I don't know.. maybe it could be called also "self-righting pedestal spinner"...?

Accurate enough, but still too many words, I think.

When the tip is above the CM, I noticed that the precession direction becomes reversed relatively to that of spinning.

In regular tops instead precession and spinning have the same direction.

Good observation. Precession in the opposite direction of spin is called "retrograde", and it's to be expected when the CM is below the tip.

You can see this in the usual approximate expression for (slow) precession...

*p* =

*M* *g* *H* /

*I*_{3} *w*_{3},

where

*p* is the precession rate in rad/sec,

*M* is the mass,

*g* is the acceleration of gravity,

*H* is the distance from tip to CM,

*I*_{3} is the AMI, and

*w*_{3} is the total angular speed about the spin axis.

Strictly speaking,

*w*_{3} =

*s* +

*p* cos(

*a*),

where

*s* is the pure spin rate, and

*a* is the angle between the spin axis and the vertical. But when

*s* >>

*p* or

*a* ~ 90°,

*w*_{3} ~

*s*, and the precession rate formula takes a more useful form...

*p* ~

*M* *g* *H* /

*I*_{3} *s*Now, when the CM is above the tip,

*H* is positive, but when the CM is below the tip,

*H* is negative. In the latter case,

*p* and

*s* must be of opposite signs, and the precession must be retrograde, because

*M*,

*g*, and

*I*_{3} are always positive.

While we have the precession rate formula out, note that the AMI can be written in terms of the axial radius of gyration

*K*_{3} like so...

*I*_{3} =

*M* *K*_{3}^{2}The formula then becomes

*p* ~

*g* *H* /

*K*_{3}^{2} *s*Hence, precession rate depends on the mass distribution as measured by

*K*_{3} but not on total mass.