Let’s make something!
2D to 3D
fold more complex objects
In the last tutorial, you learned how to fold more complex 3d objects with up to 20 faces. Now you can take this further: so many faces that it actually starts to look like a sphere!
When a 3d object has more than 12 faces, it’s not easy to sketch your own 2d shape for folding.
The best way to make flat shapes for more than 8 faces is with help of a computer 3d-model program. If you make a 3d object in these programs, they can ‘unfold’ it for you to print + fold + glue (they even include all the glue tabs)
But even if a computer can make a complex folding pattern for you, it can be impossible to know what edges should be glued together. 16
19
22
3
1
7
20 20
18 18
This is why the computer program also includes matching numbers next to all the edges. (that way you know that #2 matches with #2, and #433 matches with #433).
For this tutorial, we already made a folding pattern that you can just cut out (see the last page). It’s a pattern for a 50-sided volume, called a pentacontagon.
Just like the simpler shapes that you cut before, this flat shape has many edges that need folding, and only a few need to be glued together. Which edges need to be glued, depends on the way that the shape was drawn (any volume can be drawn in different ways).
In this shape, you’ll have to glue 26 pairs of edges (that’s why its numbers are 1-26).
Also, you might notice: the 3d volume will end up being pretty tiny! Why? Because in order to fit all of the faces in one piece of paper, it all needs to be tiny. How do you make it bigger? By printing it on a larger sheet of paper.
You can also make it bigger by making the drawing larger and then splitting it into smaller pieces. You will learn all about this in future tutorials.
polygon names:
Once polygons start getting complex (around 8 faces), it’s still easy to remember their names: 8= octahedron, 12 = dodecahedron, 20= icosahedron. But what do you do when it gets to 50 or hundreds of faces? Easy. There is a naming table: (see how 50 is called ‘pentacontagon’) HUNDREDS
TENS
ONES
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
-hecta-dihecta-trihecta-tetrahecta-pentahecta-hexahecta-heptahecta-octahecta-enneahecta-
-deca-icosi-triaconta-tetraconta-pentaconta-hexaconta-heptaconta-octaconta-enneaconta-
-hena-di-tri-tetra-penta-hexa-hepta-octa-ennea-
All of these are Greek words. If you look carefully, you can start to understand what they mean. You can see the word ‘tetra’ (4)in ‘tetraconta’) 40, because tetraconta means ‘four-tens’ (so conta means ‘tens’). And some are words that you have seen somewhere else. For example, ‘tri’ is part of the word tricycle (3 wheels). And ‘octo’ is part of the word ‘octopus’ (8 tentacles).
-gon
9
9
26
23
23
17
15
13
19 21
16 14 5 20
2
8 11
6
4
4 10
17
15
13
10
25
18
3
22
24
7
24
12 5
21
25
14
12
2
20
19
18
8
1
11
6
3
1
16
7
22 26