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jmc

counting and probability senior

Problem

Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)
problem
Solution
Since the octahedron is indistinguishable by rotations, without loss of generality fix a face to be red. There are ways to arrange the remaining seven colors, but there still are three possible rotations about the fixed face, so the answer is .
Final answer
1680