What it shows
A four-sided frame can collapse but a triangle cannot change shape without changing the length of a side. A dome of triangles is strong and light.
The science
A triangle is the only polygon that is rigid when its sides are fixed. A square or a rectangle can be squashed into a rhombus, but a triangle cannot. Engineers brace frames with diagonals to make them stiff. A geodesic dome is built from triangles that spread a load across the whole shell, so it can span a large area with very little material.
Materials
Cost: under Rs 50. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- About 50 drinking straws
- A packet of pipe cleaners or thread
- Scissors (adult help)
- A ruler
- A flat piece of card and a small light book for loading
- A tray
Safety
For this project: An adult must cut the straws. Cut pipe cleaner ends are sharp, so bend them in.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
Step by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Cut about 50 straws to exactly the same length, say 10 cm.
Make a triangle and a square using pipe cleaners as joints and press both sideways.
Add one diagonal straw to the square and press again.
Build a pentagon from five straws, then add five more straws from its corners up to one apex point, making a pentagon pyramid.
Add five new corner points below the pentagon: join each to two neighbouring corners of the pentagon with straws, then join the five new points to each other, to make a dome of 25 straws and 15 triangles.
Stand the dome on its five lower corners, lay the flat card on the apex and place a small light book on the card to see if it holds.
Make a cube frame of 12 straws with no diagonals, load it the same way and note how it leans and folds.
Count the vertices, edges and faces of the dome, counting the open base as one face, and write what you find.
What you should see
The square folds sideways but the braced one holds its shape; the dome carries a light book while the cube frame without diagonals leans over.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01Why is a triangle rigid?
Its shape is fixed by its three side lengths.
02How can you stiffen a square?
Add a diagonal.
03Where are domes used?
In stadiums, planetariums and old monuments.
04What does Euler’s formula say?
Vertices minus edges plus faces equals 2.
Take it further
Check Euler’s formula V minus E plus F equals 2 for your dome (11 vertices, 25 edges, 15 triangles plus the open base as one face).
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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