Alright, partially because of Evilpoptart's ambition in our Minecraft server, I started work on my first mega project.

I've always wanted to make a dodecahedron in Minecraft. The shape has a lot of symmetry being a platonic solid, and it would let me show my love for geometry.
Given Minecraft's voxel nature, I need to create the shape large enough that it can be identified as a dodecahedron easily. Also, since I want to use it as a part of my house, I should build it large enough to fit my needs.
First off, there's absolutely no way I could "eyeball" the creation of the dodecahedron. I could create a cube or an octahedron by "eyeballing", but I cannot do this for a dodecahedron. Therefore, I need to create a list of vertices that can be used to construct a dodecahedron.
Now, if you had a model dodecahedron in your hands, you could lay it on one of the pentagonal faces. Doing this places one face on the ground, one on the top, and ten others all facing different sides. The dodecahedron has twenty vertices, and placing a dodecahedron in this orientation allows one to easily identify the position of ten of those vertices. Five of them are on the ground, and the other five are sitting on the top, two inscribed radii above the ground pentagon (and rotated 180 degrees.)
As for the other ten vertices, I'll save the math and just link this article if you want to learn more. (You better remember your geometry if you want to understand):
http://www.kjmaclean.com/Geometry/dodecahedron.htmlFrom there, I created an excel spreadsheet that would give me all twenty vertices of a dodecahedron laying on one of its faces on the ground, given it's center and side-length:

I choose a side length of 26. It makes the dodecahedron large enough to be recognizable as a dodecahedron. I also choose the coordinates I did, as it would place the dodecahedron's bottom base on-level with the ground level in Minecraft, and the top within the normal limits of Minecraft maps. I also rounded off the coordinates for my own sanity.
Now, it takes more than the knowledge of where the vertices are to create the dodecahedron. Otherwise, all I would have are twenty floating blocks in the ground and sky showing me the vertices of a dodecahedron. I need to create the side lengths as well to create something that is recognizable. I could eyeball the lines from vertex to vertex, but that is not the best possible way.
Instead, I'm going to use what it called
Bresenham's Line algorith It's an algorithm made to create a line given a raster space. In other words, the algorithm will allow me to create straight lines in Minecraft.
A dodecahedron has thirty sides (more specifically, edges.) I created a simple program that ran Bresenham's algorithm on every edge, and outputted each line into different text files. Here's an example of one of those files:
29,86,21
29,87,20
30,87,19
30,88,18
30,89,17
31,89,16
31,90,15
31,91,14
32,91,13
32,92,12
32,93,11
33,93,10
33,94,9
33,95,8
34,95,7
34,96,6
34,97,5
35,97,4
35,98,3
35,99,2
36,99,1
36,100,0
As you can see, doing this gives me where to place the blocks in Minecraft to create every edge.
On the next post, I will detail gathering the blocks to create the structure, pictures during its creation, and finally I will have a video with Evilpoptart showing both of our houses. Evilpoptart has other mega-plans, and believe me they will show his true character. (However, you guys will probably not see any development pictures of his house, as seeing one picture would spoil the thing he did.)