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Use the EXTRUDE command. Pick the triangle as the object to extrude and then watch the command line. You will be asked to "specify height of extrusion or direction/path/taper angle/expression". Choose the "Path" option, select the helix and then hit enter.

 

I just noticed, the above technique only works for the smaller triangle. It doesn't work for the larger triangle and I believe the reason is that the larger triangle is actually too big for the helix and causes an interference issue with overlapping geometry. If you scale the triangle down slightly, then the Extrude will work.

 

By the way, the reason why the SWEEP command is not working is because your triangles are 3D Polylines. If you want to use the SWEEP command, you will need to recreate the triangles as a standard polylines.

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