luc_pop

11-02-2001, 01:29 AM

Does anyone know a algorithm to make a sphere out of hexagons?

thank you

thank you

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luc_pop

11-02-2001, 01:29 AM

Does anyone know a algorithm to make a sphere out of hexagons?

thank you

thank you

11-02-2001, 05:00 PM

I know no particular algorithm, per se, but I do know a bit about tiling the sphere with hexagons. Time for a crash course.

First, it's not actually possible to make a convex polyhedron out of just hexagons. You need exactly 12 pentagons or something similar. With that stipulation, there are a lot of ways to make a hexagon-pentagon. I'll describe the two simplest ways.

The first way involves a polyhedron knwon as a rhombic triacontahedron (triaconta meaning 30). The coordinates of the vertices of a RTCH are: (1,phi,0) in all forms that don't reverse the order, (phi,1/phi,0), also in all non-reversing forms, and (1,1,1), phi being the golden ratio of (1+sqrt(5))/2=1.618034 Cycle each set through all the positive and negative things, that is, (1,1,1),(1,1,-1),(1,-1,1)...(-1,-1,-1), and you get 32 points... these can be combined in 30 faces (and 60 edges) to make a convex sphere thingy... Take the edges and trisect them to get points for one of the various ways to make a hex-pent sphere.

The other way is to use a soccerball configuration. use the (phi,1/phi,0) and (1,1,1) coordinate sets from last time, find the centers of the 12 pentagonal faces they make, and dilate copies of the points by about 1/2 around those centers. Use these copies as your vertices. If I'm confusing you, email me at doobadan@aol.com and I'll explain more explicitly, maybe I'll have some coordinates ready, too.

Vorn

Vorn the Unspeakable

First, it's not actually possible to make a convex polyhedron out of just hexagons. You need exactly 12 pentagons or something similar. With that stipulation, there are a lot of ways to make a hexagon-pentagon. I'll describe the two simplest ways.

The first way involves a polyhedron knwon as a rhombic triacontahedron (triaconta meaning 30). The coordinates of the vertices of a RTCH are: (1,phi,0) in all forms that don't reverse the order, (phi,1/phi,0), also in all non-reversing forms, and (1,1,1), phi being the golden ratio of (1+sqrt(5))/2=1.618034 Cycle each set through all the positive and negative things, that is, (1,1,1),(1,1,-1),(1,-1,1)...(-1,-1,-1), and you get 32 points... these can be combined in 30 faces (and 60 edges) to make a convex sphere thingy... Take the edges and trisect them to get points for one of the various ways to make a hex-pent sphere.

The other way is to use a soccerball configuration. use the (phi,1/phi,0) and (1,1,1) coordinate sets from last time, find the centers of the 12 pentagonal faces they make, and dilate copies of the points by about 1/2 around those centers. Use these copies as your vertices. If I'm confusing you, email me at doobadan@aol.com and I'll explain more explicitly, maybe I'll have some coordinates ready, too.

Vorn

Vorn the Unspeakable

MikeC

11-03-2001, 03:21 PM

Just out of interest, why would you want to? I'm intrigued.

Omaha

11-03-2001, 08:36 PM

I think you can make a polyhedron out of just hexagons, but not just pentagons. You can use both and come up with something though, something like the infamous buckyball.

DFrey

11-03-2001, 09:02 PM

One of the Platonic solids is made from just pentagons. None of them can be made with just hexagons. In fact, I can't think of any solids off hand that can be made with just hexagons, be it Platonic or otherwise. You can build a sphere-like solid from hexagons and pentagons (the truncated icosahedron also called a soccer ball by some).

[This message has been edited by DFrey (edited 11-03-2001).]

[This message has been edited by DFrey (edited 11-03-2001).]

luc_pop

11-04-2001, 05:24 AM

I saw the movie "The Lawnmover Man" and in a scene one of the characters was in a sphere made of hexagons (computer generated).

So I want to make such a sphere in OpenGL to work as an file explorer. On the hexagons i will display the files and directorys name and you should be able to do whatever you want with them in 3d (copy, delete, create new files and so on).

If you wander how I will display the names I will make a texture class that uses .ttf files and displays the text as a texture.

check: http://www.freetype.org/

So I want to make such a sphere in OpenGL to work as an file explorer. On the hexagons i will display the files and directorys name and you should be able to do whatever you want with them in 3d (copy, delete, create new files and so on).

If you wander how I will display the names I will make a texture class that uses .ttf files and displays the text as a texture.

check: http://www.freetype.org/

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