The classic《Geometry and the Imagination》by D.Hilbert and S.Cohn-Vossen mentioned 4—dimensional space 120—cell and 600—cell.They are themost complicated two of the regular polytopes in 4—dimensional space.andthe...The classic《Geometry and the Imagination》by D.Hilbert and S.Cohn-Vossen mentioned 4—dimensional space 120—cell and 600—cell.They are themost complicated two of the regular polytopes in 4—dimensional space.andthey are a pair of conjugate regular polytopes.Their vertex number,edgenumber,face number and 3—dimensional cell number are respectively 600,1200,720,120 and 120,720,1200,600.Owing to people’s limited imagina- tion,it is difficult for people to make the 4—dimensional models.So,up tonow.people fail to watch their complete images.展开更多
This paper has proved Euler-Poincare formula. so as to verify the correctness of the data of 《The Cardinal List of Orbits of the Regular Polytopes in EN》.
文摘The classic《Geometry and the Imagination》by D.Hilbert and S.Cohn-Vossen mentioned 4—dimensional space 120—cell and 600—cell.They are themost complicated two of the regular polytopes in 4—dimensional space.andthey are a pair of conjugate regular polytopes.Their vertex number,edgenumber,face number and 3—dimensional cell number are respectively 600,1200,720,120 and 120,720,1200,600.Owing to people’s limited imagina- tion,it is difficult for people to make the 4—dimensional models.So,up tonow.people fail to watch their complete images.
文摘This paper has proved Euler-Poincare formula. so as to verify the correctness of the data of 《The Cardinal List of Orbits of the Regular Polytopes in EN》.
