Module[{vc, fi},
{vc, fi} =
PolyhedronData["Octahedron", {"VertexCoordinates", "FaceIndices"}];
GraphPlot3D[
Graph[DeleteDuplicates@
Flatten[UndirectedEdge @@@ (Sort /@
Partition[#~Append~First@#, 2, 1]) & /@ fi]],
VertexCoordinateRules -> vc, PlotStyle -> Thick]]