Rhombdod Project
From Illvilja
Introduction
So what on earth is this? Well, this project is simply about how to make better and cooler maps for various games (wargames in particular). To do that, there are two areas this project will focus on:
- How to create, use, visualize and understand a 3-dimensional game map using Rhombic Dodecahedrons as the building blocks (here is a nice picture illustrating how such bodies fills up a 3D space). In this area, the project will also look a bit deeper into some useful things to keep in mind when creating consistent and useful game maps in such a 3D space, both for pen and pencil kind of games, for boardgames as well as for computer games and simulations. For a (very) trivial example of a map based on such a rhombic dodecahedron 3D-space, take a look at the logotype for this website at the upper left corner!
- All other kind of funky ideas vaguely associated (or not associated at all) with the work of using Rhombic Dodecahedrons for 3D game maps. This include
- game maps based on the 4-dimensional 120-Cell (a 4D body consisting of 120 Regular Platonic Dodecahedrons which has been put together as described here) as well as a combination of that 120-cell together with Rhombic Dodecahedron (yes, I'm a madman).
- nice things like "hybrid connector-border terrain" and such.
- such topological surfaces you get when you take a bunch of hexagons and put them together (at least in a topological sense) with pentagons and heptagons. As an example of such a surface is the classical football, also known as truncated icosahedron which is made up by 32 polygons (12 pentagons and 20 hexagons). If adding more hexes to such a map, one get's a kind of map that were used in some boardgames of the 80's (Cerberus from Task Force Games for instance) where the map were thought to be a hex map wrapped over the surface of a icosahedron, using pentagons instead of hexagons at the icosahedron's corners. A nice kind of map to use if you wanted to simulate a game taking place on a globe such as our own world.
- other stuff I don't recall right now (or have not yet though out).
So, that is enough of a description of the project for today... oh, the name "Rhombdod" is simply a shortened down version of the name "Rhombic Dodecahedron" which frankly is quite unwieldly. "Rhombdod" is almost pronounceable, and also, it does not exceed the magical word length limit of 8 characters.
A Brief Introduction to 3D Rhombdod Space: Piled Oranges
To get a very basic understanding of how the Rhombdod Space is organized, imagine a bunch of oranges neatly piled up as a pyramid in the grocery store. First you have an empty counter where you put oranges in a layer, organized in neat rows so they form a square pattern. Once that is done, you can add another layer of oranges, where each 2nd layer orange is placed in the indentation formed between four oranges in the 1st layer. Once that in turn is done, you add oranges in a similar fashion to form the 3rd layer, the 4th and so on until you have a neat, pyramid style pile (or you are generally satisfied with it's height). For the sake of simplicity, we assume that we have fairly equal sized oranges (otherwise the regularity of the pile would be impossible to maintain).
So, what can we say about this pile of oranges? First, the oranges are laid out in their heap in a similar fashion as the rhombic dodecahedrons are laid out in space. But using that made believe pile of oranges (yes, I'll provide illustrations eventually) makes it a bit easier to depict how the rhombic dodecahedron 3D space looks like. But back to what we can actually observe: the first layer of oranges were organized in a square map fashion. This is also true for the 2nd, 3rd etc layers. So any "horizontal cut" in the pile will result in a "square map of oranges". Also worth noting, on the resulting pyramid (or at least on the sloping sides of neat orange the heap if it is not high enough to actually form a pyramid) the oranges are organised in a hex map fashion! That means, that there are also ways to "cut" the pile which will result in hex map organized cuts of oranges, in addition to the cuts that result in square map cuts of oranges.
This means, that not only can the rhombic dodecahedrons be used to completely fill up a 3D space, one can then cut through that space in such a way (there are actually 3 such ways) which results in a cut consisting of a square map of dodecahedrons, and other ways (there is 4 such ways) that results in the dodecahedrons to be cut into what is a hex map! This means, that if one uses the rhombic dodecahedron to fill up the 3D space, one better have to be prepared to not choose between either using hexagon based or square based movement, but instead, one have to be ready to use both hex and square based movement!
--IllvilJa 23:17, 18 October 2006 (CEST)
