**This tutorial is missing information about sloped planes & arbitrary polyhedra.**

Blocky shapes, such as squares and rectangles, are relatively easy to make in Minecraft, because of the fact that the world is made up of square blocks. On the other hand, other shapes, such as circles and triangles, are more difficult to make. Although there can never be a perfect circle or perfect triangle in the blocky world of Minecraft, this tutorial shows the closest to a circle or triangle you can make.

Any blocks can be used when making the shapes from this tutorial, with the exception of gravity blocks such as sand if the shape includes height as one of its dimensions.

Some helpful sites, listed up here for convenience:

- Circles: https://minecraft.fileion.com/circle-generator
- More circles: https://donatstudios.com/PixelCircleGenerator
- Spheres: https://oranj.io/blog/VoxelSphereGenerator (includes some hints on stair use)
- Several shapes and even buiding forms: https://www.plotz.co.uk

## Usage and Basics[]

Knowing how to build triangles and circles can be very beneficial if you build very often. Although knowing how to build these shapes will not help you at all with survival skills, when making statues, pixel art, house, and/or large fountains, adding triangles and circles to your building will give it much more depth.

Once you know how to build certain shapes, you can build an infinite number of things, and impress other players greatly. Some ideas include a statue made only of triangles, a mansion which looks like a giant sphere from the outside, or a giant oval arm. There are so many possibilities of things to build when you don't have to stick to building squares and rectangles - use your creativity!

The two main categories of shapes are 2-dimensional and 3-dimensional. 2-dimensional shapes consist of only 2 of the following: height, length, or width. 3-dimensional shapes consist of all 3. 3-dimensional shapes are usually either a combination of two different 2-dimensional shapes, or two 2-dimensional shapes of the same type but rotated different ways. To make specific shapes, read on.

## Angled lines[]

Line | Slope | Angle | Steps | Line | Slope | Angle | Steps |
---|---|---|---|---|---|---|---|

1/16 | 3.58° | 16, ... | 8/15 | 28.07 | 1, 2, 2, 2, 2, 2, 2, 2, ... | ||

1/15 | 3.81° | 15, ... | 7/13 | 28.30° | 1, 2, 2, 2, 2, 2, 2, ... | ||

1/14 | 4.09° | 14, ... | 6/11 | 28.61° | 1, 2, 2, 2, 2, 2, ... | ||

1/13 | 4.40° | 13, ... | 5/9 | 29.05° | 1, 2, 2, 2, 2, ... | ||

1/12 | 4.76° | 12, ... | 9/16 | 29.36° | 1, 2, 2, 2, 1, 2, 2, 2, 2, ... | ||

1/11 | 5.19° | 11, ... | 4/7 | 29.74° | 1, 2, 2, 2, ... | ||

1/10 | 5.71° | 10, ... | 7/12 | 30.26° | 1, 2, 2, 1, 2, 2, 2, ... | ||

1/9 | 6.34° | 9, ... | 3/5 | 30.96° | 1, 2, 2, ... | ||

1/8 | 7.13° | 8, ... | 8/13 | 31.61° | 1, 2, 1, 2, 2, 1, 2, 2, ... | ||

2/15 | 7.59° | 7, 8, ... | 5/8 | 32.01° | 1, 2, 1, 2, 2, ... | ||

1/7 | 8.13° | 7, ... | 7/11 | 32.47° | 1, 2, 1, 2, 1, 2, 2, ... | ||

2/13 | 8.75° | 6, 7, ... | 9/14 | 32.74° | 1, 2, 1, 2, 1, 2, 1, 2, 2, ... | ||

1/6 | 9.46° | 6, ... | 2/3 | 33.69° | 1, 2, ... | ||

2/11 | 10.30° | 5, 6, ... | 11/16 | 34.51° | 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ... | ||

3/16 | 10.62° | 5, 5, 6, ... | 9/13 | 34.70° | 1, 1, 2, 1, 2, 1, 2, 1, 2, ... | ||

