Zaldron
Sex Cauldron
Posts: 9682
Registered: 08-00 |
AirRaid said:
Exactly.
A dodecahedron is still just a 3D shape though.
Which is why I said "definition". In four dimensions, you can build a regular solid with 720 regular pentagons instead of just 12. What you see here is a projection to 2D space, or just a surface, your monitor's surface. A projection consists of sacrificing length and angle fidelity in a given geometric object in order to visualize it in a inferior number of dimensions. In a 3D cube with all sides length equal to 1, a orthogonal projection to screen will, depending on the view's rotation, sacrifice all or some of the 90 degree angles, and change the lengths of sides to less than 1 for some or all.
Note that with clever rotation, you can maintain a large portion of a cube's definition intact, if for example your projection is aligned so that the cube looks like a square, for one of its sides is facing directly to the observer/projection surface, you get 8 of the 12 sides at length 1 and many angles correctly at 90 degrees. The caveat is that 4 sides have been reduced to 0, not to mention the angles conformed disappear completely. Knocking down a further dimension, projecting a 2D projection of a cube into a line by scaling it vertically or horizontally to 0% makes it even less obvious. At this point it looks like it could be anything really.
This is what you're seeing, the 720 pentagons, subdivided into some triangles, odd shapes and such as done in a Megamynx (a dodecahedron's version of the Rubik cube, a special subdivision that allows you to twist the pieces unencumbered), with their side lengths and real angles modified to fit in a 2D projection.
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05-13-08 20:55 
