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If the molecule has some symmetry, the degenerate atomic orbitals (with the same atomic energy) are grouped in linear combinations (called symmetry-adapted atomic orbitals (SO)), which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations (SALC).
The plane in question is the Coxeter plane of the symmetry group of the polygon, and the number of sides, h, is Coxeter number of the Coxeter group.
The symmetry group of an n-sided regular polygon is dihedral group Dn (of order 2n): D2, 4D4, ...
A Schläfli symbol is closely related to reflection symmetry groups, also called Coxeter groups, given with the same indices, but square brackets instead p,q,r,....
In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope).
There are two Coxeter groups associated with the 10-orthoplex, one regular, dual of the 10-cube with the C10 or 4,38 symmetry group, and a lower symmetry with two copies of 9-simplex facets, alternating, with the D10 or 37,1,1 symmetry group.
There are two Coxeter groups associated with the 7-orthoplex, one regular, dual of the hepteract with the C7 or 4,3,3,3,3,3 symmetry group, and a half symmetry with two copies of 6-simplex facets, alternating, with the D7 or 34,1,1 symmetry group.
There are two Coxeter groups associated with the 8-cube, one regular, dual of the octeract with the C8 or 4,3,3,3,3,3,3 symmetry group, and a half symmetry with two copies of 7-simplex facets, alternating, with the D8 or 35,1,1 symmetry group.A lowest symmetry construction is based on a dual of a 8-orthotope, called a 8-fusil.
There are two Coxeter groups associated with the 9-orthoplex, one regular, dual of the enneract with the C9 or 4,37 symmetry group, and a lower symmetry with two copies of 8-simplex facets, alternating, with the D9 or 36,1,1 symmetry group.
Cyclic group, rotational symmetry group for an object with n-fold symmetry in a plane of rotation