Our Punto is my boy's car and is at his house on the other side of the city at this minute - or maybe in his work car park as he does shifts - and I can't remember what the Punto jack looks like. However the Panda one looks like this:
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It's the black scissors one top left. The head/saddle/whatever you want to call it, is this shape:
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and it straddles the sill seam, some call it the "pinch" seam, like this:
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With the broader part towards the inside. In fact I very seldom jack any of the cars up using their own jacks - If I'm at home it'll be one of my big trolley jacks and if I'm helping a family member out away from my workshop then I sling one of my wee trolleys in the boot. So addressing this question (broader side in or out?) caused me to scratch my head a bit. I reasoned that as the car rises on the jack it's going to take most of the weight on the inner side of the sill seam because the car will tilt away from the side being jacked up so probably the bigger side of the jack head will face inwards? Then I had a brainwave, If in doubt take a look at the manual - Revolutionary or what? - and it shows the jack being used in this orientation It's very important to realize it's the floor section which is reinforced and designed to take the weight and not the sill seam so when buying an aftermarket jack you need to get one which allows this.
You may notice the red jack in the first picture? That was an aftermarket jobbie supplied as part of a kit for my daughter in law's Mazda - jack, wheel brace and spacesaver - from an online seller of used spare wheel kits. It's a generic item which actually isn't suitable as it's not deep enough to clear the sill seam - don't like the look of the inward facing "teeth" either which look as though they have been specially designed to damage paintwork. Luckily I already had a suitable jack from another car so this one has joined my stock of "may be useful one day" bits and pieces.
Many years ago I made my own jacking blocks from substantial pieces of wood covered in bits of old commercial vehicle inner tube. Here you can see a couple of them:
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The rubber faced blocks straddle the sill seam and, because they are relatively long the weight is spread out so you're much less likely to have a partially corroded sill fail.
So be very careful buying generic items - some are pretty poorly made too - but more than anything look carefully at the head and be sure it's going to clear the sill seam. Personally I'd be trying breakers for a genuine Fiat one from a scrapped car.