What is the 3d representation of hexagon?

How many sides would it have? I am thinking about a game but need to visualize a hexagon in 3d.

Originally posted by sonhouse
How many sides would it have? I am thinking about a game but need to visualize a hexagon in 3d.

I don't think your question is properly constrained to arrive at definitive answer, but I could be wrong.

Originally posted by joe shmo
I don't think your question is properly constrained to arrive at definitive answer, but I could be wrong.

Yeah, I googled it and found there is no such thing, icosahedron with 20 sides might be the nearest shape I can use for my game.

do you mean like, a all hexagon faces 3d thing?

Originally posted by Banana King
do you mean like, a all hexagon faces 3d thing?

I think that is impossible. I have to compromise.

Originally posted by sonhouse
I think that is impossible. I have to compromise.

Yeah it is impossible. Hexes make a plane. Pentagons make a dodecahedron. That's the best you can do.

Originally posted by sonhouse
How many sides would it have? I am thinking about a game but need to visualize a hexagon in 3d.

If you are envisioning a set of hexagons on a closed surface wherein a player can move from one to another, but if and only if the two share a side, you can possibly escape the problem of depicting the entire figure either mathematically or visually. In the design stage, designate the hexagons H1, H2,... and designate that they have sides H1a-f, H2a-f, etc. At a given 'move', specify the allowable moves in a list. An allowable move might have side H1a being also side H2d, so a player can get from H1 to H2 via that shared side. Of course other hexagons might be depicted as interfaced to H1 as options. Then, when a player reaches a position where he has a limited number of moves, you can visualize the moves as a graphic of the hexagons involved. After each move, the newly available hexagons are visualized and the one that was departed from may be deleted.

You can mix pentagons and hexagons nicely to make a football. You could see that as a 3-d shape formed from 20 hexagons and 12 pentagonal holes.

http://www.google.co.uk/search?q=soccer+ball&hl=en&prmd=ivns&tbm=isch&tbo=u&source=univ&sa=X&ei=8aG8TfO-MciWhQfA1aXLBQ&ved=0CDkQsAQ&biw=1253&bih=816

Originally posted by iamatiger
You can mix pentagons and hexagons nicely to make a football. You could see that as a 3-d shape formed from 20 hexagons and 12 pentagonal holes.

http://www.google.co.uk/search?q=soccer+ball&hl=en&prmd=ivns&tbm=isch&tbo=u&source=univ&sa=X&ei=8aG8TfO-MciWhQfA1aXLBQ&ved=0CDkQsAQ&biw=1253&bih=816

This could lead to a tremendous magnetised game!

Each hex would have 6 triangular squares, with each pent 5; all leading to the middle of the hex and pent.

A set number of pieces would need to be developed (probably 17 - and not necessarily chess pieces, but pieces[again well developed] that have speacial power taking abilities), and set on a well worked hex, and 2 pents to start off. The idea, colour coded, would be to get your pieces to the other side (colour coded faces for your piece target arrival). Maybe a set of key pieces would need to arrive on the other side, on set triangles to win, and without getting caught.

Just an initial idea 😉

-m.

The ball would need to be suspended, and the magnetism strong enough to keep the pieces attached as they move around.

Good idea?? 😲

I think such a game could perhaps be mounted a bit like a classical globe of the earth rather than suspended. Perhaps the pieces could be steel pegs, fitting into holes with permanent magnets at the bottom. That way they wouldn't all stick together in the box.

Originally posted by iamatiger
I think such a game could perhaps be mounted a bit like a classical globe of the earth rather than suspended. Perhaps the pieces could be steel pegs, fitting into holes with permanent magnets at the bottom. That way they wouldn't all stick together in the box.

This kind of game would clearly be better digital, no need for magnets and so forth, the magnets would be digital. So a similar question, cubes can be stacked on one another to completely fill a volume, but how many icosahedrons can you stack up with as many faces meeting as possible? Of course there would be voids but that is ok.

Originally posted by sonhouse
This kind of game would clearly be better digital, no need for magnets and so forth, the magnets would be digital. So a similar question, cubes can be stacked on one another to completely fill a volume, but how many icosahedrons can you stack up with as many faces meeting as possible? Of course there would be voids but that is ok.

Right. It has to work on a smart phone.

Originally posted by JS357
Right. It has to work on a smart phone.

I wonder what a house would look like if it was made of stacked isocahedrons?

Originally posted by sonhouse
I wonder what a house would look like if it was made of stacked isocahedrons?

Here is an image

http://www.steworks.com/oldcontent/archive/img1a16.html

It looks like if you put them edge on they tile the plane like hexagons, with another layer fitting on top (but not flush, my head can't work out how close, can anyone else?)

2 thirds of the way don the wikipedia entry:
http://en.wikipedia.org/wiki/Icosahedron

A dandelion-head like thing shows they stack very well if you let them get smaller as they go out from the middle.