regular 12-sided and regular 20-sided bodies bound to the same ball have equal surface circumference.
2。 If the regular 12-sided body and the positive 20-faceted body are connected to the same ball, then the ratio of volume to the two is equal to the ratio of the surface area.
3。 The volume of the regular 12-sided body attached to the same sphere is greater than the volume of the positive 20-sided body, and the volume of the regular 6-sided body is greater than the volume of the positive 8-sided body.
4。 The regular 12-sided body and the regular 20-sided body that are connected to the same ball have a common inner receiving ball, and the regular 6-sided body and the regular 8-sided body also have a common inner receiving ball.
5。 If the regular 12-sided body, the regular 20-sided body and the regular 6-faceted body are connected to the same sphere, then the ratio of the volume of the regular 12-lacedron to the volume of the positive 20-sided body is equal to the ratio of the side length of the regular 6-sided body to the side length of the regular 20-sided body.
In fact, the Platonic cube has other, deeper connotations. We only analyze from the number here, these five regular polyhedra its face number contains 4, 6, 8, 12, 20 five numbers, the product obtained by multiplying these five numbers is equal to 46080, after reading the article "Shen Liu Theory and Technical Application (II): Deciphering the Hidden Magic of Shen Liu", we can know that this number is the product number 46080, which implies the operation law and mystery of life, is this also a coincidence?
Through mathematical analysis and calculation, it is shown that with 6 as the base, the four numbers of 42, 64, 720 and 46080 can be obtained.
I call them cardinality 6, sum number 42, product number 46080, explicit number 64, hidden number 720.
The great sage Lao Tzu of the East gave the numbers 6 and 42, and the great sage of the West, Plato, told 46080. Now that 3 of the five numbers have been deciphered, it is getting closer and closer to the truth of the world. Five counts together, there will be a miracle!
So who controls the other two? Where to look for it? Can you guess?
Next article I will take you with me to find the final answer. Continue the legend!
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