Analysis of clustering results Suppose that i have multidimensional dataset and performed some partitioning clustering on it. Is there any way to find out what objects in a particular cluster have in common (except the fact that clustering algorithm decided to put them together)?

I've read many times that clustering is not a well-posed problem in general and that one should not overinterpret its results but still people are trying to cluster multidimensional data and make some practical sense of the results. I just can't find any good source on how the interpretation is done in practice.

Any tips and resources will be highly appreciated.
You can write code to analyze this. But this is very much data specific.

In some cases like k-mrans, you already get cluster averages. So you can easily compare the averages.

If you don't have major correlations in your data, then histograms can be insightful. Make stacked histograms, colored per cluster, to see if there is a different distribution in each attribute. Etc.
There are so many ways to do this, and they are not specific to clustering.