Crease options with sharp corners

I have removed faces from sphere and in edit mode set crease edges to 1 .

i1064.photobucket.com/albums/u368/grit3/bevel/sub1_zpsv9buepbb.png

But you see that creased edges in detached smaller object have sharp corners. Contrary, on sphere there are not sharp corners with the same edge creasing set to 1.

There could be crease option to make this happen.

ChameleonScales suggested this would be called Sharpen all/selected vertices or maybe Make corners .