Can you have a three-sided, three-dimensional shape?

Me and my friend were just discussing usual kind of things and somehow this came up in conversation. It seemed a simple enough question to ask ourselves but we found ourselves struggling to come up with any regular 3-dimensional shape with only 3 sides. The least we could imagine was four, a simple triangular based pyramid. So we decided to leave it there and I made a mental note to look it up on the internet when I got a chance.

Now i did a very small bit of research before trying to work it out, well actually I say research, i just found a forum online and had a read through, there seemed to be quite a few experts, or knowledgeable people there, which knew a thing or two about geometry and that sort of thing.

Lets try and answer this question in a simpler way first, can you have a regular 2-sided, 2-dimensional shape. So in this question we are looking for a regular 2-dimensional shape, by regular i mean like a square, a pentagon, an octagon. The fewest sides i can imagine a 2-dimensional shape having would be 3, a simple triangle. But you can say you can get a semicircle, where the curved edge counts as 1 side, and the flat edge as the second side. In which case you are then using a 1 dimensional line and a 2 dimensional curve to get your 2 sided object. So we conclude that you can only get a 2-sided, 2-dimensional shape using atleast one 2-dimensional curved line. And by only using 1-dimensional lines we can obtain only a three-sided shape as the least sided shape. Follow that? I’ve pretty lost managed to lose it myself just thinking about how to put it.

Definitely not 3 sided.

So, ignoring curved lines, the minimum sides for a 2-dimensional shape is made of 1-dimensional lines. Now if we think about a simple regular 3-dimensional shape, like say a cube, it is made of 2-dimensional squares. So we can guess that a regular 3-dimensional shape, ignoring curved surfaces, is only made of 2-dimensional surfaces. As a little added extra bit i’m just thinking does that mean that to get to a 4-dimensional shape we would need to make it out of these simple regular 3-dimensional shapes, ignoring curves? Hmmm that is an interesting thought. But impossible for me to imagine, and most humans i would hazard a guess.

So anyway, from there i tried to imagine a regular three-dimensional shape made of triangles…..I couldn’t……I retreated back to the forum. There i found someone had posted something about seeing a 3-dimensional object from one angle you could see 3 sides had to all interact at one point, or something like that i forget exactly what it was. But it got me thinking, when you look at a cube directly onto a corner you see 3 faces which all meet at that corner, so what if you could bend them all round again to interact at a corner on the other side? I couldn’t imagine it with a cube, but i quickly realized i could just think of a rugby ball, except with it having 3 curved surfaces instead of 4. I’d done it! I’d managed to imagine a 3-sided 3-dimensional object. Although i did have to bend the rules a bit, haha.

Only coincidental it says dimension on the ball, I was amused though

Imagine something like this, except the seems along the side would be much sharper and pointier. Kind of like how a 50p coin looks, curved but still with pointy edges.

I think i’ve come to the conclusion that:

  1. I can’t do research very well at all, and
  2. There is no 3-sided, 3-dimensional object which only uses 2-dimensional shapes.

I don’t like the use of curved surfaces, because it just feels like cheating, once I could break that invisible rule i kind of set for myself i found i could imagine many things, for example: a two-sided 3-dimensional shape would just be 2 intersecting spheres, and you could either use the non intersecting or intersecting parts to get your shape. And another simple 3-sided, 3-dimensional shape could be a cylinder, but it doesn’t look as nice. There you go, take what you will from that.

Here‘s a link to that forum i so reference. They start talking about hollow 3D shapes aswell, which i just completely ignored for my own purposes.