Cross Sections of a Regular
4-dimensional 600-cells Polytope.
by 'Literka'.
Picture above it is a central cross section of a regular polytope with 600 cells.
Polytope of 600 cells is a 4-dimensional regular polytope such that each
cell is a regular tetrahedron (see Plato’s polyhedrons). One of the 3-dimensional
central cross section of such polytope is contained in a symmetry hyperplane of
this polytope. This cross section looks like this:
It is a polyhedron of 80 faces. Each vertex of this polyhedron is a common point
of 6 or 5 edges. There are 12 vertices being common points of 5 edges and 30
vertices being common point of 6 edges. Each face is a triangle and there are 20
faces being equilateral triangles. Each of these 20 faces is a 2-dimensional
face of 600-cells regular polytope.
A picture at the top of this page presents another cross section of 600-cells
regular polytope. Computer shows that there are 156 faces of this polyhedron
(cross section). However, computer counts twice any cell which is 2-dimensional
face of a polytope. It looks that there are not such faces, but ‘Literka’ is not
sure about it.
The last example looks like this:
Computer shows that there are 214 faces of this polyhedron (cross section), but
as before ‘Literka’ is not sure about it.
