Here I figured that my camera has either three or six blades.
But yesterday I took another shot at night with the same setup which has twelve srokes:
The camera is a Canon 550D and I used the same 18-135 lens for both the shots.
Is this possible with 3 or 6 blades?
Yours has 6 blades. There are a few ways of finding out for sure:
Look at the shape of light bursts or bokeh in pictures. I can see how your image above is a bit confusing but it's actually 6 shapes (each with two "outer lines") rather than 12. Likewise, the shape of the bokeh in this shot clearly shows it was taken with a 7-blade lens. However, that won't always work: it depends on the aperture the shot was taken with, and some lenses have more curved blades that lead to very round bokeh.
Look at the lens. As others have pointed out, the aperture blades are in the lens, not the camera body. Normally the camera keeps the aperture wide open (regardless of the setting you may have chosen) until you actually press the shutter: this is to let plenty of light through the lens while you're composing and focusing your shot. However, your camera has a button that forces the aperture to close to the currently set value and lets you see the blades very clearly. On a Canon it's a small round button, positioned just below the lens release button (you can see it on the bottom right image here). So, to see the aperture blades for yourself:
Find the lens specifications online. You'll find a spec for most lenses and that should tell you how many blades it has. I searched for "canon 18 135" and the Canon specification page came up in my Google results. As we suspected: 6 blades.
It's not your camera that has blades, the aperture diaphragm (located in lens) has them. With different lenses, your camera will have different number of aperture blades.
The Canon 18-135 lens has 6 circular aperture blades.
