According to the glossary we have next to our regular trionian longitude and latitude the laptitude in the marp, garp direction. A short derivation:
tetra sphere: x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> + w<sup>2</sup> = R<sup>2</sup>
north / south: x<sup>2</sup> + y<sup>2</sup> = R<sup>2</sup> ==> R [ cos(α) , sin(α) ]
east / west (at y = y<sub>0</sub>): x<sup>2</sup> + z<sup>2</sup> = R<sup>2</sup> - y<sub>0</sub><sup>2</sup> = r<sup>2</sup> ==> r [ cos(β) , sin(β) ]
marp / garp (at (y,z) = (y<sub>0</sub>,z<sub>0</sub>): x<sup>2</sup> + w<sup>2</sup> = R<sup>2</sup> - y<sub>0</sub><sup>2</sup> - z<sub>0</sub><sup>2</sup> = r<sup>2</sup> ==> r [ cos(γ) , sin(γ) ]
Thus the position is given by the triplet ( α , β , γ ). zero for α is given by the planetary equator, for β it is given by some chosen meridian, zero for γ is given by? (the polar equator(?))
if not mistaken ( α , β , γ ) correspond then to the tetrasphere point: R [ sin(α) , cos(α) cos(β) , cos(α) sin(β) cos(γ) , cos(α) sin(β) sin(γ) ]
With γ = 0 this mimics the situation on a regular trionian sphere (for other γ it might well be that some modification is needed, probably adding cos(γ) to the y slot)
{ note: x in the south - north direction, y toward the 0-meridian, z toward the 0-???, w perpendicular to all of them (???) }
Just trying to make sense.
Assuming that there would be a polar and solar equator would mean that a tetronian planet behaves like the rotatope duocylinder { x<sup>2</sup> + y<sup>2</sup> = R<sup>2</sup>, z<sup>2</sup> + w<sup>2</sup> = R<sup>2</sup> } whose surface points are given by: R [ cos(ρ) , sin(ρ) , cos(θ) , sin(θ) ] and thus those planets are dually rotating through tetraspace.
I've no idea how to map the positions here in longitude, latitude and laptitude.
The tetrasphere point of view only needs some "greenwich meridian", and some "what sil we callit" to pinpoint a zero laptitude.