PuristS,
Before I start this review, a quick note. I'm not a watch expert (and I don't plan to be) but I'm a watch aficionado or better, a person that loves watches.
Based on that, don't expect an horological review, but just an user review.
With that in mind, let's start.
Here's the watch that we go to discuss:
IntroductionAs PuristS, we buy/ trade watches looking for something that can perpetuate us and be, as much humankind products can be, eternal. I believe that’s the central motivation for mechanical watch collection.
A mechanical watch is, under my view, a technological device made to last and a mechanical watch that takes the horological technology to the upper limits, combined with a fantastic esthetic design that makes any the heart of any PuristS/watch aficionado beat faster.
When JLC combined the amazing “dual wing” project of the Duomètre with a tourbillion and, not satisfied with that, made the tourbillion a tridimensional entity, that uses the precession (precession is a change in the orientation of the rotational axis of a rotating body) as a model for the tourbillion movement, they moved the horological art to another very high level.
Here's precession, as we can read about here:
https://en.wikipedia.org/wiki/Precession 
(Precession of a gyroscope - From Wikipedia)
The dual wing designIf we reduce a mechanical watch as an ingenious way to perform a controlled delivery of the energy stored on a spring to power a balance wheel and subsequently the hands, we should agree that any other feature that’s added to the watch (chronograph, moon phase, date, GMT time etc.) will disturb the energy delivery and consequently impacting the watch accuracy.

(Pocket watch image from Wikipedia)
This impact of complications on accuracy can be minimized, but it’s always there.
JLC invention of the “dual wing” isolates the delivery of power into two main springs, one for the basic watch (balance wheel or tourbillion) and another for the added complications. The target is accuracy and it’s a very smart solution, I believe.
On a summary, the dual wing, or Duomètre, one main spring powers the displays and other features. The other main spring powers the bi-axial tourbillon, in our case here, that regulates the watch, maintaining a very high accuracy.
Here's a picture (by Nicolas) from the "dual wing" used on a chronograph:

Notice, on the left, the two power barrels. One for the watch itself and another for the chronograph complication.
The watchBasically, the Spherotourbillion reviewed here is a manual wind watch (two directions of winding, each one loads one of the mainsprings) with 460 parts.

The watch carries generous dimensions (42mm case, without considering the crown and 14.1mm thickness) with a case made of pink gold.
On the inside, the movement is a Jaeger-LeCoutre 382.
This watch offers the following functions: Date, Hours, Minutes, Seconds, 24-hour reference time or second time-zone, Fly back seconds (or better saying, resettable running seconds), Tourbillon and Twin Power-Reserve indicators.
It dresses very comfortable on my wrist and, to “fly under the radar”, the tourbillion is hidden by any long sleeved shirt. The gold case weight adds presence on my wrist and is not heavy as I initially imagine.
The dial has a fantastic looking silvered, crystallized grained with polished “4N appliques” (4N, thanks to Master “Alkiro1”, means pink gold (18ct) ). Enough say that it matches perfectly the overall watch design and attracts attention without being too bling.
The strap complements the watch with an alligator matte chocolate toned. It also arrived with another strap, this one an alligator matte blue dark toned.
The gold pin buckle closes the discrete and nice set.
Finally, the watch is protected with a 5 bar water resistance, meaning to me that I need to remove it even to wash my hands.
Using the watchMovementThe Sphero is powered by the JLC caliber 382, manually wound.

This movement beats at 21600 bph and has a power reserve for the regulator and the functions (each with its own power source) of around 45 hours.
As any high-end movement, the caliber 382 is decorated and, to my taste, without excess.
Pure beauty, IMHO.
Wearing the SpherotourbillionIf I say that wear the Sphero is a pleasure, I’m understating. It’s more an honor to be able to strap this work of art on the wrist.
The case and lugs balance perfectly on my wrist and, even considering the weight of the gold case, it “dresses” very comfortably.
From my watches, the Jaeger-LeCoultre Spherotourbillion is currently on the top of my “feel great” watches list.

Introducing the SpherotourbillionThe following picture shows the mains parts of the watch.

(Picture extracted from the Spherotourbillion user guide)
One interesting point on the Spherotourbillion is the pusher (6).
When pressed it resets the “Small Seconds Hand”. This helps to set the watch precisely without the need to stop the tourbillion. Cool, isn’t?

(Another picture from the Spherotourbillion user guide)
The main crown has three positions:
1) Winding. Each direction winds a barrel, as noted by the power reserve indicator.
2) Adjust the main "dial", on a GMT fashion.
3) Adjust the 24 hours "dial".
Pictures of itBecause if the shining bezel and case, the Spherotourbillion is not an easy watch to capture.
If I use the (Patent pending) Nicolas “soft box” or a commercial “soft box”, the case looks dull. If I don’t use any “soft box”, I got a reflex galore.
I tried to capture it the best I could, but I need very much to improve my photo skills to show the watch in full glory.

A B&W picture of the Spherotourbillion

This ends my user review of the Spherotourbillion. It's more a tribute to this fantastic watch than a serious review.
Later, when I got more familiarity with this watch, I plan to do a better examination of it.
Thanks for seeing.
Cheers,
Nilo
Note:
I would like to say a very warm thank you to the local Jaeger-Lecoultre team, in particular to Mr. M., Mrs. E. and Mr. G. that made this dream possible.