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.)
[asy]import three;
import math;
size(180);
defaultpen(linewidth(.8pt));
currentprojection=orthographic(2,0.2,1);triple A=(0,0,1);
triple B=(sqrt(2)/2,sqrt(2)/2,0);
triple C=(sqrt(2)/2,-sqrt(2)/2,0);
triple D=(-sqrt(2)/2,-sqrt(2)/2,0);
triple E=(-sqrt(2)/2,sqrt(2)/2,0);
triple F=(0,0,-1);
draw(A--B--E--cycle);
draw(A--C--D--cycle);
draw(F--C--B--cycle);
draw(F--D--E--cycle,dotted+linewidth(0.7));[/asy]<spanclass=′latex−bold′>(A)</span> 210<spanclass=′latex−bold′>(B)</span> 560<spanclass=′latex−bold′>(C)</span> 840<spanclass=′latex−bold′>(D)</span> 1260<spanclass=′latex−bold′>(E)</span> 1680 countingdistinguishabilitygeometry3D geometryoctahedronrotationgeometric transformation