Karate

Stances
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Gyakuzuki Dachi is closely related to Junzuki Dachi. So closely related in fact that I'd be tempted to say that it is derived from it, except that I'm not sure which was derived from which. Gyakuzuki Dachi is named after the formidable Gyakuzuki - perhaps the most powerful punch in Karate. Gyaku means 'reverse' and of course zuki means punch, thus 'Reverse punch'.
Gyakuzuki Dachi can be formed by first forming Junzuki Dachi, and then moving your front foot diagonally to one side (to widen the stance) and backwards (to shorten the stance). The difference should be such that the distance from the heel of the Junzuki Dachi front foot to the toe of the Gyakuzuki Dachi front foot is no more than one foot (but usually no less than half a foot). When in Gyakuzuki Dachi the typical thing to be doing is of course a Gyakuzuki. This is the same as a Junzuki (((until these extra punch nodes go up, see Junzuki Dachi))) but punching with the rear arm. The front fist is placed on the hip.
As with Junzuki Dachi there is some disagreement over the exact detail of Gyakuzuki, but generally if you start with what you consider to be a valid Junzuki, and then widen and shorten it as above you should be on the right track.
Most styles agree that the rear (punching) shoulder should be turned in slightly to that you're in a reverse half facing torso alignment.

As stated in Junzuki Dachi, this is one of the 8 or so basic stances that are used in the early Kata.

Here is a semi advanced tip for Gyakuzuki Dachi:
Many styles dictate that when performing step-Gyakuzuki techniques the rear foot should describe an arc from its starting position, towards the front foot and then out to its ending position where it becomes the new front foot. There are a variety of explanations for this. Here are two that I know of.
This movement is quite likely to be your introduction to the principle of punching with the entire body. As you bring the rear leg up towards the front, turn the toes towards the front foot and then as the foot continues to its destination keep the toes pointing at this angle until just as you step down. When you step down, turn the foot back to a forward facing position, lock your knee out and attempt to follow this twist like a wave up through your hips, abdomen and finally into your shoulders. Up until this point your arms should not have moved at all. Only now do you pull back your outstretched arm and when the maximum possible energy is stored up in that other shoulder, launch the punch. It should fly out like a greased cat from a burning kennel. This is unfortunately one of the hardest techniques to explain, but if you practice this foot twisting motion you should begin to feel some extra strength you weren't aware of. Be careful if testing powerful punches against a bag, that you tense your wrist up or you may damage it.

The other technique is a little simpler. Again, perform the little half-moon with your rear leg but this time perform a little outward circular flick with your leg before you put it down. This is a small footsweep motion, designed to break the stance of your opponent causing them to fall onto your punch. Obviously it relies upon them being in a forward weighted stance.

When you perform stepping Gyakuzuki Dachi techniques, do not bob up and down. The Gyakuzuki Dachi is quite a low stance on account of the width, length and bent front knee. If you bob up and down you are slowing down the movement and also making it hard to perform accelerations over the course of the entire step. You would effectively break the step into two parts - a useless 'up' half-step and a 'down' half-step that would be too short to be effective in applying forces. Stay low and make sure that the line of 'drive' is straight.