I possess a tetrahedron, or triangular pyramid, formed of six sticks
glued together, as shown in the illustration. Can you count correctly
the number of different ways in which these six sticks might have been
stuck together so as to form the pyramid?
Some friends worked at it together one evening, each person providing
himself with six lucifer matches to aid his thoughts; but it was found
that no two results were the same. You see, if we remove one of the
sticks and turn it round the other way, that will be a different
pyramid. If we make two of the sticks change places the result will
again be different. But remember that every pyramid may be made to stand
on either of its four sides without being a different one. How many ways
are there altogether?

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