| 翻訳と辞書 |
Void Cube
The Void Cube is a 3-D mechanical puzzle similar to a Rubik's Cube, with the notable difference being that the center "cubes" are missing, which causes the puzzle to resemble a level 1 Menger sponge. The central "spider" used on the Rubik's Cube is also absent, creating holes straight through the cube on all three axes. Due to the restricted volume of the puzzle it employs an entirely different structural mechanism from a regular Rubik's Cube, though the possible moves are the same. The Void Cube was invented by Katsuhiko Okamoto. Gentosha Education, in Japan, holds the license to manufacture Void Cubes.
==Solution==
The Void Cube is slightly more difficult than a regular Rubik's Cube due to parity. The lack of center cubes alters the parity considerations. A 90˚ rotation of a face either on the regular Rubik's Cube or on the Void Cube swaps the positions of eight cubes in two, odd parity, four cycles. Overall, a face turn is an even permutation. On the regular cube a 90˚ rotation of the whole cube about a principal axis swaps the positions of 24 cubes in six, odd parity, four cycles. On the regular cube a whole cube rotation is an even permutation. On the other hand, lacking center cubes, a 90˚ whole cube rotation on the Void Cube swaps 20 cubes in five, odd parity, four cycles. Thus, a whole cube rotation on the Void Cube is an odd permutation. In consequence, on the Void Cube turning the faces of the cube together with whole cube rotations can produce an arrangement where two cubes are swapped and the rest are in their original positions. This and other odd parity arrangements are not possible on the regular Rubik's Cube and afford the solver an additional challenge. These permutations are solvable with a number of simple algorithms.〔(Solution algorithms )〕
To see the relationship between parity on the regular cube and the void cube consider the regular cube. A regular cube solution takes a scrambled cube to the identity cube where the color of all the edge and corner facelets match the center facelets. A void cube solution takes a scrambled cube to an arrangement where the color of the edge and corner facelets match each other regardless of the color of the center facelet. These "cat's eye" arrangements are formed by rotating the edge and corner cubes as a whole with respect to the center cubies. This may be done in 24 different ways but because of parity only 12 may be formed by turning the faces of the cube. Odd parity void cube positions are formed on odd parity "cat's eye" regular cube positions.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Void Cube」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|