Henry Ernest Dudeney/Modern Puzzles/141 - The Six Submarines/Solution

Modern Puzzles by Henry Ernest Dudeney: $141$

If five submarines, sunk on the same day, all went down at the same spot where another had previously been sunk,

how might they all lie at rest so that every one of the six U-boats should touch every other one?

To simplify we will say, place six ordinary wooden matches so that every match shall touch every other match.

No bending or breaking allowed.

In fact, this has been simplified even further, and the submarines have been modelled as simple cylinders.

Martin Gardner, in his $1968$ repackaging 536 Puzzles & Curious Problems, references his own article in his $1959$ collection The Scientific American Book of Mathematical Puzzles and Diversions in which the question is answered in Seven Touching Cylinders, with $7$ appropriately-dimensioned cylinders.