135 60stars Astrology Season 6 Appendix 4 : Let the rhombus be a part of everyone's group!

60stars astrology

English version

By Tokyo-Tanuki

60stars Astrology Season 6

135　60stars Astrology Season 6 Appendix 4 : Let the rhombus be a part of everyone's group! 

1. Now, today we will talk about  "Rhombuses".

Tanu-chan drew this picture before.

(Fig.1)

When we look at the diagonals regular polyhedra, 

The 1's family: triangles and hexagons

The √2 family: quadrilaterals and octagons

The Φ family:  pentagons and decagons

Since I feel that a circle can also be a regular polyhedron (sphere), let's include π in that group.

So, I thought that π is also a member of 1, √2, and φ.

2.  But, in fact, if you think about it in terms of a rhombus,

A rhombus whose length and width is 1　　　　

This is a square, so we can make a cube.

A rhombus with length and width of 1:√2 (a rhombus with a silver/white ratio)　

Wow, we can make a beautiful dodecahedron.

Rhombus with length and width 1:φ (golden ratio)　　

Wow, we can make beautiful dodecahedrons, icosahedrons, and icosahedrons.

...and you can see that everyone of integers, √2, and φ get along well with each other.

Also, for example, we can make a 90-hedron by using a rhombus of the silver ratio and a rhombus of the Golden Ratio , so the lateral cooperation of them is also perfect.

3.  Now, there is π, who seems to be the friend who is left out of the group.

Tanu-chan has been thinking of a rhombus of 1:π (called a pi rhombus) and trying to find a way to get him to join our group.

I've been thinking about it for about six months, but it's not easy...

Of course, it doesn't have to be 1:π. 

At this point, √2:π or something like that would be fine.

Tanu-chan thinks that by combining rhombuses well, it is possible to make a polyhedron that looks like a sphere, but if possible, I would like to make a sphere, not like a sphere.

If you have found a good way, please let Tanu-chan know!

🌟　🌟　🌟　🌟

4. By the way, there is a reason besides the fact that I feel sorry for rhombuses.

Well, triangles, quadrilaterals, and pentagons have a relationship between side lengths and diagonals, each of which is

1 and  1

1 and √2

1 and  φ = (√5 + 1)/2

...Yes, I wrote before.

But something is missing, isn't it?

Yes, √3.

√3 comes up a bit later for the first time as a short diagonal of a regular hexagon.

... In terms of order, it's a bit late.

So, the famous rhombus,

(1) one whose ratio of diagonals is 1:√2

(2) one whose ratio of diagonals is 1:Φ

(3) one with the ratio of diagonals 1:√3

and some others,

but I think it is a good idea to include the (3) rhombus, which is an equilateral triangle attached to a regular polygon, in the group of regular polygons!

Then, if the side of the rhombus is 1, we will have a diagonal of √3, which is nice.

Furthermore, this rhombus also has that famous right triangle with 30° : 60° : 90° and length 1 vs. 2 vs. √3 built in, so it's full of goodies.

(Fig.2)

For the most part, rhombuses are symmetrical, so they can be considered more well-formed than regular pentagons, right?

5.  5. When I write it like this, maybe people will think,

"A rhombus doesn't have the same angles for each of its faces as a square or equilateral triangle!"

"There is no regular polyhedron corresponding to a rhombus!"

But, you know, if you look at just one face, it is true, but if you look carefully at the whole picture, you will see that there is a rhombus-like face.

Well, in other words, for example, there are many kinds of polyhedron, or  “ Da Vinci's Star”？？？？

.... Of course, if you say Tanu-chan is crazy, oh well, that's true.

Ultimately, the question is, what is a regular polyhedron in the first place?

...Anyway, the above is just my fantasy.

🌟　🌟　🌟　🌟

I'll probably start the second half of Season 6 (6-6 Middle East and Africa section - 6-9 Russia and Eastern Europe section), soon.

...If I don't start, guess why !

CHAO💕.

Tanu-chan💓　TOKYO-TANUKI💛