1/5 | 11.31° | 5, ... | 7/10 | 34.99° | 1, 1, 2, 1, 2, 1, 2, ... | ||

3/14 | 12.09° | 4, 5, 5, ... | 5/7 | 35.54° | 1, 1, 2, 1, 2, ... | ||

2/9 | 12.53° | 4, 5, ... | 8/11 | 36.03° | 1, 1, 2, 1, 1, 2, 1, 2, ... | ||

3/13 | 12.99° | 4, 4, 5, ... | 11/15 | 36.25° | 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, ... | ||

1/4 | 14.04° | 4, ... | 3/4 | 36.86° | 1, 1, 2, ... | ||

4/15 | 14.93° | 3, 4, 4, 4, ... | 10/13 | 37.57° | 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, ... | ||

3/11 | 15.26° | 3, 4, 4, ... | 7/9 | 37.87° | 1, 1, 1, 2, 1, 1, 2, ... | ||

2/7 | 15.95° | 3, 4, ... | 11/14 | 38.16° | 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, ... | ||

3/10 | 16.70° | 3, 3, 4, ... | 4/5 | 38.66° | 1, 1, 1, 2, ... | ||

4/13 | 17.10° | 3, 3, 3, 4, ... | 13/16 | 39.09° | 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, ... | ||

5/16 | 17.35° | 3, 3, 3, 3, 4, ... | 9/11 | 39.29° | 1, 1, 1, 1, 2, 1, 1, 1, 2, ... | ||

1/3 | 18.43° | 3, ... | 5/6 | 39.81° | 1, 1, 1, 1, 2, ... | ||

5/14 | 19.65° | 2, 3, 3, 3, 3, ... | 11/13 | 40.24° | 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, ... | ||

4/11 | 19.98° | 2, 3, 3, 3, ... | 6/7 | 40.60° | 1, 1, 1, 1, 1, 2, ... | ||

3/8 | 20.56° | 2, 3, 3, ... | 13/15 | 40.91° | 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, ... | ||

5/13 | 21.04° | 2, 3, 2, 3, 3, ... | 7/8 | 41.19° | 1, 1, 1, 1, 1, 1, 2, ... | ||

2/5 | 21.80° | 2, 3, ... | 8/9 | 41.63° | 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

5/12 | 22.62° | 2, 2, 3, 2, 3, ... | 9/10 | 41.99° | 1, 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

3/7 | 23.20° | 2, 2, 3, ... | 10/11 | 42.27° | 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

7/16 | 23.63° | 2, 2, 2, 3, 2, 2, 3, ... | 11/12 | 42.51° | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

4/9 | 23.96° | 2, 2, 2, 3, ... | 12/13 | 42.71° | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

5/11 | 24.44° | 2, 2, 2, 2, 3, ... | 13/14 | 42.88° | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

6/13 | 24.78° | 2, 2, 2, 2, 2, 3, ... | 14/15 | 43.03° | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

7/15 | 25.02° | 2, 2, 2, 2, 2, 2, 3, ... | 15/16 | 43.15° | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, ... | ||

1/2 | 26.57° | 2, ... | 1 | 45.00° | 1, ... |

This table shows the segments of lines from angles 0 to 45 degrees. To create a line of arbitrary direction, find the angle or slope closest to what you want, then build the segment provided under Line. Build the next segment at the corner of the block and repeat as necessary.

For convenience, here are two links that will generate (approximately) the above sequences of steps:

- Set m=slope<=1. If you need a slope m>1, for example, m=8/5, use 1/m = 5/8 and instead of building horizontally, build vertical stacks of the given sequence.
- Set d=degrees<=45. Similarly, if you need an angle d>45, for example d=75, consider the complementary angle 90-d=15, and do the same as above.

Set the range for n as far as necessary for maximal accuracy, default is 1-20. The slope and angle chosen in the links are purposefully very close to each other, 3/17 = 0.176470588 and arctan(10 degrees) = 0.172792435, a difference small enough that won't be noticed for ~270 blocks. (Note arctan(3/17) ~= 10.007980degrees).

## 2-dimensional shapes[]

These 2-dimensional shapes have only length and height, or only length and width. Most 3-dimensional shapes are based on one or more 2-dimensional shapes.

