Hubert: Am I right when I say the shins are parallel to the body’s plane in this position ?
Well the body has three major planes so the question in that form lends itself to misinterpretation.
If you are doing this pose either sitting or supine then the shins would be perpendicular to the mid-sagital plane of the body.
Another way to think of it is that the shins are parallel to the front edge of your mat.
The shins are parallel to the frontal plane but perpendicular to the sagital plane.
It was bad wording on my part. I thought using the word plane will indicate that I am thinking of the chest. Obviously, it did not. 
Just reading over this thread and thought I would offer up some info. According to Baron Baptise and the Power Yoga tradition, the pose is called Double Pigeon, and the Sanskrit name is Dwapada Rajakapotasana.
Here is a good pic. and other useful info: Yoga Download – Online audio yoga classes in mp3 format with free printable pose guides
Jamie
Yep Baron does have his own names for some things, doesn’t he.
I’m not sure you can call something 10 years old a “tradition” though.
well…despite all those postures…I am sitting on my office chair in lotus or half lotus posture most of the day…that seems to help me open my hips…
and it also gives a good posture for my back.
nadine
Does anyone know (maybe inner athlete) if bicycle racing has a negative affect on the hips…at least in so far as yoga is concerned? I work very consistently on my hips when I do asana, but it is just a very long slog. I don’t want to hurt myself again, so I don’t force anything. I am just wondering if that area of my body is perhaps exceptionally stiff compared to other people. I never did any stretching when I used to race. My hamstrings were also really, really tight when I started doing asana. I could barely get my fingers to within four or five inches of my toes when I started. They however, have loosened up much more readily. My hips can just be very discouraging at times.
Sean