Stylus shape?

The answer to your question is the line contact shape . It comes with different names as many have mentioned but they are basically the same shape with slightly different contours . They are more dificult to set up correctly but as long as you guide yourself with the same principal as for any other stylus shape you'll be ok , you just have to be more exact .
Eliptical would be #2 and conical #3 . 
Always remember that stylus shape is not the only determining factor in sound quality nor is it the most important but rather it is many factors that when each is placed in its proper place gives you the best performance possible in a given situation

back in the 70's, the 'shibata' stylus was pretty popular. where doe's it stand today? or is it still available??

Great profile, some of the best LOMC cartridges like Miyajima comes with Shibata profile today. 

Soundsmith’s Full Stylus Explanation Here

https://www.sound-smith.com/articles/stylus-shape-information

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essentially 3 types of Stylus: conical; elliptical; advanced (see chackster’s list of advanced shape types/names above)

each providing progressively more groove side-wall contact surface.

both fidelity and stylus life increase progressively as side-wall contact surface increases. As noted, advanced shapes need more careful alignment to get the benefit, and avoid damage they can cause if misaligned. they also go deeper in the grooves, so the lp’s cleanliness is more important for quiet play.

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Jico gives the amount of playing time where a stylus will maintain its specified level of distortion at 15kHz in 4 categoties, breaking the advanced into 2 categories:

• Spherical / Conical - 150hrs
• Elliptical - 250hrs
• Shibata/Line contact - 400hrs
• SAS/MicroRidge - 500hrs

So, advanced shape sounds better, costs more, but lasts much longer.
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Shape/increased groove side-wall contact also reduces wear of the lp’s groove.

Required tracking forces vary, the force increases/decreases wear of both stylus and groove wall
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The material of the shaft/cantilever the tip is mounted on varies: light weight and stiffness both desirable, aluminum/boron/gems saffire, ruby, / rare earth metals .. thin/stiff equals brittle, so progressively more caution is advised.

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then you get into the cartridge body type and refinement, the specifications reveal some/much about that, but only your ears count.

Dear @g_nakamoto : Ortofon use Shibata shape in some of the cartridge models.

Btw, """  advanced shape sounds better, costs more, but lasts much longer..."""

lasts much longer?: this is a misunderstood because the time lasting an stylus does not depends on its shape but for other reasons as  clean it and clean the LP surface because in theory the advanced  shapes  increased groove side walls makes a longer lasts time but that " increased groove.." in reality does not happens due to the tonearm tracking error and non perfect accurated cartridge/tonearm alignment along that not all LPs are say 180grs. and comes with no waves that affects the stylus rake angle during cartridge tracking.

I own many cartridges with elliptical stylus shapes that have more hours than the ones stated by Jico and we have a good example with the spherical stylus shape in the Denon 103 that last for " ever " ( I own too. ).

Regards and enjoy the MUSIC NOT DISTORTIONS,
R.

I don't read or know of an audiophile that after 400-500 hours re-tipped his Lyra Titan or even after 1K.
R.