These are 7 cylinders all mutually touching on their edges.
They were found in 2013 by Sándor Bozóki and Lajos Rónyai at
Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI);
and Tsung-Lin Lee at National Sun Yat-sen University, Taiwan.
Here are links to their research:
http://www.sciencedirect.com/science/article/pii/S0925772114000819
http://arxiv.org/abs/1308.5164

I have rotated the cylinders such that one of them lies flat on the ground and five of the others intersect the ground at a steep enough angle to not need support. Unfortunately one of the cylinders will need support and it is a bit of a pain to remove the support from model.