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Polyhedrons and Geometry Help
Zyre
Registered User regular
Registered User regular
I am looking into the idea of creating a very simple 3D environment editor. But some logistics have been bothering me. The basic premise is this, I want to be able to specify variables to every intersection point in the wireframe, as well as all the planes inside of the polyhedron I use. Example, I want this plane to be solid, and to display a grass texture.
Logically, you would use cubes for this, but as I am a big fan of Hexagons, I was looking into possibly using some kind of 3d hexgonal polyhedron that is a zonohedron (fits snuggly together like a honeycomb without any space between them, like cubes). The more complex the shape and more sphere like it gets this becomes impossible. The closest polyhedron I was able to find that resembeled what I thought I wanted was one that consisted of hexagon and pentagon faces, but it was too much of a sphere, so I needed to take a step back. I am begining to think that maybe I'm over thinking this and I need to go with a more basic shape? Triangles can be used to make hexagons, so what if I used a 4 faced polyhedron pyramid out of triangles. It has less faces than a cube but allows for more creativity in the wireframe layout due to the angles.
The crux of my design issue though is I was hoping to be able to move around in a larger polyhedron with more faces and verticies. I think I'm looking for a 26 faced polyhedron that is also a zonohedron and I don't think it exists. I'd like to be in the center of my polyhedron, and have the ability to go in 26 directions from my location - the cardinal 8 (N, NE, E, SE, S, SW, W, NW), +45 degrees up of each of those, and 45 degrees down, as well as straight up and down. (8x3=24+2=26 - Which is also kinda neat because I could use each face as a letter...) but the idea would be if I moved in any of these 26 directions I would exit that polyhedron through a face and enter a identically shaped polyhedron at the opposite face that I exited from.
The closest examples I've been able to find are; http://en.wikipedia.org/wiki/Rhombic_dodecahedron - http://en.wikipedia.org/wiki/Truncated_octahedron - http://en.wikipedia.org/wiki/Rhombo-hexagonal_dodecahedron
These don't have enough faces for the movement system I was envisioning, but are the most complex zonohedrons that would honeycomb. There is of course the http://en.wikipedia.org/wiki/Hexagonal_prism but it doesnt have any diagonals movement, and would be very similar to if I went with cubes, I would have to pass through an edge to move diagonally from polyhedron to polyhedron with these, and I am hoping for a face-to-face movement in every direction.
I hope someone understands what im talking about. Am I overthinking this? Are simple polyhedrons the way to go?
Logically, you would use cubes for this, but as I am a big fan of Hexagons, I was looking into possibly using some kind of 3d hexgonal polyhedron that is a zonohedron (fits snuggly together like a honeycomb without any space between them, like cubes). The more complex the shape and more sphere like it gets this becomes impossible. The closest polyhedron I was able to find that resembeled what I thought I wanted was one that consisted of hexagon and pentagon faces, but it was too much of a sphere, so I needed to take a step back. I am begining to think that maybe I'm over thinking this and I need to go with a more basic shape? Triangles can be used to make hexagons, so what if I used a 4 faced polyhedron pyramid out of triangles. It has less faces than a cube but allows for more creativity in the wireframe layout due to the angles.
The crux of my design issue though is I was hoping to be able to move around in a larger polyhedron with more faces and verticies. I think I'm looking for a 26 faced polyhedron that is also a zonohedron and I don't think it exists. I'd like to be in the center of my polyhedron, and have the ability to go in 26 directions from my location - the cardinal 8 (N, NE, E, SE, S, SW, W, NW), +45 degrees up of each of those, and 45 degrees down, as well as straight up and down. (8x3=24+2=26 - Which is also kinda neat because I could use each face as a letter...) but the idea would be if I moved in any of these 26 directions I would exit that polyhedron through a face and enter a identically shaped polyhedron at the opposite face that I exited from.
The closest examples I've been able to find are; http://en.wikipedia.org/wiki/Rhombic_dodecahedron - http://en.wikipedia.org/wiki/Truncated_octahedron - http://en.wikipedia.org/wiki/Rhombo-hexagonal_dodecahedron
These don't have enough faces for the movement system I was envisioning, but are the most complex zonohedrons that would honeycomb. There is of course the http://en.wikipedia.org/wiki/Hexagonal_prism but it doesnt have any diagonals movement, and would be very similar to if I went with cubes, I would have to pass through an edge to move diagonally from polyhedron to polyhedron with these, and I am hoping for a face-to-face movement in every direction.
I hope someone understands what im talking about. Am I overthinking this? Are simple polyhedrons the way to go?
Zyre on
0