We explore solutions to a Martin Gardner puzzel using math and then modeling it with CAD software with no real intention to 3d print our solutions.
Four golf balls can be placed so that each ball touches the other three. Five half-dollars can be arranged so that each coin touches the other four. Is it possible to place six cigarettes so that each touches the other five? The cigarettes must not be bent or broken.
The Touching Cigarettes from My Best Mathematical and Logic Puzzles, p. 5 dover 
GARDNER, Martin, 1994. My best mathematical and logic puzzles. New York: Dover. ISBNÂ 978-0-486-28152-0. dover