SOLUTION: this formula is used to calculate the rotational angle of a pentagonal planar surface for the purpose of creating a dodecahedron using software: Blender: *180*acos(1/sqrt(5))/pi

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Question 1026571: this formula is used to calculate the rotational angle of a pentagonal planar surface for the purpose of creating a dodecahedron using software: Blender:
*180*acos(1/sqrt(5))/pi
it calculates the angle to be:
64.435
I would've thought the number inside "5" could be changed to calculate the rotational angle of other surfaces (hexagonal, square, so on).
The rotation of a square planar surface would be 90 deg.
That's not what the formula turns up.
I tried it in Excel using:
=180*ACOS(1/SQRT($C2))/3.14159G5
where the cell ($C2 - $C10) are populated with single incremental values
from 4 to 12.
The result for "5" is consistent with the above result.
The result for "4" is not.
It calls into question the accuracy of the results from 6 to 12 as well.
Since I don't understand the formula to begin with, and therefore am making assumptions in changing the variable, I don't know if it's a problem with the formula or my assumptions.
Is there a way to accurately calculate the rotational angles of planar surfaces of varying equal side lengths other than five?
If so, what would that formula be?
Say, for example a hexagon?
The end result here, using a square would be that four square planes rotated 90 degrees would form square walls. The floor of which would be square.
Likewise, using pentagons, lining them up, side by side, and rotating them each at 64.435 degrees, the end result is identical the square above, the floor would be a pentagon. And so on.
This web page should better, I hope illustrate the problem as well as point to the likely solution:
http://blender.stackexchange.com/questions/28829/set-edge-as-axis-for-surface-rotation
Thanx

Answer by ikleyn(52796)   (Show Source): You can put this solution on YOUR website!
.
this formula is used to calculate the rotational angle of a pentagonal planar surface for the purpose of creating a dodecahedron using software: Blender:
*180*acos(1/sqrt(5))/pi
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1. The formula used to calculate the rotational angle of a regular pentagon is  .

2. The formula in your post is incorrect.


3. And, surely, it is not applicable for a square.


4. You use wrong (incorrect) sources and make wrong (incorrect) conclusions.


5. All that you need is to calculate the central angle of your regular polygon.

   It is equal to    in radians or    in degrees, 
   where "n" is the number of sides/vertices of your regular polygon.


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