Mostly construction toys are to make whatever you imagine. Having a high bounce component, I was picturing, would give another dimension to movement, imaginary weapons, Technic-like Goldberg machines and of course gravity fed explosions.

The areas on the ball would have to lose curvature. The depth being enough to raise the partial and full studs needed to attach standard blocks. On the other side, it would have to be flatterned and reverse stud patterm cut out.

Since only one pair of couplings is used, the ball may have to be blocked in by a constructed box or spanned between a framework construction. Both require the ball size to fit the quanta of the construction toy.

So, would the three stud faces always share one notional
vertex of the imaginary die, while the three tube faces
shared the opposite notional vertex? Or would you
sometimes have two opposite faces both studded, or both
tubed?

I think those two are the only possible distinct
configurations - either a pair of three-petaled flowers
interlocked, or a pair of "U"s interlocked- say if you can
think of any others.

From your description, there would always be three pairs,
which would imply that your set of pieces would not
include any with, say a mostly smooth and perfect
sphere, having a connector on one side only.

I would be asking for those, and also for some pieces
where the connectors, whether male or female,
corresponded to the faces of a notional tetrahedron, not
a notional cube.

Any of the Platonic solids can be tried, but increasing numbers of faces yield progressively closer approximations to a sphere.

Once the dodecahedron is reached, there may be little or no difference in behaviour to a sphere; although mathematical modelling may indicate divergence, depending on size and external factors (air resistance, coefficient of restitution) there may not be much in it.

Great excuse for throwing stuff off tall buildings, tho, so [+].

Because of trying to keep the standard building block orientation of stud to tube, the sphere will be cut between two parallel planes that will have only a unit brick factor between,Any shape not having parallel planes may give unique models but each attached construction to the sphere, can't link up to the others. Although there are fudges like unique and orientation changing bricks.

The surface could be stepped trading off the spheres randomly bouncy curvature for block grip capability and orientation conformity.

An off parallel studding, may allow sphere to sphere connection but it would be interesting if the angles would bring the second sphere back into the overall brick alignment consensus.