halloween-flat-unit-möbius-deltahedron.4b : 無料・フリー素材/写真
halloween-flat-unit-möbius-deltahedron.4b / Ardonik
| ライセンス | クリエイティブ・コモンズ 表示-継承 2.1 |
|---|---|
| 説明 | Once you've relaxed the requirement that every angle be convex, it is quite interesting what you can make using only an equilateral triangle as your building block.Geometrically speaking, you could think of this so-called 120-Deltahedron A as a member of the dodecahedron's extended family. Like the dodecahedron, this object consists of 12 pentagonal shapes connected three-per-vertex (and color-coded for your convenience). The convex hull of this shape is a very slightly cumulated dodecahedron, and I suspect that this is true of all Möbius Deltahedra with respect to their originating Platonic solids.Were you to "inflate" a Möbius deltahedron so its vertices were all equidistant from its center, the result would be a spherical map of all of the intersections of that deltahedron's planes of symmetry. As a result, there are only a small number of possible Möbius deltahedra, each representing a sort of "collapsed spherical map" of intersecting symmetry planes.I also noticed in passing that this polyhedron bears a superficial resemblance to an excavated rhombic triacontahedron, though the "rhombs" in Möbius deltahedra are unfortunately non-planar. I'd like to create other Möbius deltahedra in order to explore this relationship further, and perhaps make a toroid by attaching them to one another. That would require a lot of triangles, though. |
| 撮影日 | 2010-10-21 21:36:23 |
| 撮影者 | Ardonik |
| タグ | |
| 撮影地 | |
| カメラ | Canon PowerShot A470 , Canon |
| 露出 | 0.067 sec (1/15) |
| 開放F値 | f/3.0 |
| 焦点距離 | 13714.28571 dpi |