Six- Dimensional Space
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High Quality Content by WIKIPEDIA articles! Six-dimensional space is a term used to describe any space that has six dimensions, i.e. six degrees of freedom, and which needs six pieces of data, or coordinates, to specify a location in this space. There are an infinite number of these, but the ones that are of most interest are simpler ones which are models of some aspect of our environment. Of particular interest is six dimensional Euclidean space, in which 6-polytopes and the 5-sphere are constructed. Formally six-dimensional Euclidean space, 6, is generated by considering all real 6-tuples as…mehr

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High Quality Content by WIKIPEDIA articles! Six-dimensional space is a term used to describe any space that has six dimensions, i.e. six degrees of freedom, and which needs six pieces of data, or coordinates, to specify a location in this space. There are an infinite number of these, but the ones that are of most interest are simpler ones which are models of some aspect of our environment. Of particular interest is six dimensional Euclidean space, in which 6-polytopes and the 5-sphere are constructed. Formally six-dimensional Euclidean space, 6, is generated by considering all real 6-tuples as 6-vectors in this space. As such it has the properties of all Euclidian spaces, so it it linear, has a metric and a full set of vector operations. In particular the dot product between two 6-vectors is readily defined, and can be used to calculate the metric. 6 × 6 matrices can be used to describe transformations such as rotations which keep the origin fixed.