Touching Pencils

Can you arrange 6 new identical pencils in space such that every two of them touch each other? What if you have 7 pencils?

Remark: The construction doesn’t need to be stable.

Below you can see solutions for 6 and 7 pencils. The construction with 6 pencils is stable, the construction with 7 pencils – not.

We do not know where this puzzle originated from. If you have any information, please let us know via email.