12 orthgons:---part6:Penton, understanding it

The Penton has a very interesting characteristic. see picture for the details.

I had studied the a little more and found you can get some central angel of those nonconstructive regular polygons.

I will show it in following articles.

12 orthogons---part 5: Penton

Penton is pentagon. It is most interesting orthogon among the 12s. It is confused me a long time for the ratio. I think the wiki ration might be wrong as I mentioned before. To check all the possible rectangle, the most like one is that the dark blue one in the picture. You can see it is same with 4 small rectangles. So the Bipeton has two possibilities also: one is 70° and another is 55.5°. this will explain the penton ratio reasonably.

12 orthogons---part4:Trion and Hecton

Trion and hecton are interesting. It is clear that the name comes from the triangle and hexagon. see picture for details. You might be noticed that the outside rectangle of Hexagon is the trion. So that why the internal rectangle is selected. the yellow square is the unit square. so the ratio is easy to understand.

12 orthogons---part 3: Auron

Auron is golden rectangle. it is no question. But for the Biauron, there is two possibilities, see picture for the details. In wiki, it is first one, but in other article, it is second one. I think second one may be more attractive.

12 orthogons----part 2: squre

most of the orthogons direct from the square or its orthogonal,that might be why call the "orthogons". In the picture, you can see 6 orthogons.

12 orthogons---part 1:review of the drawing method

I study 12 orthogons by chance and read wiki times to understand these drawing method. And I had found that there might be some mistake to explain the ratio for some of them.

I checked at internet and found one web which published the all 12 orthogons . It showed that my concern is correct. But the drawing method had a little mistake even the ration is correct. So I decided to redraw all these 12 orthogons. Most method is same except the Penton.

I will post the reason in following articles .