I need to create cyllinder with 16 vertices on top but only 4 vertices on bottom plane. Im trying to merge faces and dissolve edges, but the resulting object looks deformed, cut out.
The simplest way I can think of for merging a square with a 16-gon is connecting each of the square's vertices to the 4 closest 16-gon vertices, then creating the 4 remaining triangles
(Select, Select, Select, F)
Otherwise, you can start from a 16-cylinder and merge 4 vertices at the time:
(Select 4, S+0, repeat 4 times, then W and "Remove doubles").
This will create 4 4-edged faces instead of only triangles.
These are the results (first method left, second method right):
which are definitely "cut out" (you are cutting 75% of the vertices after all), but not deformed.
Note: before attempting any smooth shading, an Edge split modifier is advised!
My approach would be to use a circle with 16 vertices, and one with 4 vertices.
Add both in while in edit mode so they are part of the same object,and then use bridge edge loops operator with Ctrl+E then L
You can then quad cap the 16 vert side with grid fill ( Ctrl+F then G )and fill the other as well with F