The Origami Forum

I was folding a piece of paper when I thought - is it possible to only have 5 points from a single square?

This becomes very difficult if you include all internal points and class a point as anything from 1-179 degrees.

Ive managed to make 5 points from a rectangle.

Maybe I'm completely missing something.

Has anyone done this?

Maybe I'm missing something - but a waterbomb base has 5 points (four 45-degree points and one 90-degree point).

Yes, Mark is right. The waterbomb base is the one that popped up in my head too.

saj

But then there are internal points created by the reverse folds.. These are inside the model.

It includes every point not just the ones you can see.

If by point you mean "vertex" or "corner", then a square has 4 points.
Folding one corner to the center (say), produces a pentagonal shape that has 5 points.

But the layer folded (the original corner of the square counts as a point.

not just the outside points any point from the entire peice of paper.

Well, your definition of "point" seems a trifle idiosyncratic. Take this example: fold a square in half from side to side. Now how many points does it have?

Considered as a traditional origami base, it has no points at all. By your definition, however, it has six.

But even with this definition it is still fairly easy to create 5 points from a square: fold in half along the diagonal, and then in half again. Voila: 5 points (one of which is hidden inside another one).

Yes technically my definition of a point isnt origami- like but that is the challenge.

However with the diagonal fold in half and then in half again there are 6 flaps as
there is a 90 degree flap at the bottom.
3 on the outside
and 1 hidden

Thanks for your time

Fold a square in half diagonally.
Unfold it.
Fold one edge of the square so that it lies along the crease you've just made.
Then, I think, you have five "points".

Unfortunately not

just tried it

you make a 5 sided shape which has 5 points and then there is the point that was folded in (the original corner of the square)

I think the challenge might be impossible as to make 1 extra point from a square means that other points will be created.

SO using my definition of a point I believe the challenge is impossible.

WAIT I JUST REALISED


I was wrong a few post back folding in half diagonally and the in half diagonnally again produces 5 points not 6.

Therefore this method does it.

So it is possible to make 5 points only fromn a single square by folding in half diagonally and then again diagonally.

Well done!

T wrote:Unfortunately not

just tried it

you make a 5 sided shape which has 5 points and then there is the point that was folded in (the original corner of the square)

I think the challenge might be impossible as to make 1 extra point from a square means that other points will be created.

SO using my definition of a point I believe the challenge is impossible.

I musn't have explained this very well - the method I describe produces a 4 sided shape with 4 points and a point (a corner) that is folded in.

I could describe the shape another way by saying that it looks like a kite base that has had one of its flaps unfolded.

And yes, Mark's method works too.

JMcK wrote: And yes, Mark's method works too.

Oops, just realised that it doesn't. It creates six points - two 45 degree ones, two 90 degree ones and two 112.5 degree ones.

Sorry, I should have realised that my instructions were ambiguous - I meant in half along the diagonal, and then in half again along the other diagonal. This gives a right angled triangle which is one quarter of the area of the original square. The points were correctly described by T:

there is a 90 degree flap at the bottom.
3 on the outside
and 1 hidden

T just made a slight error in saying that 1+3+1=6, before correcting himself.

Sorry, Mark; I see what you mean now.