Polygon planner
Hexagons, octagons and other polygons for towers and floors. Choose the number of sides and the width, then build it row by row. Click blocks you have already placed to keep track of your progress.
Build pattern
Sides
| Side | Blocks | Steps along the side |
|---|
Click a side to see it on the grid and in the explanation below. A corner block counts for both sides that meet there.
Row by row
| Row | Start | Pattern | Blocks |
|---|
Build tips
- Mark the centre first and count from there to the corners. The list of corners at the bottom tells you which column and row each corner is in.
- Then build side by side. A sloping side is made of steps; follow the numbers in the Sides table.
- Sides with the same slope have the same pattern, only mirrored. On an octagon with a side up, the four straight sides are the same and so are the four sloping ones.
- For a tower, finish the first layer completely. After that every layer goes straight up.
- An even number of sides with a side up gives straight sides that run neatly along the grid. An odd number of sides is never fully symmetrical both left to right and top to bottom.
3D and layer-by-layer build plan
To Minecraft
Download the design as a schematic file and paste it into your world with WorldEdit, or build it from a hologram in Litematica.
Shopping list
Add the amounts for this design to your list. There you see everything together, converted to stacks and shulker boxes.
How it is calculated
History and fun facts
Regular polygons in ancient Greece
A regular polygon has sides that are all the same length and angles that are all the same size. Around 300 BC Euclid showed how to draw a triangle, square, pentagon and hexagon with only a compass and a straightedge.
Much later, in 1796, the young Carl Friedrich Gauss proved that a 17-sided polygon can be drawn this way too. He was so proud of it that he decided to become a mathematician.
Octagons in churches and castles
Builders often chose an octagon as a step between a square and a circle. The Dome of the Rock in Jerusalem, from 691, has an octagonal floor plan. Many baptisteries, such as the Baptistery of Florence, are octagonal as well.
Castel del Monte in southern Italy was built in the 13th century for Emperor Frederick II. It is an octagon with an octagonal tower on every corner.
Hexagons in nature
Bees build their honeycomb from hexagons. That way the cells fit together without gaps and use little wax.
At the Giant's Causeway in Northern Ireland there are thousands of basalt columns. Most of them have six sides. In Minecraft, hexagonal floors and towers are popular for the same reason: they look round and are still easy to build.
Why a polygon in blocks is tricky
A straight side along the grid is easy. A sloped side becomes a series of steps, like a pixel line on a screen.
The tool first calculates the real corner points. Then it picks, row by row, the blocks closest to each line. Sides with the same slope get the same pattern, only mirrored.
Where you use polygons in Minecraft
Octagonal towers suit castles and lighthouses. Hexagons look good for garden pavilions, fountains and sci-fi buildings.
A polygon with many sides looks almost like a circle, but it has straight parts where windows and doors fit easily.
Did you know?
- The Dome of the Rock in Jerusalem was completed in 691 and has an octagonal floor plan.
- Castel del Monte has eight octagonal towers around an octagonal courtyard.
- Carl Friedrich Gauss was 18 when he found in 1796 how to construct a regular 17-sided polygon.
- The Pentagon near Washington is a five-sided building and opened in 1943.
- Honeycomb is made of hexagonal cells.
- In many countries a stop sign is an octagon.
About this tool
The Polygon Planner is a free Minecraft polygon generator for hexagons, octagons and other shapes with 3 to 12 sides. You choose the number of sides and the width over the points, from 5 to 200 blocks.
With Orientation you choose Point up or Side up. For the shape you pick a thin outline, a thick outline or a filled floor. You also set the wall thickness yourself. With the layers option you turn it into an octagonal tower in one go.
The Sides table shows how many blocks each side has and which steps a sloped side uses. Click a side to see it in the grid. The row-by-row list tells you where each row starts and how many blocks to place. Click placed blocks to keep track of your progress.
The 3D view and the layer-by-layer build plan show the result from every side. With the block palette you use up to 12 block types. The materials calculator converts everything to stacks and shulker boxes.
You can download the design as a .schem file for WorldEdit or Litematica. It is handy for anyone who wants to build a Minecraft hexagon or octagon without doing the maths.
Frequently asked questions
How do I build an octagon in Minecraft?
Choose 8 sides and set Orientation to Side up. Then the four straight sides are equal and so are the four sloped sides. Mark the center first, count out to the corner points from the list, and then build side by side.
Why is my pentagon not symmetrical?
A polygon with an odd number of sides is never the same left-to-right and top-to-bottom at once. It is the same on the left and right when a point or side is exactly at the top. That is maths, not a bug in the tool.
What does width over the points mean?
That is the distance from one corner to the opposite corner, through the middle. It is the largest size of the polygon. With Side up, the width from side to side is a bit smaller.
How do I make a hexagonal tower?
Choose 6 sides, a thick outline and the number of layers you want. Finish the first layer completely. After that every layer goes straight up. For the roof you can use the tower roof planner with a similar width.
How many blocks do I need?
At the top you see the count per layer and the total, also in stacks. A corner block counts only once, even though it belongs to two sides. With the Add to my list button you add it to your other designs.
Can I build this in Bedrock?
Yes, the grid and the row-by-row list work in every edition. The .schem file is meant for Java Edition with WorldEdit or Litematica.