A hexadecagon is the closest you can get to a circle when block modelling in Minecraft, although it seems like a lot of patience, a perfect regular hexadecagon can be made in Minecraft very easily
with the use of block modelling programs.
I will talk through the maths that I did in order to work out the measurements for the hexadecagon, and will discuss how to use them for creating hexadecagons in your own models.
Making this shape in Minecraft will require 8 elements (pictured on the right). I made the size of the sides of the hexadecagon 1. From here I can work out the other size for the elements.
I have cut down what we’re looking at to explain what is going on better. To work out the interior angles of any regular polygon you can draw lines from corners to the centre of the shape to form isosceles triangles. This will give you n triangles, to work out the angle x which will be the same for all triangles formed in this way is to divide 360 by n, where n is the number of sides of the polygon. x = 360/16 x = 22.5
As the triangles we have formed are isosceles the other 2 angles are the same. y = (180 – 22.5)/2 y = 78.75
From here I used an online triangle calculator to calculate the length of the other 2 sides in the triangle. The length is 2.563. I then created a larger triangle which consisited of the length of the element, (which I was trying to find) and one side of two isosceles triangles which were opposite each other in the hexadecagon p.
p is double the length of an isosceles triangle p = 2.563 x 2 p = 5.126 I again used the triangle calculator to find the length of the element, which worked out at 5.028.
This means you can create a perfect hexadecagon in Minecraft by using 5.028 x 1 elements, but this is actually a ratio, meaning you can use elements that are 10.056 x 2 or 15.084 x 3 (this is the size I used for the cauldron). You can use any size element as long as both measurements are multiplied by the same value.
If you wish to make a hexadecagon, akkechi has made some tutorial videos about constructing this shape in cubik studio over on the cubik studio forum simply change the values to be a ratio of 5.028:1.