| 词条 | Grand 600-cell | |||||||||||||||||||||||||||||
| 释义 |
In geometry, the grand 600-cell or grand polytetrahedron is a regular star 4-polytope with Schläfli symbol {3,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is the only one with 600 cells. It is one of four regular star 4-polytopes discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids. The grand 600-cell can be seen as the four-dimensional analogue of the great icosahedron (which in turn is analogous to the pentagram); both of these are the only regular n-dimensional star polytopes which are derived by performing stellational operations on the pentagonal polytope which has simplectic faces. It can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of said (n-1)-D simplex faces of the core nD polytope (tetrahedra for the grand 600-cell, equilateral triangles for the great icosahedron, and line segments for the pentagram) until the figure regains regular faces. The Grand 600-cell is also dual to the great grand stellated 120-cell, mirroring the great icosahedron's duality with the great stellated dodecahedron (which in turn is also analogous to the pentagram); all of these are the final stellations of the n-dimensional "dodecahedral-type" pentagonal polytope. Related polytopesIt has the same edge arrangement as the great stellated 120-cell, and grand stellated 120-cell, and same face arrangement as the great icosahedral 120-cell.
With its dual, it forms the compound of great grand stellated 120-cell and grand 600-cell. See also
References
External links
1 : Polychora |
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