I am not sure what your question is here. The calyx is the green covering of the bloom bud. When the flower opens the calyx is on the back side of the flower. Pollen should be applied to the tip of the pistel. The pistel is the fan shaped tip of the carpel. When talking about peonies people seem to refer to placing pollen on the carpels rather than on the pistels. The pistel doesn't seem to come up to a point like they do in many other flowers but rather they are flattened and the receptive part of the pistel will be the edge of the fan shaped structure. The carpels are located in the center of the stamen boss.

It is best to open the flower of the pod parent to remove the stamen as soon as the flower bud is loose enough to get inside of it. Then generally the next day as soon as the flower opens you can begin to pollenate. I generally only pollenate flowers once and sometimes twice however it would be better to pollenate each flower for 3 consecutive days. After about the third day the carpel will not be receptive (it will no longer be sticky).

Peonies have developed toward a self infertile nature but not entirely. The carpels are receptive very soon after the flower opens and some cultivars perhaps become receptive concurrent with opening. However the stamen seems to have to further mature before pollen will become active which happens a few days later. I think with most cultivars that have fertile carpels and fertile pollen there is an overlap of fertility between carpels and pollen which allows for some self pollenation.

If cross pollenating herbaceous peonies I especially like to cross pollenate using a pod parent that is a Japanese type bloom. These flowers do not have pollen and there is no chance of self pollenation.

Dave, I hope this helps,

Leon.