To Get Real Shapes and New Data of 120-Cell and 600-Cell
For commemorating great mathematician H. S. M. Coxeter
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This research will be helpful to people to display the 2-dimensional projective models of 4-variable actual problems in many fields, in order to investigate deeply those actual problems. By using the theory of N-dimensional finite rotation group of the regular polytopes, the author establishes the 2- dimensional projective model of 4-dimensional rectangular coordinate system, and deduces a transformation matrix, and adopts it to display successfully the 2-dimensional real shapes of two most complicated regular polytopes 120-Cell and 600- Cell. The author calculates all the vertex coordinates a...
This research will be helpful to people to display the 2-dimensional projective models of 4-variable actual problems in many fields, in order to investigate deeply those actual problems. By using the theory of N-dimensional finite rotation group of the regular polytopes, the author establishes the 2- dimensional projective model of 4-dimensional rectangular coordinate system, and deduces a transformation matrix, and adopts it to display successfully the 2-dimensional real shapes of two most complicated regular polytopes 120-Cell and 600- Cell. The author calculates all the vertex coordinates and determines the joint relations between adjacent vertices of the regular polytopes 120-Cell and 600-Cell. Also, this provides a pattern for displaying the 2-dimensional projective model of 4-variable actual problem.
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