We survey basic properties and bounds for q-equivelar and d-covered
triangulations of closed surfaces. Included in the survey is a list of the
known sources for q-equivelar and d-covered triangulations. We identify all
orientable and non-orientable surfaces M of Euler characteristic
0>Ο(M)β₯β230 which admit non-neighborly q-equivelar triangulations
with equality in the upper bound
qβ€β21β(5+49β24Ο(M)β)β. These
examples give rise to d-covered triangulations with equality in the upper
bound dβ€2β21β(5+49β24Ο(M)β)β. A
generalization of Ringel's cyclic 7mod12 series of neighborly
orientable triangulations to a two-parameter family of cyclic orientable
triangulations Rk,nβ, kβ₯0, nβ₯7+12k, is the main result of this
paper. In particular, the two infinite subseries Rk,7+12k+1β and
Rk,7+12k+2β, kβ₯1, provide non-neighborly examples with equality for
the upper bound for q as well as derived examples with equality for the upper
bound for d.Comment: 21 pages, 4 figure