Parametric shapes
Mathematical shapes in blocks: a hyperboloid tower of straight lines, a saddle roof, Gaudí arches, wavy facades, a Guggenheim ramp, a DNA tower, a Möbius strip and torus knots. Choose the shape and the sizes, and build it layer by layer. At the bottom you find every formula with the numbers of your design.
100% = narrowest point at the top, like a Shukhov tower.
0 = only at the bottom and the top.
Odd = one side, like a real Möbius strip.
Click a layer in the front or side view. Further back is darker; in the top view, lower is darker.
Build breakdown
Per layer, from top to bottom
Width is the number of columns from the first to the last block. Click a layer to view it.
| Layer | Width | Measure | Blocks |
|---|
Layer 1, row by row
| Row | Start | Pattern | Blocks |
|---|
Build tips
- First put a pole on the centre point, or for a facade a line along the foot. From there you count the columns and rows of every layer.
- Hyperboloids, hypars and catenaries stand by themselves. Floating shapes like a Möbius strip or a knot are built with scaffolding underneath that you remove later; the plinth carries the lowest point.
- Choose Closed if the shape has to keep out water or mobs. Thin uses fewer blocks and looks the same from a distance.
- A lattice of lines looks best in iron bars, chains or wall blocks. With colour bands along the shape you can see the straight lines of a hyperboloid or hypar extra well.
- In Minecraft a ramp climbs in steps of one block. Put stairs or slabs on the edges of each step for a smooth slope.
- Large shapes? Use the schematic download with WorldEdit or Litematica and build along with the hologram.
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 along with a hologram in Litematica.
Shopping list
Add the amounts of this design to your list, per colour and part. There you see everything together, converted to stacks and shulker boxes.
How it is calculated
History and fun facts
Straight lines, curved shape
A hyperboloid looks like an hourglass or a cooling tower, but it is made entirely of straight lines. The Russian engineer Vladimir Shukhov saw a chance in this in the 1890s. Straight steel bars are cheap and strong, and together they form a light, sturdy tower.
His best-known work is the Shukhov Tower in Moscow from 1922. The Kobe Port Tower in Japan (1963) and many power station cooling towers have this shape too. In Minecraft you see the straight lines best with iron bars or chains.
Hanging chains and Gaudí
In the 17th century, Robert Hooke found that a hanging chain, turned upside down, gives the strongest shape for an arch. This shape is called a catenary.
Antoni Gaudí used this idea in Barcelona. He hung chains with small bags of sand and looked at the model in a mirror, upside down. That is how he found the arches for his churches. The attic of Casa Milà has a row of white catenary arches, and the Sagrada Família is full of them.
Saddle roofs made of concrete
A hypar, or hyperbolic paraboloid, is a surface that curves like a saddle or a Pringles crisp. This surface can also be made from straight lines only. That means the formwork for concrete can be built with straight planks.
The architect Félix Candela built thin concrete shells in this shape in Mexico. A famous one is the Los Manantiales restaurant in Xochimilco from 1958. You can choose his umbrellas of four hypars on one column in this tool.
Spirals, helices and loops
The Guggenheim Museum in New York (1959) by Frank Lloyd Wright is one long spiral ramp. You walk upward past the art. Parking garages use the same idea.
We know the double helix from DNA. James Watson and Francis Crick described that shape in 1953, partly based on X-ray images by Rosalind Franklin. A Möbius strip, which has only one side, was described in 1858 by August Möbius and Johann Listing. Torus knots are loops that wind around a doughnut shape.
Parametric design
Today, architects draw shapes with formulas on a computer. Change one number and the whole shape changes. This is called parametric design. Zaha Hadid became world famous for it, with flowing buildings such as the Heydar Aliyev Center in Baku.
This tool works the same way. You pick a shape and a few numbers, and the formula works out every layer in blocks. At the bottom of the page you can see the formula with your numbers.
Did you know?
- The Shukhov Tower in Moscow was built in 1922 as a radio tower.
- A Möbius strip has only one side and one edge. If you cut it along the middle, you get one long loop instead of two.
- The Gateway Arch in St. Louis (1965) has the shape of a catenary and is 192 metres tall.
- Gaudí worked on the Sagrada Família from 1883 until his death in 1926.
- The Guggenheim Museum in New York opened in 1959, half a year after Frank Lloyd Wright died.
- A trefoil knot is the simplest real knot. As a torus knot it goes 2 times around the axis and 3 times through the hole.
About this tool
With this Minecraft shape generator you build mathematical shapes from blocks. Choose a hyperboloid (a tower of straight lines), a saddle-shaped hypar roof, a catenary arch, vault or dome, a wavy facade, a spiral ramp, a double helix like DNA, a Möbius strip or a torus knot.
Each shape has its own measurements, such as the radius and waist of a hyperboloid, the span and height of an arch, the wavelength of a facade or the number of half twists in a Möbius strip. You choose a solid wall or a lattice, the thickness, a base and colour bands along the height, around the shape or along the shape. More than twenty examples help you get started, from the Shukhov Tower and a Pringle roof to a Gaudí arch, the Guggenheim ramp and a trefoil knot.
The layer plan shows every row of blocks. You can view the shape in 3D and from the front, the side and above. The tool counts the blocks per colour and part and converts them into stacks. At the bottom you find every formula with the numbers of your design, so you can see how the shape is made.
With the block palette you pick your own blocks, and with the .schem download you paste the shape into your world with WorldEdit or Litematica. This tool is for builders who want something special, such as a Minecraft hyperboloid tower, a modern art piece in your city or a vault in the style of Gaudí.
Frequently asked questions
What is a hyperboloid and how do I build one?
A hyperboloid is a tower that is narrower in the middle, like an hourglass or a cooling tower. It is made of straight lines that run diagonally around each other. Choose the Hyperboloid shape, set the bottom radius and the waist, and build layer by layer. With Lattice as the fill, the lines show best.
How do I build a floating Möbius strip or knot?
Build a scaffold below the shape, for example from scaffolding or dirt, and remove it later. Turn on the base: it supports the lowest point. In Minecraft most blocks do not fall, so the shape just stays in place once it is finished.
What is the difference between Closed and Thin?
With Closed, blocks also connect at the diagonals, so there are no gaps. Choose this if the shape must hold back water or mobs. Thin uses fewer blocks and looks the same from a distance.
How do I make a smooth ramp?
In Minecraft a slope always goes up in steps of one block. Place stairs or slabs on the edges of each step. Then the ramp becomes smooth enough to walk up without jumping.
How many blocks do I need?
At the top you see the total, in stacks, the size and the busiest layer. With Add to my list, you put the counts per colour and part on your shopping list, converted into stacks and shulker boxes.
Can I build this in Bedrock?
Yes, with the layer plan, which works in every edition. The .schem file is for Java Edition with WorldEdit or Litematica. For large shapes that saves a lot of work.