Geodesic dome triangles

[205alive]

I'm constructing a geodesic dome from cardboard. The first of the two triangles I'm using is equilateral with a side length of 345mm and height of 300mm. The second should be isocelean (sic?), with one side being the same 345mm - but what should the remaining side lengths be?

Can anyone give me the easiest formula to determine the unknown side lengths, please?

[Liszt]

How does an equilateral triangle have different length sides?

[205alive]

Perpendicular height.

[mph1977]

Liszt said:

How does an equilateral triangle have different length sides?

as 205alive posted 2 minutes after your original post, the perpendicular height ...

apologies if this is due to smartphone related duplication

[Devil2575]

Liszt said:

How does an equilateral triangle have different length sides?

It doesn't.

It's sides are 345mm which means that it's height is 300mm i.e. vertical line from middle of one side to the intersection of the other two lines (298.77mm actually)

[Devil2575]

Does the size of the second triangle not depend on how big you wish to make the dome?

[Devil2575]

http://science.howstuffworks.com/engineering/struc...

According to this link you only need one one size of equilateral triangle.

[205alive]

Devil2575 said:

Does the size of the second triangle not depend on how big you wish to make the dome?

Er...pass!

[205alive]

Devil2575 said:

http://science.howstuffworks.com/engineering/struc...

According to this link you only need one one size of equilateral triangle.

So it does, paragraph six line two - thanks for that, been a bit confused - I found a good geodesic model for google sketchup, but the two triangles used in the model definitely have different areas, according to the face/component/etc info you can bring up.

Will find out tomorrow when I set about my cardboard triangles.

[Devil2575]

Post a picture when you're finished!

[Simpo Two]

Something has to be different; if you just stuck identical equilateral triangles together you'd make hexagons and get a flat plane not a dome... I think...

[mph1977]

Simpo Two said:

Something has to be different; if you just stuck identical equilateral triangles together you'd make hexagons and get a flat plane not a dome... I think...

However that assumes you are working in only two dimensions

a leather football is made up of flat pieces of leather be they the strips / bananas layout or the mixture of hexagons and pentagons ...

[Simpo Two]

mph1977 said:

mixture of hexagons and pentagons ...

Precisely - not all the same. Also the material is flexible and pressure is applied from one side to distort it.

To make a dome you need something rigid so you're subject to pure geometry. It either works out flat or it doesn't

[Flibble]

Simpo Two said:

Something has to be different; if you just stuck identical equilateral triangles together you'd make hexagons and get a flat plane not a dome... I think...

Depends how many you stick together, sticking 6 together gives a flat hexagon, if you stick 5 together though you get a wide cone shape, 4 gives an open ended pyramid, 3 an open ended tetrahedron.
You can make icosahedrons, octahedrons and tetrahedrons from just identical triangles, so you could make a simple dome from a truncated icosahedron for instance.

[205alive]

Just to update, it hasn't really worked out so far and, despite the ray of false hope offered yesterday, looks like common geodesic wisdom is suggesting it won't happen.

I did get an icosahedron out of it, as well as various more useless structures. Will have another crack tomorrow just in case there is the possibility of even knocking a third of a sphere up, as I would consider that a small but exciting success, given the current status of my life/empty void.

[Simpo Two]

205alive said:

I did get an icosahedron out of it, as well as various more useless structures. Will have another crack tomorrow just in case there is the possibility of even knocking a third of a sphere up

You might end up inventing a completely new shape, and call it a 205aliveagon

Perhpas it will be the shape they beat the can of pineapple chunks into in 'Three Men in a Boat'...

[205alive]

In view of the results, steohedron is more appropriate (rhymes with 'light'). Never mind.