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In geometry, Prince Rupert's cube (named after Prince Rupert of the Rhine) is the largest cube that can pass through a hole cut through a unit cube, i.e. through a cube whose sides have length 1, without splitting the cube into two pieces. Its side length is approximately 6% larger than that of the unit cube through which it passes. The problem of finding the largest square that lies entirely within a unit cube is closely related, and has the same solution.〔〔〔 ==Solution== If two points are placed on two adjacent edges of a unit cube, each at a distance of 3/4 from the point where the two edges meet, then the distance between the two points will be : These two points, together with a second set of two points placed symmetrically on the opposite face of the cube, form the four vertices of a square that lies entirely within the unit cube. This square, extruded in both directions perpendicularly to itself, forms the hole through which a cube larger than the original one (up to side length ) may pass.〔 The parts of the unit cube that remain, after emptying this hole, form two triangular prisms and two irregular tetrahedra, connected by thin bridges at the four vertices of the square. Each prism has as its six vertices two adjacent vertices of the cube, and four points along the edges of the cube at distance 1/4 from these cube vertices. Each tetrahedron has as its four vertices one vertex of the cube, two points at distance 3/4 from it on two of the adjacent edges, and one point at distance 3/16 from the cube vertex along the third adjacent edge.〔 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「Prince Rupert's cube」の詳細全文を読む スポンサード リンク
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