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If you take six lines forming the Star of David, then it is impossible to split the lines forming one large triangle from the lines forming the other one.

EDIT. Oh sorry, I misunderstood the concept. If I do understand it correctly now, the dimension is at least 6: on the picture below the 6 lines can be split in any way.

6lines

EDIT2. It is not an example, as Gjergji and Cain notice below.

show/hide this revision's text 2 added 231 characters in body

If you take six lines forming the Star of David, then it is impossible to split the lines forming one large triangle from the lines forming the other one.

EDIT. Oh sorry, I misunderstood the concept. If I do understand it correctly now, the dimension is at least 6: on the picture below the 6 lines can be split in any way.

6lines

show/hide this revision's text 1

If you take six lines forming the Star of David, then it is impossible to split the lines forming one large triangle from the lines forming the other one.