Enantiomorphs homochirality classes

The unlabeled triangle is the simplex in E (2-simplex) and the unlabeled tetrahedron is the simplex in (3-simplex) evidently, whether enantiomorphous -simplexes can be partitioned into homochirality classes depends on the dimension of E". Recall that an /j-simplex is a convex hull of + 1 points that do not lie in any (n - l)-dimensional subspace and that are linearly independent that is, whenever one of the points is fked, the n vectors that link it to the other n points form a basis for an n-dimensional Euclidean space An n-simplex may be visualized as an n-dimensional polytope (a geometrical figure in E" bounded by lines, planes, or hyperplanes) that has n + vertices, n n + )/2 edges, and is bounded by n + 1 (u — l)-dimensional subspaces. It has been shown that the homochirality problem for the simplex in E is shared by all -sim-... 

Certain types of knots and links exist as topologically chiral enan-tiomorphs. Such enantiomorphs cannot be interconverted by continuous deformation ( ambient isotopy ). Homochirality classes can therefore be defined for this type of mathematical object. ... 

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