Creating a 3D spiral look uses the 3D rendering along with Symbols. It is easier than it looks to create this cool 3D spiral.
Create a rectangle for a stripe.
Duplicate the rectangle to create a set of stripes.
Use the Direct Selection tool to select the right edge and move the stripes up to create a slight angle to the lines.
Open the Symbols Panel. Window >Symbols. Select all the stripes and drag them into the Symbols panel. The Symbol Options dialog will appear. Name the Symbol, choose Graphic as the Export Type and click OK.
The Symbol of the stripes will appear in the Symbols panel. You can delete the original stripes you created as they are now saved as a Symbol.
Create another rectangle for the 3D Revolve.
Open the 3D under the Effects menu. Effects > 3D > Revolve. Click the Preview button to see the results. Click OK.
This will create a 360° rendering of the rectangle. Click in the Map Art... button next to the Preview box.
The Map Art panel is where the stripes are mapped to the artwork. Use the arrows to cycle through the 3D surfaces until you get to the side of the render.
From the Symbol dropdown menu, choose the Stripe Symbols you created. (The only way to map artwork to a render is by way of Symbols.)
With the Symbol place in the Map Art window, you can position the Symbol to the art.
To fit the stripes to the entire render, click the Scale to Fit button.
Click the Invisible Geometry check box to make the 3D shape invisible, leaving just the stripes on the shape. Click OK.
Use the cube to rotate the shape to get the spiral effect at the desired angle.
The end of the stripes may not line up when you are previewing the render.
Click on the Map Art… button and rotate the Symbol by hovering outside the corner and turning the stripes until the line ends end up aligning with their ends. There is no magic to this, it just takes a bit of patience and careful rotating. Click OK when done.
Once the ends are lined up, this is the final render. Choose Object >Expand Appearance to render the object as editable shapes. The invisible shape the lines wrapped around is still there so that will need to be removed. Use the Direct Selection tool to find the edge of the Invisible shape, choose Select > Same > Fill Color to select all the invisible shapes, then delete them.
Ungroup the objects. You may have to ungroup them twice to be able to select the sets of lines. They are grouped in the front set, back set and the tail set.
Add colors to the stripes to make it look like they wrap around in a 3D spiral.