Thank you. Some species make bisexual cyathia, but not others. Compare these two types of cyathia, which are bigger than the ones on E. polygona and thus easier to see in detail.
The first is male, the second is female. The male parts look like yellow balls on the end of many little sticks. The yellow is actually the pollen. Dab a fine paintbrush into the pollen and you will see it transfers to the brush, and then move it to the female you want to pollinate. The female parts have 3-fold symmetry and come out of the middle of the cyathium. And of course only females make fruit.
Here is a male polygona for comparison. These plants often pollinate each other here without any need for human involvement.
The important thing to remember is that the fruit will open explosively when it is ripe, scattering the seeds to the four winds. So you have to bag it in advance or do what I do, which is wait for the fruit to change color and then collect it at that point to pop within a paper envelope. For example (also bupleurifolia because the parts are bigger and easier) this color change to brown which happens a day or so before the fruit pops.
E. flanaganii can be propagated by cuttings which can form a new "head" -- the caudex with many arms. Usually mature plants will offset on their own over time and you can grab these offsets (formed next to the mother plant) to root and grow on in individual containers. I have a crested plant that reverts regularly and leaves me new heads to cut and propagate. E. inermis (like several other medusas) generally has to be grown from seed. Which is not particularly hard, for what it's worth.
This is the mother of the polygona hybrids above. Not in flower at the moment but if you look carefully you can see female parts left over from the last time around. And if you look extra carefully at the far left side, you can see two light brown capsules still attached to the plant after popping open and releasing their seeds.