SubD Triangles

Rhino Rhino for Windows
1

I’m finding it difficult to create a flat subD that is a series of triangular faces all using a single central point (like the inside of a orange). I know it’s possible because I can make a cone, delete the bottom faces, then project the whole thing to the Cplane. Is it possible to:

Convert two points along an edge of a 4 edge (or more) face joined into one point to make a triangle. This new point would retain all connections of the previous two points.

2

you can stitch points together. you will have an easier time doing this in box mode.

3

In case you have a boundary curve, a quick way to generate a flat triangle fan SubD is by extruding the boundary, turn it into a SubD and use the Fill SubD Hole command.