*Note: Each of these demonstrations for the shapes only shows how the perimeter of the shape should look. If you would like, you can fill the center of the shape in. Also, remember that for the grids, the shapes will look wider than they really are.*

### Right Triangle[]

Right triangles are perhaps the easiest triangle to make, because of the fact that two of their sides are straight lines, going either vertical or horizontal. Only one side is diagonal. The following grids show how to make a right triangle with a 4 block base and height, and one with a 9 block base and height.

#### Right triangle extensions[]

You can make right triangles with different bases and heights, but they are harder to make, because they don't use an exact line for the diagonal side. The right triangle shown before is for a 45-degree diagonal side.

For a diagonal side with a 65 to 70 degree angle, repeatedly place 2 blocks upwards for the diagonal line, before going towards the vertical line, like so:

For a diagonal side with a 20 to 25 degree angle, repeatedly place 2 blocks horizontally for the diagonal line, before going towards the vertical line, like so:

For angles in between 25 and 45, and angles between 45 and 65, you must use combinations of patterns from both of the slopes that the angle is in between. (see Angled lines above)

### Equilateral Triangle[]

Equilateral triangles are a little bit more abstract than right triangles, but they still have a clear way to build them. First, build a line of blocks however long you want your triangle to be. Then, build one block up on the edges of the lines. Continue by building in sets of 2 blocks up, going 1 block inwards each time. Look at the following grids for examples:

Notice how the triangles look more triangular the bigger they are.

Triangles made in this way have angles of 70 degrees at the bases and 54 degrees atop, and the sides are 20% longer than the base. A true equilateral triangle has sides of 60 degrees, which can be approximated using the "angled lines" char above as a 30-degree angle from the perpendicular or vertical. This could be approximated by doing a 1-block segment every (alternately) two and three 2-block segments, but this may end up looking uneven, and the difference will only be apparent for fairly large triangles. A perfectly equilateral triangle is possible if it is not orthogonal to any of the coordinate axes, but rather orthogonal to the space diagonal of a block.

### Parabolas[]

Parabolas are conic sections that are U-shaped curves. A formula for a parabola is y = x^{2}. Using this, it is relatively simple to build. Just step 1 block, then increase the number of blocks by a constant.

### Circles[]

Circles are rather difficult to make in Minecraft, partially because of the fact that unlike triangles, there is not one way to make any size of circle; each size uses a completely different arrangement of blocks. As you look at the different sizes of circles, you will see that not all of them have the same shape, and none of them are a perfect circle. This is because different sizes of circles must have different arrangements of blocks, so that they can look as close to a circle as possible.

The pattern of blocks for every circle cannot be explained, because, like mentioned earlier, each size has a completely different pattern. The best way to make a circle is to just experiment with different block arrangements, or look at images made by other people who experimented with block arrangements and made a circle. The diagrams only show quarter circles; the full circles are obtained by reflecting the quarter-circles along the top and left edges. For circles with odd diameters, reflect along the center of the first line of blocks.

Even diameters

Odd diameters

You can use this generator to create other sizes. donatstudios.com

## 3-dimensional shapes[]

3-dimensional shapes are composed of length, width, and height, and are usually made up of either 1 or several 2-dimensional shapes. 3-dimensional shapes are often much more complex than 2-dimensional.

### Sphere[]

### Pyramid[]

To make a pyramid, first make a square and build a pillar in the middle to denote the height. Then start at the midpoint of one of the sides and build up by a number of blocks, and after every set of those blocks go in by one or two blocks and repeat until hitting the top. Then repeat on all 4 sides. Then, starting from the top, connect the 4 sides of each level of the pyramid with a square ring. Progress downward, each square bigger than the last, until hitting the bottom. For an even better pyramid, use stairs or slabs to smooth the angle. For a steeper pyramid, use a steeper angle, and vice versa.

### Cone[]

You can use a similar process as with a pyramid, but with circles instead. Start with a circular base and decrease the size of the circle as you go up. To create a concave or narrowing cone, increase the height of each layer as you rise. For a convex cone, start with thicker layers and decrease the height of each layer.

## Trivia[]

- If you have Microsoft Paint, or any similar art tool, you will have an easier job with drawing 2d shape blueprints in Minecraft. Select a shape from the tool bar and set it to be the thinnest setting. Then draw the shape, and zoom in all the way. You should be able to tell how the pixels are arranged, and that may help with building the shape in Minecraft.